{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Radiative losses analysis with ModeSimulation\n",
        "\n",
        "`ModeSimulation` can be used to simulate small radiative losses, without\n",
        "the need for a full FDTD simulation. Since these losses are often very\n",
        "small (on the order of $10^{-5}$ dB/cm), careful tuning of the\n",
        "parameters is necessary to ensure good convergence.\n",
        "\n",
        "In this notebook, we will benchmark the required parameters to\n",
        "accurately calculate the imaginary part of the effective index for two\n",
        "types of losses: substrate leakage and bend losses.\n",
        "\n",
        "For more information about `ModeSimulation`, refer to this\n",
        "[tutorial](https://www.flexcompute.com/tidy3d/examples/notebooks/ModeSimulation/).\n",
        "\n",
        "## Substrate leakage losses\n",
        "\n",
        "In this example, we will simulate radiative losses into the substrate\n",
        "for a strip waveguide fabricated in SOI, where the SiO₂ layer is thin\n",
        "enough to allow losses into the Si layer.\n",
        "\n",
        "We will compare our results with the ones obtained in the paper of\n",
        "`P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, \"Modelling leaky photonic wires: A mode solver comparison\", Optical and Quantum Electronics 38:731–759, (2006).`\n",
        "[DOI:\n",
        "10.1007/s11082-006-9025-9](https://link.springer.com/article/10.1007/s11082-006-9025-9),\n",
        "where the authors benchmarked the radiative losses of the structure\n",
        "depicted above, using different numerical methods.\n",
        "\n",
        "<img src=\"img/RadiativeLossesModeSolver.png\" width=\"450\" alt=\"Schematic\">"
      ],
      "id": "9c18f8a4-c2dc-4d5e-9460-0deac6243dc1"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import tidy3d as td\n",
        "from tidy3d import web"
      ],
      "id": "49d42f30"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Defining the simulation domain\n",
        "\n",
        "We start defining a function for creating the `ModeSimulation` object.\n",
        "\n",
        "Since we are interested in losses, some attributes must be carefully\n",
        "defined.\n",
        "\n",
        "1.  The default boundary condition (BC) for the `ModeSimulation` object\n",
        "    is PEC. To study losses, we need to define a PML layer. This\n",
        "    requires adding a tuple to the `num_pml` argument of the `ModeSpec`\n",
        "    object, specifying the number of PML layers in each plane dimension.\n",
        "\n",
        "    Note that the PML is added **inside** the simulation plane, so it is\n",
        "    necessary to ensure that the simulation plane is large enough to\n",
        "    prevent the PML from being too close to the structures. A good way\n",
        "    to check this is by calling the `ModeSimulation.plot()` method.\n",
        "\n",
        "2.  To study low losses, we set the `precision` argument to `double`, so\n",
        "    the results will have more than six significant digits."
      ],
      "id": "40ac1fad-8f7b-4c9a-98c4-fe70a2549e35"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "# defining the function for creating the ModeSimulation object\n",
        "\n",
        "\n",
        "def mode_solver_substrate_loss(\n",
        "    resolution,\n",
        "    npml,\n",
        "    delta_override=None,\n",
        "    size=(3, 4.3),\n",
        "    num_modes=3,\n",
        "    target_neff=2.41,\n",
        "    fields=[\"Ex\", \"Ey\", \"Ez\"],\n",
        "):\n",
        "    # waveguide structure\n",
        "    wg = td.Structure(\n",
        "        geometry=td.Box(size=(td.inf, 0.5, 0.22)),\n",
        "        medium=td.Medium(permittivity=3.5**2),\n",
        "    )\n",
        "\n",
        "    # SiO2 layer\n",
        "    box = td.Structure(\n",
        "        geometry=td.Box.from_bounds(rmin=(-td.inf, -td.inf, -100), rmax=(td.inf, td.inf, -0.11)),\n",
        "        medium=td.Medium(permittivity=1.45**2),\n",
        "    )\n",
        "\n",
        "    # Si substrate\n",
        "    substrate = td.Structure(\n",
        "        geometry=td.Box.from_bounds(rmin=(-td.inf, -td.inf, -100), rmax=(td.inf, td.inf, -1.11)),\n",
        "        medium=td.Medium(permittivity=3.5**2),\n",
        "    )\n",
        "\n",
        "    # mesh override region\n",
        "    if delta_override:\n",
        "        mesh_override = [\n",
        "            td.MeshOverrideStructure(\n",
        "                geometry=td.Box(center=(0, 0, 0), size=(0, 1.5, 1)),\n",
        "                dl=(delta_override,) * 3,\n",
        "            )\n",
        "        ]\n",
        "    else:\n",
        "        mesh_override = []\n",
        "\n",
        "    grid_spec = td.GridSpec.auto(\n",
        "        min_steps_per_wvl=resolution, wavelength=1.55, override_structures=mesh_override\n",
        "    )\n",
        "\n",
        "    sim = td.Simulation(\n",
        "        size=(4, size[0], size[1]),\n",
        "        grid_spec=grid_spec,\n",
        "        structures=[wg, box, substrate],\n",
        "        run_time=1e-12,\n",
        "        boundary_spec=td.BoundarySpec.all_sides(boundary=td.PML()),\n",
        "        symmetry=(0, -1, 0),\n",
        "    )\n",
        "\n",
        "    mode_spec = td.ModeSpec(\n",
        "        num_modes=num_modes,\n",
        "        target_neff=target_neff,\n",
        "        num_pml=(npml, npml),\n",
        "        precision=\"double\",\n",
        "    )\n",
        "\n",
        "    mode_solver = td.ModeSimulation.from_simulation(\n",
        "        simulation=sim,\n",
        "        plane=td.Box.from_bounds(\n",
        "            rmin=(0, -size[0] / 2, -((size[1] - 0.3) / 2 + 0.3)),\n",
        "            rmax=(0, size[0] / 2, 2 + (size[1] - 0.3) / 2),\n",
        "        ),\n",
        "        mode_spec=mode_spec,\n",
        "        freqs=[td.C_0 / 1.55],\n",
        "        fields=fields,\n",
        "    )\n",
        "    return mode_solver"
      ],
      "id": "c696d87c"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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/fAwfPjzbZiU/m3/605+y/z+uuuoqHHrooQW3/eCDD3DRRRcBAA4++ODsULd8\nvvzlL2PhwoUYNGgQVq1aNaBZaKgyDOJERETU8M444wzMmjULqqpixYoVeWf6yRfE693ixYuzs6Rc\ncskluPXWW13uUWPxxtt3IiIiIhddddVVUBQFhmFkb+pvBNZUkKFQCBdffLHLvWk8DOJERETU8CZN\nmoTTTz8dAPC73/2uJvPUe826detw3333AQDOPfdc24f8UGkM4kREREQAfv7znyMSiaC9vb3sRabq\n2c9//nMkEgkMHToUP/rRj9zuTkPiPOJEREREALbbbjvceuuteOKJJ7Bo0SLoug5N82dUisViWL58\nOaZNm4Zvfetb2ZVjyVm8WZOIiIioDH68WZPc5c+3eUREREQ2CwQCmDZtGgBghx12cLk35Ac8I05E\nRERE5ALerElERERE5AIGcSIiIiIiFzCIExERERG5gEGciIiIiMgFDOJERERERC5gECciIiIicgHn\nEacB0XUdK1euBAC0tbVBUfjejoiIiGrHNE10dnYCAMaOHVvXq5/Wb8/JE1auXInx48e73Q0iIiJq\nQJ9++inGjRvndjeqxiBOtvjxtddueeSl9aEkIE0AAhCi15cl+veznG3qFetn/d6tXyiZw0kJpHX7\nj6koCkSv2qSUME2z4m3qFetn/XbVr6pqn+3cJoTAdddd53Y3BoxBnAakra2t5xOR/Y8nCCGgbhkq\nY1qZHMhkDgVQtnS1z3Po+5xfsH7W79n6pbGlUyqCoUBNDmGaZp9goShKdhhdsef8gvWzfjvqNwzD\nU29QrIXh++SQOsQgTgPS8wMrAQhEgm72JiOlA4oChDRgq9aeXxrxFNAV7/kF0xrJPJf7NS/UUAus\nn/V7sX4jHYVQAlCDgxBsq93l5Vgsho6OjuzngwcPBoB+X2tubq5ZH9zE+ln/QOtft24dEokEDMNA\nKBSqUU/LY5omYrEYANT9GycGcWoYmYBhZoNH7wAC+DuEAayf9QONXL8VMKzg0TuAAP4OYQDrZ/2N\nXb+X1ffbCKIKRYI9ZwJ783sIsbB+1t/I9Tc3N2fPBPbWKCGE9bP+Rq7fqxjEiYiIiIhcwCBODSV3\nnKylK64gnnKhQw5j/ay/kevPHSdr6ejoyI439TPWz/obuX6vYhCnhpHvZrXel+n9HkZYP+tv5Prz\n3azW+zK938MI62f9jVy/l/FmTWoI+UJIz5jY3BvY/DdelvWz/kauP18I6T0mNvcGNr+Nl2X9rL+R\n6/c6nhEn3yseQvrfwOa3M4Osn/U3cv2lQkjuDWx+OzPI+ll/I9dfDxjEyddKhRCLX8MI62f9jVx/\nqRBi8WsYYf2sv5HrrxccmkK2ktILq24JQAK6IdHZDQCZPrWGDYQ1E4W6GNYAGVLQlVABAJ3dgDQN\nRIJeqKly8ZRVC+sHWL9n6zcNQKi2N1tuCLEUmme5Xi/Ts37W38j11xMGcbKHtSS2NFztRqYPKgwJ\nmCYQUDP9aQkmEFLSMPXiu4YUQAYCiKbCAICuOCCNFMKBdK17batE2qqB9QOs38v1SzMNKPYG8UpD\niMUvYYT1s/5Grr/ecGgK+Y4pBUzZ89JuCSYqChLhQBotwUT282gqjEQ6YGsfa6knhGWwftbfSPVX\nG0Is9X6ZnvWz/kauvx7xjDjZQyJzVrwGl5groRsC0jo9LwRaI0AkGARQ2TQQTVqmFOsyfTTdDKF6\nf5hCPKUgmlazVyhawwbrZ/3wcv2mjEHY9HtjoCHEUq9nBlk/669l/VQbDOJkKyHcu8iS1gG9V04I\nqAJNYRVAdX/km8KAUHpudosmFQjFu1O7xVNb+miFsIiJSJD1s36P16+omQMNkF0hxFJvYYz1s/5a\n1y+lHEgXqQAOTSFfyA3hqgJoNpxkq5fZJMqdHaNSrJ/110P9docQS71cpmf9rN+J+lOpFHS9xI0m\nVDEG8Tyi0SieeeYZXHXVVZg6dSomTJiAlpYWNDc3Y4cddsDMmTMxb948W4+5YsUKXHLJJdh5553R\n3NyMoUOH4stf/jJuv/12JJNJx9qoR7khXABQbHxlez2M1CqEWVg/6/dy/bUKIRavhzHWz/qdrN80\nTZimt4fo1Rshea2hn+985zu47777Sm536qmn4i9/+QtCodCAjvf000/jtNNOQ2dnZ97nd911Vzz7\n7LPYeuuta9pGNTZt2oShQ4fix9f+CBDC8cv2uSFcUzLD1RUFCGnAVq32/cKodeCphpN9Yv2svxbH\nMtJdEEoAanAQgm3jK9q31iHErWOVi/WzfifrX7duHQzDgJQSgUAAwaB7vwBN00R3dzeuu+46tLe3\nY8iQIa71ZaB4RryIHXbYATfccAPefvttdHV1IRqN4oUXXsAhhxwCAHjkkUdw5plnDugY77//Pk4+\n+WR0dnZiu+22w5NPPomuri58/vnnuPnmmxEIBLB48WJMnz694CUhO9qoR/lCeKCGdz147cyg08GQ\n9bN+L9XvdDDy2plR1s/6na6/d/BOp9NIpdz7BZBO19eUssUwiOcxduxY3H///fjoo49wxRVXYI89\n9sgOTTnssMMwb948HHbYYQCABx98EP/5z3+qPtYPfvADxGIxNDc348UXX8Rxxx2HlpYWjBw5Epdd\ndhl+//vfAwDeeust/OlPf6pZG/XG6RBu8UoYcevsLOtn/V6o362zk14JY6yf9btRfyAQgNJr3Kdb\nYdxvY9UZxPP46U9/ipkzZ/Z5wfWmaRp+8pOfZD9/8sknqzrOp59+irlz5wIAzjvvPIwbN67fNmed\ndRZ23nlnAMAdd9xRkzbsIUpvYhO3QrjF7TDi9hAJ1s/63azf7SECbocx1s/63axf0zRXw3gqlfLV\n2XCAQbxqEydOzD5evXp1VW088cQT2cennnpqwe1OOeUUAJkhKB9//LHtbdQTt0O4xa0w4nYIs7B+\n1u9G/W6HEItbYYz1s34v1K8oCgKBnkW+nArjfgzhAIN41dauXZt93NraWlUb1pCWUCiEPffcs+B2\n+++/f/bxG2+8YXsbdkrX8GqRV0K4xekw4pUQZmH9rN/J+r0SQixOhzHWz/q9VH8wGHQ0jOeGcE3T\nfDOvOYN4lR5++OHs4ylTplTVxgcffAAA2HbbbaFphRPl+PE9MwlY+9jZhp10szZh3Gsh3OJUGPFa\nCLOwftbvRP1eCyEWp8IY62f9XqzfqTCeG8IDgUCf49Y7D0SZ+vPZZ5/h9ttvBwBss802OP7446tq\n54svvgAAjBgxouh2vZ+39rGzjVI2bdpU8LnevxwsuglAty8oezWEWzKByMwGpcy/9gUlr4YwC+sH\nWH/t6vdqCLHUegVG1s/6vVy/NZOKFZStf+2a2jBfCA8Gg76ay9xDcaY+JJNJnHrqqdl3vb/85S8R\niUSqaisajQIAwuFw0e16t2/tY2cbpQwdOrSMrSR637BpVxj3egi31CqMeD2EWVg/wPrtr9/rIcRS\nqzDG+ll/PdRfqzBeKIT7jQcjjXdJKfE///M/WLhwIYDMLCUnn3zygNsVYuAzjtjRhh00RUI3M33J\nhHEJTa1uHJduiGxbVtuaKlF6WJjIvC+QJqTp3BRHYQ2QIQVdCRUA0NkNSNNAJFjdO/d4ymors39r\n2EBYMyE9eiKA9bP+quo3DUCo/b5cLyHEYncYY/2sv57qtzuMN0oIBxjEK3LxxRdj1qxZAIAZM2YM\neCrAlpYWbNq0CfF4vOh2vZ9vaWmxvY1S2tvbCz7X0dGRGX++JS9rig4pFRgy84dVNwWkNBFQK0sP\naUOBIXvOBKrCgKaYmYBdilQBSEipw9SdneM1pAAyEEA0lblC0RUHpJFCOFDZnd6JtNWGAQBoCSYQ\nUtJw8H1FVVg/66+0fmmmAaVvEK+3EGKxK4yxftZfj/XbFcYbKYQDDOJlu/baa/GrX/0KAHDkkUfi\n4Ycfhqr2P4tTiWHDhmHlypVYv3590e16Pz9s2DDb2yil0qVjA6oJGMiGcUOqgIGyw3gmhPd8b1Vh\nVBzk3WSFDiuMWP+WG8Z6QlhGSzBRcZBzE+tn/UD19ddrCLEMNIyxftZfz/UPNIw3WggHGMTLcvPN\nN2cX8DnooIPwxBNPIBQKDbjdL33pS3j77bexYsUK6LpecNaTTz/9tM8+drdhC2uI+JZLzAENEEbP\nMBVDqhCmUnKYim4IGDJ3OIoAUMGbHiEAISCEBkVz5xdYk5b5VliX6aPpZgi19GX6eEpBNK1mrzC0\nhg1EgkEA9fWLiPWz/nLrN2UMYsvvjXoPIZZqwxjrZ/1+qL/aMN6IIRxgEC/pt7/9LS6//HIAwH77\n7Yc5c+agqanJlrb33XdfPPjgg0gmk3j77bex77775t3u9ddfzz7eZ599bG/DTkL0DCcJaAB63WyZ\nCeWi4M2W+W/MzOxTeUcACBVCcW/sfFMYEErPzXbRpAKhFL6BLZ7aso0VwiImIkEVFb0J8RDWz/rL\nql9RAaEgnjQRTXVkv1yvIcRSaRjzSwizsP7Grr/SMN6oIRzgPOJF3XPPPbjgggsAAHvssQeefvpp\ntLW12db+jBkzso97z0ue69FHHwUA7LLLLpgwYYLtbdRSQMsEakuhecbrZXaUSpU7z3K9zI5RKdbP\n+surX0Vnd8/VsnoPIZZy55n2WwizsP7Grr/cecYbOYQDDOIFPfLIIzj77LMhpcSkSZPw3HPPVTxW\nupTx48fj2GOPBQDcddddWLZsWb9t/vznP+PDDz8EgOybArvbqLVSYdyvIdxSKoz4NYRZWD/rL1Z/\nIq0hmuz5gfdLCLGUCmN+DWEW1t/Y9ZcK440ewgEG8bzmzJmDM844A6ZpYuedd8a8efMqvsERyIzF\nFkL0+SHMdfPNN6O5uRnRaBSHHXYY5syZg1gshvXr1+PWW2/FueeeCwDYa6+9cPbZZ9esjVorFMb9\nHsIthcKI30OYhfWz/kL1R5M999v4LYRYCoUxv4cwC+tv7PoLhXGG8AwfRp6Bu/nmm7Mvjg8//BCj\nRo0quv0RRxyB559/vqpj7bLLLvjb3/6G0047DZ999hmmT5/eb5tdd90VTz75ZMEbMe1owwn9x4z3\nfd6vIdySf9GTHn4NYRbWD7D+fPVnfhG0NQlfhhBLoTHDFr+GMAvrb+z6C40ZtzRqCAd4RtwTjj76\naCxatAgXXXQRdtppJ0QiEQwePBj77bcfbr31VrzxxhvYeuuta96GE3LPjFv8HsItuWcGLX4PYRbW\nz/rz1d8S0hEJ+f/PUe6ZUYvfQ5iF9Td2/blnxi2NHMIBnhHP66WXXrKlnQ8++KDsbbfddlvcfvvt\nuP3226s+nh1tEBEREZEz/H8Kgjwld0y4pdBsKn6TOybYUmg2Cb9h/aw/X/3RpIZ4sn4W7apW7phg\nS6HZNPyG9Td2/bljwi2FZlNpFAzi5Jh8N2aWM7WhX+S7Ma+cqd38gvWz/mL1d3ZLX4eRfDfmlTO1\nnV+w/sauP9+NmeVMbdgIODSFHFF0dpTcGzh1/40XLz47Ru4NbP4bL8z6WX+h+k09iWgqDKDy5cDr\nRanZMapdDr1esP7Grr/U7CiVrsDpNzwjTjVXaorCchf9qVelpqgrd9GTesX6WX+x+sMBHS2hnh94\nv50ZLBXCyl30pV6x/sauv1QIL3fRHz9jEKeaKneecL+G8XLnifZrGGP9rL+8+g20NYns534JI+XO\nE+3XMMb6G7v+cucJb/Qw7rMBAOQ2KXvChG4I6GbPH1dNkdBUCSnz7QloKgD07JMZppLZpzICkACk\nCWm6l+bjKQVdCRXWPMmtYQNhzYQscE9aWANkyNoH6OwGpGkgEqzPm9hYP+svq37TAISKSEiB1jTY\nN5fpK12spdA806yf9dejShfrKTTPeCMMU2EQJ3tYeVsaAIC0ocCQPWfCVGFAU8xMQC5CUwApFRgy\nE0Z0U0BKEwG1gjAiVQASUuowdXfOKiTSgS3jXjPfj5ZgAiEljVLvC0IKIAOB7JjZrjggjRTCgf53\nmnsZ62f95dYvzTSgZH7e/RJGql0xkfWzfqD+6692xcxGDeMcmkK2y4RwNfu5KoyKgnRANaEKI/u5\nIVWkjfp5qfaEkIyWYKKiIBUOpNESTGQ/j6bCSKT7L4LgVayf9Q+k/nq/TD/QZctZP+uv5/oHumx9\nIw5T4RlxsocEIADd1GDI3OEoAoBacNd8AhogDJkdpmJIFcJUyhumIgQgBITQoGjOnkmIpxRE02r2\nCkFr2EAkGARQ2Tv6Jg0QKrLDFKLpZgjV+8MUWD/rr7R+U8YgRN/fD/V6ZnCgIczC+lk/UH/1DzSE\nWxrtzDiDONmq75hwIKAJ9IxbqUxAQ87Uhpm2ypraUAAQKoRS3bGrEU8B0aQCYYWQiIlIUEWlb0Is\nTWFAKD03u0WTCoTi3antWD/rr6p+Rc0UmqPewohdIczC+lk/UD/12xXCLY0Uxuvnej95XN/AW2h2\nlErVy2wq5c4OUal6mU2D9bP+WtRfL5fp7Q5hFtbP+uuhfrtDuKVRhqkwiJPt7ArhFq+H8VqFEIvX\nwxjrZ/21rN/rYaRWIczC+lm/l+uvVQi3NEIYZxAnW9kdwi1eDeO1DiEWr4Yx1s/6najfq2Gk1iHM\nwvpZvxfrr3UIt+QL472PW+8YxMlWtVya3mth3KkQYvFaGGP9rN/J+r0WRpwKYRbWz/q9VL9TIdyS\nG8Z1XYcQzt0DVksM4lRXvBLGnQ4hFq+EMdbP+t2o3ythxOkQZmH9rN8L9Zum6WgIt+SGcb9gECeb\nVLr6ZfXcDuNuhRCL22GM9bN+N+t3O4y4FcIsrJ/1u1m/ruswzZ7fP06FcIsfwziDONUlt8K42yHE\n4lYYY/2s3wv1uxVG3A5hFtbP+t2oP51OuxrCLcFgEJrmn9m3GcSpbjkdxr0SQixOhzHWz/q9VL/T\nYcQrIczC+lm/0/X3nq3ErRDe+/h+wSBOdS1fGO/1ht02XgshFqfCGOtn/V6s36kw4rUQZmH9rN+N\n+hVF8cTCOlI6NyS2lhjEqe7lhnEJe8O4V0OIpdZhjPWzfi/XX+sw4tUQZmH9rN/J+hVFgaIwOtqJ\n303yhdwwbpiAbgy8Xa+HEEutwhjrZ/31UH+twojXQ5iF9bN+J+r329hsr+B3lGwlZQ3GhZRJUwFA\nQDczc4umDYnuhIFIsLo+xVMKuhIqgMz+rWEDYc2EiyUWFdYAGbL6DHR2A9Jk/azf4/WbBiDUATdj\nBSQrOFj/Vhuc6iWEWVg/6wdqW380GoVh2HCGi/pgECd7WPPqS3d/SDUFMEwNEgKQEl1xQBophAOV\nrcKVSAcQTYUBZOppCSYQUtIwPbCaZzEhBZABq+9g/azf8/VLMw0oAw/igH1hpN5CmIX1s36gdvVH\no1E7ukk5GMTJdxQhIXvNa26FknLDSE8IyWgJJioOMm6y+mrVwPpZf++vl1Lv9Q80jNRrCLOwftYP\nNG799YhBnOwhkTkrbsMl5gETAqoAVEUCyPQnmm6GUEtfpo+nFETTavYMf2vYQCQYBODBgbFFNGmZ\n/xXWMAXWz/q9Wr8pYxA2/96oNoz4JYSwftYPNG799YZBnGwlhEfu/xWApgo0hczszWbRpAKhFL7Z\nLJ7aso0VQiImIkEVVpivN01hQChg/awfgIfrV9RMR21WaRjxWwhh/awfaNz664lHUhNRbZQ7m0S9\nzA5RKdbP+hu5/nJnk/BrCGH9rL+R668XDOLke6XCiF9DiIX1s/5Grr9UGPF7CGH9rL+R668HHJpC\nDSETLHqGqWT+NXs9zvBbCLGwfoD1N279hS7T5z72awhh/awfaNz6vY5BnBpG/jDSw68hxML6Adbf\nuPUXCyOA/0MI62f9QOPW72UcmkINJfcyvcXvIcTC+ll/I9efe5ne0ighhPWz/kau36sYxImIiIiI\nXMAgTg0l98Y0S6HZJPyG9bP+Rq4/98Y0S6HZJPyG9bP+Rq7fqxjEqWHkmx2inKnd/IL1s/5Grj/f\n7BDlTO3mF6yf9Tdy/V7GmzWpIRSfoq3/bBJ+Gy/L+ll/I9dfaoq2chc9qVesn/U3cv1exzPi5Hul\n5kkud9GTesX6WX8j118qhJS76Em9Yv2sv5HrrwcM4uRr5S5W4tcwwvpZfyPXX+5iJX4NI6yf9Tdy\n/fWCQ1PIVlL2nxrNeQKQgG5IdHYD1sIlrWEDYc1EoS6GNUCGFHQlVABAZzcgTQORoBdqqlw8ZdXC\n+gHW79n6TQMQqu3NVrpiYKF5luv1Mj3rZ/2NXH89YRAne4gt/0rD1W5k+qDCkIBpAgE105+WYAIh\nJQ1TL75rSAFkIIBoKgwA6IoD0kghHEjXute2SqStGlg/wPq9XL8004BibxCvdtluv4QR1s/6G7n+\nesOhKeQ7phQwZc9LuyWYqChIhANptAQT2c+jqTAS6YCtfaylnhCWwfpZfyPVX20IsdT7ZXrWz/ob\nuf56xDPiZA+JzFnxGlxiroRuCEjr9LwQaI0AkWAQQGXTQDRpmVKsy/TRdDOE6v1hCvGUgmhazV6h\naA0brJ/1w8v1mzIGYdPvjYGGEEu9nhlk/ay/lvVTbTCIk62EcO8iS1oH9F45IaAKNIVVANX9kW8K\nA0LpudktmlQgFO9O7RZPbemjFcIiJiJB1s/6PV6/omYONEB2hRBLvYUx1s/6a12/lHIgXaQCODSF\nfCE3hKsKoNlwkq1eZpMod3aMSrF+1l8P9dsdQiz1cpme9bN+J+pPpVLQ9RI3mlDFGMSp7uWGcAFA\nsfGV7fUwUqsQZmH9rN/L9dcqhFi8HsZYP+t3sn7TNGGa3h6iV28YxKmu5YZwTbE3hFu8GkZqHcIs\nrJ/1e7H+WocQi1fDGOtn/W7Ub5omUin3fwEIaxxenWMQp7qVL4QHanjXg9fCiFMhzML6Wb+X6ncq\nhFi8FsZYP+t3uv5gsOcXTDqddjWMp9P1NaVsMQziVJecDuEWr4QRp0OYhfWzfi/U73QIsXgljLF+\n1u9G/YFAAEqvS85uhXG/jVVnECebOHeJyK0QbnE7jLgVwiysn/W7Wb9bIcTidhhj/azfzfo1TXM1\njKdSKV+dDQcYxKnOuB3CLW6FEbdDmIX1s3436nc7hFjcCmOsn/V7oX5FURAI9Czy5VQY92MIBxjE\nyWbpGl4t8koItzgdRrwSwiysn/U7Wb9XQojF6TDG+lm/l+oPBoOOhvHcEK5pmm/mNWcQJ1vpZm3C\nuNdCuMWpMOK1EGZh/azfifq9FkIsToUx1s/6vVi/U2E8N4QHAoE+x613DOJkO7vDuFdDuKXWYcSr\nIczC+ll/Lev3agix1DqMsX7W7+X6ax3G84Xw3rO3+AGDONmk7yUiu8K410O4pVZhxOshzML6WX8t\n6vd6CLHUKoyxftZfD/XXKow3QggHAA9GGqpnmiKhm5kZVHQTgC6hqdWN49INkW3LaltTJUoPCxOZ\n9wXShDSdm+IorAEypKAroQIAOrsBaRqIBKtbhSyestrK7N8aNhDWTEiPLmrG+ll/VfWbBiDUfl+u\nlxBisfpm9dn6t9o+s37WX0/1WwHZCs7Wv9UG50YJ4QCDONllS17WFB1SKjBk5g+rbgpIaSKgVpYe\n0oYCQ/acCVSFAU0xc0+85ydVABJS6jB1Z+d4DSmADAQQTYUBAF1xQBophAOV3emdSFttGACAlmAC\nISUNB99XVIX1s/5K65dmGlD6BvF6CyEWu8IY62f99Vi/XWG8kUI4wKEpVAMB1YQqjOznhlSRNsp/\nqWVCeM8fZlUYFQd5N4UDabQEE9nPo6kwEunybyzpCWEZLcFExUHOTayf9Q+k/noNIZaBDlNg/ay/\nnusf6DCVRgvhAM+Ik10kMmfFt1xiDmiAMHqGqRhShTCVksNUdEPAkLnDUQSA/peuCxICEAJCaFA0\nd36BNWmZb4V1mT6aboZQS1+mj6cURNNq9gpDa9hAJBgEUF+/iFg/6y+3flPGILb83qj3EGKp9swo\n62f9fqi/2jPjjRjCAQZxspkQPWe+AxqAXjdbZkK5KHizZf4bMzP7VN4RAEKFUJxb8TNXUxgQSs/N\ndtGkAqEUvtkuntqyjRXCIiYiQRUVvQnxENbP+suqX1EBoSCeNBFNdWS/XK8hxFJpGPNLCLOw/sau\nv9Iw3qghHODQFKqxgJYJ1JZCs6nUy+wolSp3Nol6mR2jUqyf9ZdXv4rO7p6rZfUeQizlDlPwWwiz\nsP7Grr/cYSqNHMIBBnFyQKkw7tcQbikVRvwawiysn/UXqz+R1hBN9vzA+yWEWEqFMb+GMAvrb+z6\nS4XxRg/hAIemkEP6D1PJfJ59vIXfQrglE6zMbODK/Gv2epzhtxBmYf0A689ffzQZyo4+81sIsRQa\nppD7mPWzfj/WX2iYSu7jRgzhAIM4OShvGO/FryHckj+M9PBrCLOwfoD156s/84ugrUn4MoRYioUx\nwL8hzML6G7v+YmEcaNwQDnBoCjksd5iKxe8h3JJ7md7i9xBmYf2sP1/9LSEdkZD//xzlDlOw+D2E\nWVh/Y9efO0zF0sghHGAQJyIiIiJyBYM4OSr3xkxLodlU/Cb3xjxLodkk/Ib1s/589UeTGuLJ+lm0\nq1q5N+ZZKl30pV6x/sauP/fGTEuli/74DYM4OSbf7CjlTG3oF/lmxyhnaje/YP2sv1j9nd3S12Ek\n3+wYA1mBsd6w/sauP9/sKANZgdNPGmBULnlB0SkK88ym4rfx4sWnqOs/m4TfxguzftZfqH5TTyKa\nCgMofwXCelNqirpKV2CsN6y/sesvNUVhpStw+g3PiFPNlZonvNxFf+pVqXmiy130pF6xftZfrP5w\nQEdLqOcH3m9nBkuFsHIXfalXrL+x6y8Vwstd9MfPGMSppspdrMevYbzcxVr8GsZYP+svr34DbU0i\n+7lfwki5i7X4NYyx/sauv9zFeho9jPtsAEBtfPzxx1i4cCHWrl0LAJg8eTK+8pWv2NL2vffeiy++\n+KLkdrvssguOPfbYkttFo1G8+OKLWLVqFUKhECZMmIADDzwQiuLMey4pe8KEbgjoZs8fV02R0FQJ\nKfPtCWgqAPTskxmmktmnMgKQAKQJabqX5uMpBV0JFdY8ya1hA2HNhCxwT1pYA2TI2gfo7AakaSAS\nrM+b2Fg/6y+rftMAhIpISIHWNNg3l+krXTGx0DzTrJ/116NKV8wsNM94IwxTYRAv4Pe//z1mz56N\nhQsXYtOmTX2e+5//+R/bgvgtt9yC9957r+R2M2fOLBrE0+k0fvrTn+LWW29Fd3d3n+fGjBmD3/zm\nN5gxY8aA+1uQlbelkemPocCQPeFfFQY0xcwE5CI0BZBSgSEzYUQ3BaQ0EVArCCNSBSAhpQ5Td+es\nQiId2DLuNfP9aAkmEFLSKPW+IKQAMhDIjpntigPSSCEc6H+nuZexftZfbv3STANK5ufdL2Gk2mXL\nWT/rB+q//mqXrW/UMM4gXsD999+PV199FQCwww47YO+998YjjzxSs+NNmjQJRx99dMHn995774LP\nSSkxc+ZMPProowCAiRMn4pBDDkEsFsOcOXOwatUqfO1rX8M999yD73znO3Z3vZ9MCFezn6vCqChI\nB1QTMJBtw5AqYKCyMO6inhCS0RJMVBSkrG2tNqx/6yWMsX7WP5D66z2MVBvCLKyf9QP1W3+1IdzS\niGGcQbyA8847D9dccw32228/DB06FIlEoqZBfJ999sEtt9xS1b6///3vsyH8sssuw0033QQhMqeo\nN23ahGOOOQYLFizAOeecg4MPPhg77LCDbf3OkgAEoJsaDJk7HEUAUAvumk9AA4Qhs8NUDKlCmEp5\nw1SEAISAEBoUzdlfXvGUgmhazV4haA0biASDACr7JdKkAUJFdphCNN0MoXp/mALrZ/2V1m/KGITo\n+/uhXsPIQEOYhfWzfqD+6h9oCLc0WhhnEC9g5syZbnehLOl0Gj/5yU8AZM6a33jjjdkQDgBDhgzB\nQw89hJ122gmpVAo//elPce+999asP33HhAMBTaBn3EplAhpypjbMtFXW1IYCgFAhlOqOXY14Cogm\nFVjf/syNaSoqfRNiaQoDQum52S2aVCAU705tx/pZf1X1K2qm0Bz1FkbsCmEW1s/6gfqp364Qbmmk\nMM5ZU+rcCy+8gM8//xwAcMEFF+S9KXP77bfHV7/6VQDA448/jmQyWYOe9A28hWZHqVS9zKZS7uwQ\nlaqX2TRYP+uvRf31MpuE3SHMwvpZfz3Ub3cItzTKbCoM4nXu2WefzT4+6qijCm5n3Vza1dWF1157\nraZ9siuEW7wexmsVQixeD2Osn/XXsn6vh5FahTAL62f9Xq6/ViHc0ghhnENTPKKrqwtz587F8uXL\nIYTAyJEj8eUvfxnbbLNN0f0WL14MABg2bBhGjx5dcLvdd989+/i9997DYYcdZk/Hc9gdwi39h6nA\nEytw1jqEWDJtem8FRtbP+p2o36uX6Wsdwiysn/UD3qu/1iHckm+Yiiw0D3IdYhD3iMcffxyPP/54\nv68ffvjhuPHGG7HPPvvk3W/ZsmUAgLFjxxZtv/fz1j7lyp2+sbfev4SA2gZjr4Vxp0KIxWthjPWz\nfifr91oYcSqEWVg/6we8U79TIdySG8Z1Xe9zP1w9YxD3gEAggD322APbb789Ro0ahU2bNuHVV1/F\nsmXL8MILL+CAAw7ArFmzcMopp/Tbt7OzEwDQ1tZW9Bitra399inX0KFDK9q+lrwSxp0OIRavhDHW\nz/rdqN8rYcTpEGZh/awfcL9+0zRhmj3D5Wodwi25YdwvGMRddv311+Owww7DoEGD+nxdSolZs2bh\n3HPPRSwWwze/+U3svvvu2GmnnfpsF4/HAQChUKjoccLhnnl9rX3stWX+Qge4HcbdCiEWt8MY62f9\nbtbvdhhxK4RZWD/rB9yrX9d1V0K4xY9hnDdruuxrX/tavxAOAEIInHHGGbjvvvsAAMlkEjfccEO/\n7ayAXermhd4zpfQO5eVob28v+PHpp59W1JZd3LqB0+0QYnHrBj7Wz/q9UL9bN7C5HcIsrJ/1u1F/\nOp12NYRbgsEgNM0/55H9U4lPnXTSSZg0aRLee+89zJ07t9/zra2tWL9+Pbq6uoq2E41G++xTiSFD\nhlS0vVMKnRmvFa+EEIvTZ0ZZP+v3Uv1Onxn0SgizsH7WDzhbf+8Tfm6F8N7H98tZcZ4RrwPWjZrr\n1q3rNwf4dtttBwBYtWpV0TZWrlzZbx8/yHdm3KzB4oNeCyEWp86Msn7W78X6nToz6LUQZmH9rN+N\n+hVF8cTCOn6ZOYVBvA70XqTHMIw+z02aNAlAJqRv2LChYBvvvfdev338IjeMS9gbxr0aQiy1DmOs\nn/V7uf5ahxGvhjAL62f9TtavKErehQOpevxu1oF3330XQGb2kqampj7PHXHEEdnHL7zwQsE2nn/+\neQBAJBLBAQccUINeuis3jBsmoBuFty+X10OIpVZhjPWz/nqov1ZhxOshzML6Wb8T9fttbLZX8Dvq\ncS+99BLefPNNAPlXzpw2bRqGDBmCTZs24Xe/+x1OO+20ftusW7cOf//73wEAxx13XE1/kUhZg3Eh\nZdJUABDQzczsLWlDojthIBKsrk/xlIKuhAogs39r2EBYM+FiiUWFNUCGrD4Dnd2ANFk/6/d4/aYB\nCHXAzdg9ZrZeQpiF9bN+oLb1R6PRflflaeAYxGvonnvuwcaNGxEOh/G9732v3/Ovvvoqxo0bV3BF\nzBdffBGnnnoqgMzloCuuuKLfNuFwGFdeeSWuuOIKzJ8/HzfffDN+8IMfZJ+Px+P41re+hXg8DkVR\n8KMf/cim6nJYMxdKd39INQUwTA0SApASXXFAGimEA5Xd1JFIBxBNhQFk6mkJJhBS0jAdmJllIEIK\nIANW38H6Wb/n65dmGlAGHsQB+8JIvYUwC+tn/UDt6u896QPZR0i/jHa32aJFi/DMM89kP9d1HVdd\ndRUAYL/99uuzuE4wGMSFF17Yr40vfelL+PDDDzFo0KA+L2rL6aefjkceeQR77bUXJk6ciFGjRmGr\nrbZCe3s7XnnlFbz++usAMlMZ/u53v8O5556bt6/pdBrHHHMM5s2bBwCYOnUqpk6dilgshr/97W/Z\nlTRvuummPiHdDps2bcLQoUPx4x//CICAKtw/XWhKkZ3VXBGZl3dANaAq5fXNMBWkjZ5gUMm+XjGQ\nGlg/63e0ftMEFBWKGoYSLL4wWbl0Xe9zY3soFCr7kvpA9vUK1s/6a1F/PB6HruuQUkJV7XnzXC0p\nJXRdx3XXXYf29nbPzu5Wjvp6dTlowYIFBUPrwoULsXDhwuznzc3NeYN4KQcffDAWLFiAN998Mzv8\nJNfee++Nm2++GYcddljBdgKBAGbPno2LL74Yd999N1566SW89NJL2edbW1tx880345xzzqm4j2Xb\nknwVxf0lZ6UpoAgJVUgEA9b7TAWaIqAqxd93GqaAMAU0LbOdpkioSmb/emOYZnaYDutn/V6tXxo6\noAgomoAWidjWbiQS6bcEd6kwouuZU/7WduXs41Wsn/XbXX8qlcququl2EDdN0zezptTnK8wBkydP\nxqWXXlrWtoVWtTzrrLOwfv16RAr8cTn//PNx/vnn44MPPsDbb7+NtWvX4osvvkAkEsGYMWMwZcoU\nTJw4saw+tLS04I9//COuvfZaPPXUU1i5ciVCoRB22mknHHvssQ5cVpMQQiAUqPFhypBIA5oiEAkB\nWw/t/Uw1bxLcf2NhH9bvzD5e5c36jUQ3FDUENTwI4a3G1Px4RFQdwzCy48QrXRjQbqZpIpFIuNoH\nu3BoCg1IdmjKj66GFtCwzVD3L+Fv7BIIB4ERgyUOmeTxQb1EDS6xcRG00FCEh+2JrSZf5HZ3iKiA\nOXPmYNWqVYjH4xg5cqSrfUmlUvjwww/xi1/8ou6HptTf9VYiIiIiIh9gECciIiIicgGDOBERERGR\nCxjEiYiIiIhcwCBOREREROQCBnEiIiIiIhcwiBMRERERuYBBnIiIiIjIBQziREREREQuYBAnIiIi\nInKB5nYHyCcEACkhzbTbPQGkBmmakHoaRqLT7d4QURFSj8MMJN3uBhGRKxjEyRZCAIAJU4+53RVI\n2QxdN2CmNyPV+Ynb3SGiIoxkO4QWdrsbRESuYBAn3zFMjrgiIiIi72MQJ1tICQAKFK3Z1X7EUwrS\npgZNM6EEBiHYtqOr/SGi4lJyKZRAi9vdICJyBYM42UMCEAJCCbjWhXgKiCats+EKhBaGGuZLnMjL\nRCwCRQm53Q0iIlfwGj75QjwFdMV7Xs4B1cXOEBER+ZCu6253wXcYxKnu5YbwoCahMogTERHZKp1O\nM4zbjEGc6lpuCG+NmFD5qiYiIqqJZDKJWMz9GdIUxR9/7P1RBTWkfCE8EnSxQ0RERA2go6PD1TAe\nj8cZxIncxBBORETkrECgZ0IGt8J4LBZDZ6d/FutjECebCMeOxBBORETkPE3TEAr1zHLkdBiPxWLo\n6Ohw7HhOYBAnewgBU9b+MAzhRERE7tE0DYMHD85+7lQYzw3hpmnW/JhOYBAn20gzE5RrhSGciIjI\nfc3NzY6G8dwQ3tbW5psgztVOyFaZoGx/QGYIJyIi8o7m5sxK2lZAtv61vm6X3BA+ePDgPmPV6x3P\niJM9ZM+4lK64YuuZcYZwIiIi76n1mfF8IdzuoO82BnGyiYTo9WqyK4wzhBMREXlXrcJ4I4RwgENT\nyC4CUCDREtLRlcgsa9nZDUjTQCRY3TiueErZ0lZm/9awgbBmQpZqTmqQpgmpp2Ek/DPFEZEfST0O\nM5B0uxtENAB2D1NplBAOMIiTTYQAABMhpQsyEEA0FQYAdMUBaaQQDqQrai+RttowAAAtwQRCShpm\nGSvrStkMaegw051IdX5SWSFE5Cgj2Q6hhd3uBhENkF1hvJFCOMChKVQD4UAaLcFE9vNoKoxEuvwb\nK3pCeEZLMFFxkCciIiJnDXSYSqOFcIBnxMkmmXs1FSha5gemSQOEiuwwlWi6GUItPUwlnlIQTavZ\n9YFawwYiwSCA8geGC6FBqAqUwCAE23asohoickpKLoUSaHG7G0Rkk2rPjDdiCAcYxMkuEoAQEErP\nme+mMCCUnpsto0kFQil8s2U8tWUbK4RHTESCKgC1sr4IAaEoEJoKNcyXOJGXiVgEihIqvSER1Y1K\nw3ijhnCAQ1OoxiLBTKC2FJpNhbOjEBER+Ue5w1QaOYQDDOLkgFJhnCGciIjIf0qF8UYP4QCHppBD\nMsHazAZuawXOnscZDOFERET+UWiYSu7jRgzhAIM4OSh/GO/BEE5EROQ/xcI40LghHODQFHJY7jAV\nC0M4ERGRf+UOU7E0cggHGMSJiIiIiFzBIE6Oyr0x01JoNhUiIiKqf7k3ZloqXfTHbxjEyTH5Zkcp\nZ2pDIiIiql/5ZkcZyAqcfsKbNckRxaco7D+bCseLExER1b9SUxRWugKn3/CMONVcqXnCy130h4iI\niOpHqRBe7qI/fsYgTjVV7mI9DONERET+Ue5iPY0exjk0hewhAEgJaaazX4qnFHQlVFgL97SGDYQ1\nE7L/7IUAgLAGyJC1D9DZDUjTQCRYYIdCpAZpmpB6Gkais4piiMgpUo/DDCTd7gYR2ajSFTMLzTPe\nCMNUGMTJFkIAgAlTz7yLTaQDiKbCAAwAQEswgZCShqkXbyekADJg7Qt0xQFppBAOpIvv2IuUzZCG\nDjPdiVTnJ1VUQ0ROMZLtEFrY7W4QkU2qXba+UcM4h6aQ7XpCeEZLMFFRkA4H0mgJJrKfR1NhJNIB\nW/tIRERE9qo2hFsacZgKz4iTLaQEAAVJsxXRtJoZqoLMcJRIMAigsmlQmjRAqMgOU4mmmyHU8oap\nCKFBqAqUwCAE23asrBAiclRKLoUSaHG7G0Q0QAMN4ZZGOzPOIE72kIAJgWgysGWYinVjpgpArarJ\npjAglJ6bPaNJBUIpY2pDISAUBUJToYb5EifyMhGLQFFCbneDiAbArhBuaaQwzqEpZBPR5ybMQrOj\nVIqzqRAREXmX3SHc0ijDVHi6kOxhnQaHfSHckmmLi/4QERF5Sa1CuKXQmfFAwD/3jfGMONnK7hBu\n4ZlxIiIi76h1CLfkOzMej8dtP45bGMTJNkJBTc9SM4wTERG5z6kQbskN452dnVAUf0RYf1RB7pMS\niii92UAxjBMREblH13VHQ7glN4wziBP1IR07EsM4ERGR83RdRzLZsxKuUyHckhvG/YBBnOoSwzgR\nEZGz0umexfmcDuGW5uZmtLW1OX7cWuGsKVS3Cs2mQkRERLXjVgi3RCIRmKY//t4ziFNdyx/GnRsm\nQ0RE1EhCoZAnFtZhECfyiNwwntIFwgbDOBERkZ38NH+3V3CMOPlC7pjxtOFiZ4iIiHxI03j+1m78\njpI9BAApIc10yU1rJawBMqSgXdcAmJB6Ekai07X+EFFpUo/DDCRLb0hE5EMM4mSLzAr3Jkw95mo/\nQgoQUFohTRNmejNSnZ+42h8iKs5ItkNoYbe7QUTkCg5NId9RFROawrEpRERE5G08I062kBIAFCia\n+3dSC6FB0xQogUEItu3odneIqIiUXAol0OJ2N4iIXMEgTvaQAISAUDxwR7UQEIoCoalQw3yJE3mZ\niEWgKCG3u0FE5AoOTSEiIiIicgGDOBERERGRCxjEiYiIiIhcwCBOREREROQCBnEiIiIiIhcwiBMR\nERERuYBzuxVgmibef/99LFiwAAsXLsTChQuxdu1aAMDMmTNx66232nq8TZs24Y9//CPmzJmDVatW\nIRQKYcKECTj99NNx2mmnQVFKv2eyow0iIiIicgaDeAFHHnkkXnzxxbzPbd682dZj/fvf/8ZJJ52E\nNWvW9Pn6kiVL8I9//AN33XUXZs+ejcGDB9e0DSIiIiJyDk+RFmAYBiZNmoQzzzwTd955J15//fWa\nHGf58uWYPn061qxZg2HDhuFPf/oTPv74Y7zzzju49NJLIYTAv/71L5x44omQmeUra9IGERERETmL\nZ8QLeP755xEI9KwSmUgkanKcK6+8Ehs3bkQwGMS8efMwefLk7HO77747Ro0ahR/84Ad48cUX8cAD\nD2DmzJk1aYOIiIiInMUz4gX0DuG1snr1ajzyyCMAgP/5n//pE6Atl1xyCbbbbjsAwG233VaTNoiI\niIjIeTwj7qLZs2dnh4p84xvfyLuNoig47bTTcNNNN+Gtt97CZ599lg3VdrVhCwFASkgzbW+71ZAa\npGlC6mkYiU63e0NERUg9DjOQdLsbRESuYBB30YIFCwBkzr7vu+++Bbc78MADs48XLlzYJ0Tb0YYd\nhAAAE6Yes7XdakjZDF03YKY3I9X5idvdIaIijGQ7hBZ2uxtERK5gEHfRkiVLAABjx45FKBQquN0O\nO+zQbx872/Abw+SIKyIiIvI+BnEXrV+/HgAwatSootv1ft7ax842Stm0aVPB5zo6OgAAmdExChSt\nuaK27RZPKUibGjTNhBIYhGDbjq72h4iKS8mlUAItbneDiMgVDOIuikajAIBIJFJ0u6ampn772NlG\nKUOHDi29kQQgBIRS+5tcC4mngGjSOhuuQGhhqGG+xIm8TMQiUJTCV/OIiPyM1/BdZN1kKTIDrAvq\n/bxpmra34QfxFNAV73k5B1QXO0NERORDuq673QXf4elCFzU3N2PTpk0l5yiPx+PZxy0tfS/h2tFG\nKe3t7QWf6+jowPjx4ytqz265ITyoSagM4kRERLZKp9MM4zZjEHfR0KFDsWrVKnzxxRdFt+v9fO4w\nETvaKGXIkCEVbe+k3BDeGjHRnSx+dYCIiIiqk0wmEYvF0Nzs7j1hiuKPQR3+qKJO7bzzzgCAzz77\nrOhwkWXLlvXbx8426lW+EB4JutghIiKiBtDR0YFYzL3piuPxOIM4Ddxee+0FIPOCWrRoUcHtFi5c\n2G8fO9uoRwzhREREzuq96rhbYTwWi6Gz0z+L9TGIu+j444/PPn7ssccKbmc9t8MOO2DSpEm2t2EP\n54aDMIQTERE5T9O0PmuWOB3GY7FYdtpkv2AQd9Euu+yCQw45BADw29/+FuvWreu3zd///ne88847\nAIBzzjmnJm3YQgiYsjZN98YQTkRE5B5N0zB48ODs506F8dwQ7pcZ4BjEa+jggw/GqFGjio7JvuWW\nWxAMBtHe3o6jjjoKb775JoDMFEGzZs3Ct771LQDAhAkTcMEFF9SsDTtIMxOUa4UhnIiIyH3Nzc2O\nhvHcEN7W1uabIM5ZUwp44IEHcMkllxR87sknn8x+3tzcjE8++aTfdhs2bMC6deuKTi2477774p57\n7sGZZ56JRYsWYZ999kFLSwuSySTS6TSAzPL1c+fORTgcrlkbdskEZfsDMkM4ERGRd1izplgB2frX\n7tlUckP44MGD+4xVr3c8I15Ad3c31q1b1+fDEo/HCz5XjW984xt44403cPrpp6OtrQ3RaBTpdBrb\nbrstfvCDH+Ddd9/FjjsWX6rdjjYGRPaMS+mKK7aeGWcIJyIi8p5anxnPF8LdnjbRbjwjXsDMmTMx\nffr0srYtNIXOK6+8Al3Xy5piZ7fddsODDz4IAOjs7EQwGKz47LUdbVRPQvQq064z4wzhRERE3lWr\nM+ONEMIBBvGCIpEIIpHIgNoYNmxYVfu1tbUN6Lh2tVERASiQaAnp6EpklrXs7AakaSASrG4cVzyl\nbGkrs39r2EBYMyFLNSc1SNOE1NMwEv6Z4ojIj6QehxlIut0NIhoAu8N4o4RwgEGcbCIEAJgIKV2Q\ngQCiqcyZ+K44II0UwoF0Re0l0lYbBgCgJZhASEnDLGNlXSmbIQ0dZroTqc7+Y/eJyDuMZDuE5tSV\nOyKqFbvCeCOFcIBjxKkGwoE0WoI9N6hGU2Ek0uXfWNETwjNagomKgzwRERE5a6BjxhsthAM8I042\nydyrqUDRMj8wTRogVGSHqUTTzRBq6WEq8ZSCaFrNrg/UGjYQCQYBlD8wXAgNQlWgBAYh2FbDG1SJ\naMBScimUQIvb3SAim1R7ZrwRQzjAIE52kQCEgFB6znw3hQGh9NxsGU0qEErhmy3jqS3bWCE8YiIS\nVAGolfVFCAhFgdBUqGG+xIm8TMQiUJRQ6Q2JqG5UGsYbNYQDHJpCNRYJZgK1pdDUhpwdhYiIyD/K\nHabSyCEcYBAnB5QK4wzhRERE/lMqjDd6CAc4NIUckgnWZjZwW/OM9zzOYAgnIiLyj0LDVHIfN2II\nBxjEyUH5w3gPhnAiIiL/KRbGgcYN4QCHppDDcoepWBjCiYiI/Ct3mIqlkUM4wCBOREREROQKBnFy\nVO6NmZZCs6kQERFR/cu9MdNS6aI/fsMgTo7JNztKOVMbEhERUf3KNzvKQFbg9BPerEmOKD5FYf/Z\nVDhenIiIqP6VmqKw0hU4/YZnxKnmSs0TXu6iP0RERFQ/SoXwchf98TMGcaqpchfrYRgnIiLyj3IX\n62n0MM6hKWQPAUBKSDOd/VI8paArocJauKc1bCCsmZD9Zy8EAIQ1QIasfYDObkCaBiLBAjsUIjVI\n04TU0zASnVUUQ0ROkXocZiDpdjeIyEaVrphZaJ7xRhimwiBOthACAEyYeuZdbCIdQDQVBmAAAFqC\nCYSUNEy9eDshBZABa1+gKw5II4VwIF18x16kbIY0dJjpTqQ6P6miGiJyipFsh9DCbneDiGxS7bL1\njRrGOTSFbNcTwjNagomKgnQ4kEZLMJH9PJoKI5EO2NpHIiIisle1IdzSiMNUeEacbCElAChImq2I\nptXMUBVkhqNEgkEAlU2D0qQBQkV2mEo03QyhljdMRQgNQlWgBAYh2LZjZYUQkaNScimUQIvb3SCi\nARpoCLc02plxBnGyhwRMCESTgS3DVKwbM1UAalVNNoUBofTc7BlNKhBKGVMbCgGhKBCaCjXMlziR\nl4lYBIoScrsbRDQAdoVwSyOFcQ5NIZuIPjdhFpodpVKcTYWIiMi77A7hlkYZpsLThWQP6zQ47Avh\nlkxbXPSHiIjIS2oVwi2FzowHAv65b4xnxMlWdodwC8+MExEReUetQ7gl35nxeDxu+3HcwiBOthEK\nanqWmmGciIjIfU6FcEtuGO/s7ISi+CPC+qMKcp+UUETpzQaKYZyIiMg9uq47GsItuWGcQZyoD+nY\nkRjGiYiInKfrOpLJnpVwnQrhltww7gcM4lSXGMaJiIiclU73LM7ndAi3NDc3o62tzfHj1gpnTaG6\nVWg2FSIiIqodt0K4JRKJwDT98feeQZzqWv4w7twwGSIiokYSCoU8sbAOgziRR+SG8ZQuEDYYxomI\niOzkp/m7vYJjxMkXcseMpw0XO0NERORDmsbzt3bjd5TsIQBICWmmS25aK2ENkCEF7boGwITUkzAS\nna71h4hKk3ocZiBZekMiIh9iECdbZFa4N2HqMVf7EVKAgNIKaZow05uR6vzE1f4QUXFGsh1CC7vd\nDSIiV3BoCvmOqpjQFI5NISIiIm/jGXGyhZQAoEDR3L+TWggNmqZACQxCsG1Ht7tDREWk5FIogRa3\nu0FE5AoGcbKHBCAEhOKBO6qFgFAUCE2FGuZLnMjLRCwCRQm53Q0iIldwaAoRERERkQsYxImIiIiI\nXMAgTkRERETkAgZxIiIiIiIXMIgTEREREbmAQZyIiIiIyAUM4kRERERELmAQJyIiIiJyAYM4ERER\nEZELGMSJiIiIiFzAIE5ERERE5ALN7Q6QTwgAUkKaabd7AkgN0jQh9TSMRKfbvSGiIqQehxlIut0N\nIiJXMIiTLYQAABOmHnO7K5CyGbpuwExvRqrzE7e7Q0RFGMl2CC3sdjeIiFzBIE6+Y5gccUVERETe\nxyBOtpASABQoWrOr/YinFKRNDZpmQgkMQrBtR1f7Q0TFpeRSKIEWt7tBROQKBnGyhwQgBIQScK0L\n8RQQTVpnwxUILQw1zJc4kZeJWASKEnK7G0REruA1fPKFeAroive8nAOqi50hIiLyIV3X3e6C7zCI\nU93LDeFBTUJlECciIrJVOp1mGLcZgzjVtdwQ3hoxofJVTUREVBPJZBKxmPszpCmKP/7Y+6MKakj5\nQngk6GKHiIiIGkBHR4erYTwejzOIE7mJIZyIiMhZgUDPhAxuhfFYLIbOTv8s1scgTjYRjh2JIZyI\niMh5mqYhFOqZ5cjpMB6LxdDR0eHY8ZzAIE72EAKmrP1hGMKJiIjco2kaBg8enP3cqTCeG8JN06z5\nMZ3AIE62kWYmKNcKQzgREZH7mpubHQ3juSG8ra3NN0Gcq52QrTJB2f6AzBBORETkHc3NmZW0rYBs\n/Wt93S65IXzw4MF9xqrXO54RJ3vInnEpXXHF1jPjDOFERETeU+sz4/lCuN1B320M4mQTCdHr1WRX\nGGcIJyIi8q5ahfFGCOEAh6aQXQSgQKIlpKMrkVnWsrMbkKaBSLC6cVzxlLKlrcz+rWEDYc2ELNWc\n1CBNE1JPw0j4Z4ojIj+SehxmIOl2N4hoAOweptIoIRxgECebCAEAJkJKF2QggGgqDADoigPSSCEc\nSFfUXiJttWEAAFqCCYSUNMwyVtaVshnS0GGmO5Hq/KSyQojIUUayHUILu90NIhogu8J4I4VwgENT\nqAbCgTRagons59FUGIl0+TdW9ITwjJZgouIgT0RERM4a6DCVRgvhAM+Ik00y92oqULTMD0yTBggV\n2WEq0XQzhFp6mEo8pSCaVrPrA7WGDUSCQQDlDwwXQoNQFSiBQQi27VhFNUTklJRcCiXQ4nY3iMgm\n1Z4Zb8QQDjCIk10kACEglJ4z301hQCg9N1tGkwqEUvhmy3hqyzZWCI+YiARVAGplfRECQlEgNBVq\nmC9xIi8TsQgUJVR6QyKqG5WG8UYN4QCDeFkMw8Bbb72FVatWIRQKYcKECZgwYYItbT/55JNlLdc6\nfvx4HHDAASW3q2Vfq5EJ3WY2jBeaZ5yzoxAREflHuWG8kUM4wCBelJQSd955J37605/i888/7/Pc\nXnvthTvuuKOscFzMlVdeiffee6/kdjNnzix6LCf6Wq1SYZwhnIiIyH9KhfFGD+EAg3hR559/Pu68\n804AwMiRIzFlyhTEYjHMnz8fb731Fg455BA8/vjjOP744wd8rPHjx2P//fcv+PyBBx7omb5Wo1AY\n73mcwRBORETkH4XCeO7jRgzhAIN4QbNmzcoG229/+9u46667EAplxjF+9tlnOPbYY/H+++/jG9/4\nBj766COMHj16QMc7+OCDce+999ZFX6uVP4z3YAgnIiLyn2JhHGjcEA5w+sK8DMPANddcAwCYOHEi\n/vjHP2aDLQBst912eOSRR6AoCmKxGK6//nq3ulpXfQUyYbw10n/mFIZwIiIi/8qd2tDSyCEcYBDP\n65VXXsHy5csBABdeeCECgf5zYE+aNAlHH300AOChhx6Crpex0kwN1FNfiYiIiKgHg3geTz31VPax\nFWDzsZ7btGkTFixYUPN+5VNPfQX635hp6YoriKdc6BARERHVXO6NmZZKF/3xGwbxPBYtWgQAGDJk\nCLbffvuC2+2111799qmWrut466238Pjjj+Pvf/87XnvtNcTjcU/2tVr5ZkfpPUyFYZyIiMh/8s2O\nMpAVOP2EN2vm8cknnwAAtt1226Lb9X7e2qdas2bNwqxZs/p8LRgM4uSTT8ZPfvIT7LDDDp7pazWK\nT1FYep5xIiIiqj+lpiisdAVOv2EQz6OzsxMAMGjQoKLb9X7e2qdaY8eOxfbbb49Ro0Zh06ZN+M9/\n/oPNmzfjgQcewD//+U88/vjjOPLII13p66ZNmwo+V85iRKXmCS930R8iIiKqH6VCeKUrcPoRg3ge\n1uWR3rOP5BMOh/vtU6mLLroIhx9+OMaPH9/n68lkEnfccQd++MMfoqurCyeeeCLee+89jB071vG+\nDh06tKLteyt3sR6GcSIiIv8od7GeRg/jDOJ5WKE2nU4X3S6V6hnQXCoIF3L22WcX7MNll12GIUOG\n4Oyzz0ZXVxduuOEG/Pa3v3Wtr0UJAFJCmj39iKcUdCVUWAv3tIYNhDUTsv/shQCAsAbIkLUP0NkN\nSNNAJFhgh0KkBmmakHoaRmJgVyqIqLakHocZSLrdDSKyUaUrZjZyGGcQz6O1tRUbNmwoeea49/Mt\nLS016ctZZ52FG264AUuXLsU///nPfkHcib62t7cXfK6jowPjx4+HEABgwtQzx0mkA4imwgCMzDGD\nCYSUNMwSMyeGFEAGrH2BrjggjRTCgeJvNHqTshnS0GGmO5HqdH48PBGVz0i2Q2jh0hsSUV2odtn6\nRg3jDOJ5jBkzBp9++ilWr15ddLtVq1ZlH+cOGbGLEAJTpkzB0qVLsXLlSqRSKQSDPeM1nOjrkCFD\nKtq+J4RntAQTFQVpa1urDevfStogIiIiZ1Ubwi2NGMYZxPOYNGkS5s+fj7Vr12LTpk0Fg+iSJUuy\nj3fZZZea9af3UJJ0Ot0niHulr1ICgIKk2YpoWs0MVUFmOEokGARQ2WDvJg0QKrLDVKLpZgi1vGEq\nQmgQqgIlMAjBth0rK4SIHJWSS6EEanNFkYicM9AQbmm0MM4gnsfUqVNx5513QkqJ+fPnY8aMGXm3\ne/HFFwEAgUAABx54YM36Y4Xotra2fi9Ez/RVAiYEosnAlmEq1o2ZKgC1qiabwoBQem72jCYVCKWM\nGziFgFAUCE2FGuZLnMjLRCwCRanBfStE5Bi7QrilkcI4F/TJ49hjj83+z/7DH/6Qd5uOjg48+uij\nAICvfOUrJacPrNabb76J119/HQBw2GGHebivos9NmIVmR6lUJAgu+kNERORRdodwS3Nzc0Ms+sMg\nnkdLSwsuuugiAMDcuXNx33339XneMAycc8456OrqAgBcc801edv55z//ifvvvx+PPPJI3uffe+89\ndHd3F+zHokWLcOKJJ0Jmxn3gsssuq1lfB8w6DQ77QriFYZyIiMh7ahXCLY0QxnndvoAf/vCHeOaZ\nZ/DGG2/gzDPPxNNPP42pU6ciFovhgQcewJtvvgkAuPzyyzFlypS8bfzgBz/Ahx9+iEGDBuHUU0/t\n9/xPf/pT/OMf/8Dhhx+OiRMnYtSoUdhqq63Q3t6OV155Bf/85z+h65lpRq677jocdNBBNeurXewO\n4RbOM05EROQdtQ7hlnzDVGo1U50bGMQLaGpqwlNPPYUzzzwTTz75JB566CE89NBD2ec1TcM111yD\nH/3oR1UfY7fddsPcuXMxZ84czJkzJ+822267LW688Uacfvrprva1HEJBTYMxwzgREZH7nArhltww\n3tnZCUXxx6AOBvEihg0bhn/+85948803MXfuXKxcuRKhUAg77bQTTjrpJIwePbro/scffzzWrFlT\n8MV59dVX4/LLL8err76Kt99+G2vXrsUXX3yBSCSCMWPGYMqUKTjkkEOgqqVvdhxoXwdMSiii9GYD\nxTBORETkHl3XHQ3hltwwziDeQPbee2/svffeFe930003ldwmEAhg6tSpmDp1ahU966/avg6cdOxI\nDONERETO03UdyWQyO62yUyHcYh2r2EKD9cYfbyeo4fAGTiIiImel0z0L6zkdwi3Nzc1oa2tz/Li1\nwjPiVLcKnRknIiKi2nErhFsikQhM0x9/7xnEqa7lD+PODZMhIiJqJKFQyBML6zCIE3lEbhhP6QJh\ng2GciIjIToFAwO0u+A7HiJMv5I4ZTxsudoaIiMiHNI3nb+3G7yjZQwCQEtJMl9y0VsIaIEMK2nUN\ngAmpJ2EkOl3rDxGVJvU4zEDS7W4QEbmCQZxskVnh3oSpu7v0bEgBAkorpGnCTG9GqvMTV/tDRMUZ\nyXYILex2N4iIXMGhKeQ7qmJCUzg2hYiIiLyNZ8TJFlICgAJFc/9OaiE0aJoCJTAIwbYd3e4OERWR\nkkuhBFrc7gYRkSsYxMkeEoAQEIoH7qgWAkJRIDQVapgvcSIvE7EIFCXkdjeIiFzBoSlERERERC5g\nECciIiIicgGDOBERERGRCxjEiYiIiIhcwCBOREREROQCBnEiIiIiIhcwiBMRERERuYBBnIiIiIjI\nBQziREREREQuYBAnIiIiInIBgzgRERERkQs0tztAPiEASAlppt3uCSA1SNOE1NMwEp1u94aIipB6\nHGYg6XY3iIhcwSBOthACAEyYesztrkDKZui6ATO9GanOT9zuDhEVYSTbIbSw290gInIFgzj5jmFy\nxBURERF5H4M42UJKAFCgaM2u9iOeUpA2NWiaCSUwCMG2HV3tDxEVl5JLoQRa3O4GEZErGMTJHhKA\nEBBKwLUuxFNANGmdDVcgtDDUMF/iRF4mYhEoSsjtbhARuYLX8MkX4imgK97zcg6oLnaGiIjIh3Rd\nd7sLvsMgTnUvN4QHNQmVQZyIiMhW6XSaYdxmDOJU13JDeGvEhMpXNRERUU0kk0nEYu7PkKYo/vhj\n748qqCHlC+GRoIsdIiIiagAdHR2uhvF4PM4gTuQmhnAiIiJnBQI9EzK4FcZjsRg6O/2zWB+DONlE\nOHYkhnAiIiLnaZqGUKhnliOnw3gsFkNHR4djx3MCgzjZQwiYsvaHYQgnIiJyj6ZpGDx4cPZzp8J4\nbgg3TbPmx3QCgzjZRpqZoFwrDOFERETua25udjSM54bwtrY23wRxrnZCtsoEZfsDMkM4ERGRdzQ3\nZ1bStgKy9a/1dbvkhvDBgwf3Gate73hGnOwhe8aldMUVW8+MM4QTERF5T63PjOcL4XYHfbcxiJNN\nJESvV5NdYZwhnIiIyLtqFcYbIYQDLg1NSSaT2LBhAxKJBIYPH45Bgwa50Q2ykwAUSLSEdHQlMsta\ndnYD0jQQCVY3jiueUra0ldm/NWwgrJmQpZqTGqRpQuppGAn/THFE5EdSj8MMJN3uBhENgN3DVBol\nhAMOBHEpJV577TW88MILeOmll/DGG2/0m/8xEAhgwoQJOPTQQ3HooYfiK1/5CoYMGVLrrpGNhAAA\nEyGlCzIQQDQVBgB0xQFppBAOpCtqL5G22jAAAC3BBEJKGmYZK+tK2Qxp6DDTnUh1flJZIUTkKCPZ\nDqGF3e4GEQ2QXWG8kUI4UMMgvnHjRtxzzz34/e9/j08+KR6G0uk03n//fbz//vu48847EYlEcNpp\np+G8887DfvvtV6suUo1YodsK49a/5YbxnhCe0RJMVBzkiYiIyFkDDeONFsKBGgTxaDSKG2+8Ebfe\neivi8Xj26+FwGHvuuSd23XVXDB06FFtttRVCoRA2btyI9vZ2rFixAgsWLMC6desQj8dx77334t57\n78Vhhx2G2267DXvssYfdXSUbZe7VVKBomR+YJg0QKrLDVKLpZgi19DCVeEpBNK1m1wdqDRuIBIMA\nyh8YLoQGoSpQAoMQbNuximqIyCkpuRRKoMXtbhCRTaoN440YwgGbg/gDDzyASy+9FJ9//jkAYMyY\nMZg5cyZOOOEE7LnnnggGS4epZcuWYd68ebj//vsxf/58vPjii9h7773xne98B7fffjva2trs7DLZ\nRQIQAkLpmVKoKQwIpedmy2hSgVAK32wZT23ZxgrhERORoApArawvQkAoCoSmQg1zhk4iLxOxCBQl\nVHpDIqoblYbxRg3hgM2zptx22234/PPPcdRRR+H555/HZ599hhtuuAFf/vKXywrhADBu3DicffbZ\neOmll7B8+XL88Ic/RFNTE/785z/jo48+srO75IBIMBOoLYVmU+HsKERERP5R7mwqjRzCAZuD+NSp\nU/HKK6/g2WefxRFHHAFFGVjz2267LX72s59h+fLluPzyyxGJRGzqKTmpVBhnCCciIvKfUmG80UM4\nYPPQlFtuucXO5rK22mor3HjjjTVpm5yRCdZmNnBbK3D2PM5gCCciIvKPQsNUch83YggHuMQ9OSh/\nGO/BEE5EROQ/xcI40LghHODKmuSw3GEqFoZwIiIi/8odpmJp5BAOMIgTEREREbnC0aEpq1atwt13\n342XXnoJS5cuRWdnJwzDKLrPyy+/jD333NOhHlKt5d6YabHGjPOsOBERkf/k3phpqXYFTr9wLIg/\n8MAD+N///V90d3dXtF+poE71I9/sKAD63cDJME5EROQf+WZHAapfgdNPHAni77zzDr71rW/BMAyo\nqopDDjkEu+++O4YMGVJyisNtttnGiS5SjRWforD/bCoM40RERPWv1BSFjR7GHQnid955JwzDwJgx\nY/D0009j0qRJThyWPKLUPOGFpjZkGCciIqpfpUJ4pStw+pEjN2u+//77AIDrrruOIbzBlLtYT7kr\ncBIREZH3lbtYT7krcPqVI2fEW1tbAQATJ0504nDkBgFASkgznf1SPKWgK6HCWrinNWwgrJmQ/Wcv\nBACENUCGrH2Azm5AmgYiwQI7FCI1SNOE1NMwEp1VFENETpF6HGYg6XY3iMhGla6Y2chnxh0J4nvs\nsQeeeuoprF692onDkQuEAAATpp55F5tIBxBNhQFkbrZtCSYQUtIw9eLthBRABqx9ga44II0UwoF0\n8R17kbIZ0tBhpjuR6vykimqIyClGsh1CC7vdDSKySbXL1jdqGHdkaMp5552HUCiEP//5z04cjlzW\nE8IzWoKJioJ0OJBGSzCR/TyaCiORDtjaRyIiIrJXtSHc0ojDVBw5Iz527FjMmjULp512Gr7//e/j\npptuQigUcuLQ5BApAUBB0mxFNK1mhqogMxwlEgwCqOzOyyYNECqyw1Si6WYItbxhKkJoEKoCJTAI\nwbYdKyuEiByVkkuhBFrc7gYRDdBAQ7il0c6MOzaP+EknnYR//etf+L//+z9sv/32mDFjBnbaaSc0\nNTWV3G/48OEO9ZKqJgETAtFkYMswFevGTBWAWlWTTWFAKD03e0aTCoRSxmwqQkAoCoSmQg07umYV\nEVVIxCJQFJ6YIapndoVwSyOFccdSimmaeOONNxCNRvH555/jrrvuKmu/ffbZh0G8Log+N2EWmh2l\nUpzakIiIyLvsDuGWRgnjjgRxKSVOPfVUPPbYY04cjtxgnQaHfSHcwjBOVJ5XPqi/G+JHKp3olhKf\nr/oUr78xz+3ulO3Os45wuwtErqtVCLcUCuOBgH/uG3MkiD/00EPZED5jxgycc845mDx5clkra3Is\neX2xO4RbGMaJiIi8o9Yh3JIvjLe0+Oe+EkeC+N///ncAwNe//nU88MADThySXCAU1DQYM4wTERG5\nz6kQbskN452dnSVP5NYLR6pYu3YtAOA73/mOE4cjN0gJRZTebKC4AicREZF7dF13NIRbcqc2ZBCv\nwOjRowEAkUjEicORK6RjR2IYJyIicp6u60gme1bCdSqEW3LDuB84EsRnzJgBAFiwYIETh6MGwDBO\nRETkrHS6Z3E+p0O4pbm5GW1tbY4ft1YcCeKnnnoqDj30UNx8881YsWKFE4ekBsAwTkRE5Dy3Qrgl\nEonANEsv8FcPHAnimqZh9uzZOOiggzBlyhTce++9iEajThyafC5fGDf88bNJRETkOaFQyBNzefsl\niDsya8rJJ5+MxYsXAwDWr1+PM888E2effTZGjx5dcmXNxx57DJMmTXKim1SncmdTSekCYcO5MetE\nRESNwE/zd3uFI0F8+fLl+PDDD/t8zTAMrFy5suS+8Xi8Vt0iH8kN42nD1e4QERH5jqZpfcaJ08A5\nEsRPOukk7LPPPlXtO2LECJt7U5lEIoFHHnkEc+bMwapVqxAKhTBhwgScfvrpOOywwzx1HKf6mpcA\nICWk6d4PaFgDZEhBu64BMCH1JIxEp2v9IXJaBF1ud6FiGlLQwD/sRNSYHAniV111lROHsd2SJUtw\n0kknYcmSJX2+/uKLL+IPf/gDTjnlFNx3330DnpbRjuM41ddCMivcmzD1WE3aL1dIAQJKK6Rpwkxv\nRqrzE1f7Q+SkoYq7P3/ViIgu6JKrchFRY/LHbOg1sG7dOkybNg1LlixBc3Mzrr/+erz88st4+umn\nMXPmTADAo48+ijPOOMP14zjV13qhKiY0hWNTiIiIyNscOSNejfvuuw+hUAinn366K8e/5pprsHLl\nSqiqiqeeegoHH3xw9rlp06Zh7NixuOGGG/D444/jH//4B44//njXjuNUX4uREgAUKJr7d1ILoUHT\nFCiBQQi27eh2d4gc096+3u0uVGyoAqQQdrsbRESuEFJKT04vMWnSJHz66af44osvHJ8mZ8OGDdh6\n661hGAa+/e1v49577+23TTqdxrbbbovPP/8cBxxwAF599VVXjuNUXwvZtGkThg4dih//6GpoAQ3b\nDHV/OqGNXQLhIDBisMQhk3S3u0PkmFc+WO12Fyo2UlmObtmKz+V4vK7PcLs7ZbvzrCPc7gKRo6z7\nz+LxOEaOHOlqX1KpFD788EP84he/QHt7O4YMGeJqfwbCkTPi119/PZYvX1729qtXr8b7778PAPjs\ns8+wyy671Khn+T3xxBMwjMzQhm9961t5twkEAjj99NPxy1/+Eq+//jrWrl2Lrbfe2vHjONVXIiIi\nIrKXI0F89uzZePPNNyveb/jw4dh+++3t71AJr732GgBAVVVMmTKl4HYHHXQQfvnLX0JKiX//+984\n4YQTHD+OU30lIiIiIns5EsR33nln6HrxIQLJZBIrVqxAd3c3gMzY5l/96lclF/ypBWvmkTFjxhQ9\n/oQJE7KP33///YrDrR3HcaqvRERERGQvR4L4rFmzytpO13U88sgj+O53v4uFCxe6Nmn82rVrAaDk\n8I3Ro0dnH3/++eeuHMeJvm7atKngcx0dHRW1RUREREQZnpo1RdM0fOMb30AoFMLJJ5+M7373u5g/\nf77j/YhGowBQ8mx87+etfZw+jhN9HTp0aEXbExEREVFpnpxH/MQTT8TgwYPx8ssvY8OGDY4f3xpG\no6pq0e16P19q6E2tjuNUX4mIiIjIXp46I24RQmDs2LHo6OjA559/juHDhzt6/JaWFmzevBmJRKLo\ndvF4vM8+bhzHib62t7cXfK6jowPjx4+vqD0iIiIi8mgQB4D16zMLUwwbNszxYw8ZMgSrV6/Gxo0b\ni27XO6AOHjzYleM40dd6np+TiIiIyKs8OTRlyZIlWLduHXbbbTdX5ru2Zhj57LPPUGy9o95zo++0\n006uHMepvhIRERGRvTwXxFesWIEzzzwTkUgEv/3tb13pwx577AEAiMVi2ekB8/nPf/7Tbx+nj+NU\nX4mIiIjIXo4MTbniiivwySefFN1GSokVK1Zg8eLFSCQS2HXXXfGrX/0Kv/rVr/Juf9NNN9VsbPJX\nv/pVXHvttQCAf/zjHwVX9vzHP/4BIDOHdzXh1o7jONVXIiIiIrKXI0F83rx5Fa+suXjxYixevLjg\n81deeWXNgviee+6JvfbaC2+99RZ+/etf47zzzsOgQYP6bPPCCy9kV7U866yzIIRw5ThO9bUkAUBK\nSNOdud/7kBqkaULqaRiJTrd7Q+SYCLrc7kLFNKSgwQO/N4iIXOBIEN97772rmlWkmNbWVlvby3XL\nLbfgyCOPxNq1a3H88cfjL3/5C7bbbjsAmTcWX//61wFkFsq57LLL8rZxwgknYNmyZWhtbcXLL79c\ns+PY0cZAZbK9CVOP1aT9SkjZDF03YKY3I9VZ/EoMkZ8MVdz/+atURHRBl0G3u0FE5ApHgvhdd93l\nxGFsddhhh+H222/HRRddhPnz52OHHXbAuHHjEIvFsqtZDhkyBE8++WTBNwVLlizBhx9+2O8Mtd3H\nsaMNPzFMz936QERERNSPZ6cv9IILL7wQkydPxnXXXYf58+dj6dKlAIDm5maceOKJ+PnPf44xY8Z4\n4jhO9bWQzIQtChStuWbHKEc8pSBtatA0E0pgEIJtO7raHyIntbevd7sLFRuqACmE3e4GEZErGMRL\nmDp1KqZOnYpYLIbVq1cjFAph9OjRCAQCJfedPXs2EolEyVUvB3ocO9uomgQgBITiwLEKiKeAaNI6\nG65AaGGoYb7EqXHEES+9kcfo2Agd7v3eICJyE1NKmZqbmyuef/tLX/qSI8epRRv1Jp4CuuI9Q1IC\npd/7EBERUQV0XXe7C75j62DaNWvW2NlcH9FoFJ2dnAGD+ssN4UFNooyLEERERFSBdDrNMG4zW4P4\n1772NZx22mlFF5apVHd3N26++WaMGzcOH330kW3tkj/khvDWiAmV92oSERHVRDKZRCzm/gxNiuKP\nP/a2VhGJRPDII49g1113xQknnIC///3vSKVSVbW1aNEiXH755Rg3bhwuv/xytLe3IxKJ2NldqnP5\nQniEs6ARERHVVEdHh6thPB6P+yaI2zpGfM6cObjhhhtw2223Yfbs2Zg9ezaGDh2KY489FlOmTMGU\nKVOwyy679AvUhmFg1apVWLhwIRYsWIDnn38e//3vf7PPH3744bjtttswadIkO7tLdYwhnIiIyFm9\nJ3/o6OgAkLkvzUmxWMxXQ5VtDeItLS24/vrrcc455+CnP/0pZs2ahfb2dtx///24//77s9tFIhEM\nHToUoVAI7e3t2Lx5M2Rm/rs+DjzwQFx55ZWYPn26nd2kmqjBap0FMIQTERE5T9M0hEKh7OdOh/FY\nLJY9pl/U5Lz+2LFj8Yc//AFr1qzBr371K+y99959LiHE43GsXr0an376KTo6OvqE8DFjxuD888/H\nokWL8MorrzCE1wshYPZ/L2U7hnAiIiL3aJqGwYMHZz93aphKbgg3TbPmx3RCTacvHDRoEC688EJc\neOGF2Lx5M1555RW8+eabWLduHTZs2IBUKoVhw4Zh+PDhmDBhAg499FDssMMOtewS1ZA0M0G5VsGY\nIZyIiMh91hlwKxjX+sx4bghva2vzzZlxx+YRHzRoEI477jgcd9xxTh2SXJAJyvYHZIZwIiIi73Aq\njOeG8MGDBzuzUKFDuKAP2UNKSCFhpgxsTgG6kkRI2DPXaFJqiJkhAJnLUM1KEmpUR6H5eEwzAj2l\nI9kdw8b2Fbb0gageTHS7A1VQWuKADozpWofdV7zrdnfK9t836qevRHbY2BpHPGAgpUhsXt8zFCUg\nTHSrmbGpGzq7ETMEQtKekc/JXm0DQJMhoLcnkTCNGg2udp5PyiD3SSjo+WGJmSEk5cDf5/WE8Ixm\nGwM+ERERDUxIKmgyeiZs6FYlkmLg47fzhXC7Ar6X8Iw42UMAAhLNShwxGQYAxGQQgImQkq6qyaQZ\nyLQhMj+IzSJRZlsy86HogBav6thE5BBFB4Thdi+IaABCUgGMnuDcrUrAMKsOzo0SwgEGcbKJ2BLE\nw4FuwNQRM5oAADEEAaEjrFS2sFPCDG7Zd8twFLW7/DZMc0sIT0Jpaq/ouETkLBGIQ5r8U0RU7+wK\n440UwgEOTaEaCCspNKvd2c9jRhMSZvl3VibMYDbIAxWGcCIiInLFQIepNFoIB3hGnGwiJSCFgDQy\ndzKHIAGkeoap6C1AGUNLMsNRwtnPm0UCISmz7ZbXGQUwNUAPweweWnEtROQcpakdMDgFEpFfVHtm\nvBFDOMAgTnaRyCyuKdXsl0LCBJDK3mwZkxEASsGbLfPfmGn2abM8IvNhaoAeqXBfInKUqVXxM05E\nXlZpGG/UEA5waArVWEjoaFaS2c8LzabC2VGIiIj8o9xhKo0cwgEGcXJAqTDOEE5EROQ/pcJ4o4dw\ngENTyCEhoQMKeoapmKHs20CGcCIiIn8qNEwl+3iLRgzhAIM4OShvGO+FIZyIiMh/8obxXho1hAMO\nDU058MADEQ6HMXHiRHz00UcV7fPWW2/VuHfkpNxhKhaGcCIiIv/KHaZiaeQQDjgUxJPJJJLJJD74\n4APsv//+eOmll8rexzQHvkwqEREREZHXOPoWJBwOo729HV/5yldwzz33OHlo8ojcGzMthWZTISIi\novqXe2OmpdJFf/zG0SD+wAMPYPLkyUin0zjrrLNw5ZVXQsr+/1PIn/LNjlLO1IZERERUv/LNjjKQ\nFTj9xNEgPnbsWLz66qs47rjjAAA33ngjTjnlFHR3d5fYk+pdoSkKy51nnIiIiOpPoSkKy51n3O8c\nHx3f0tKCJ554AhdeeCEA4LHHHsOhhx6KtWvXOt0VckipecIZxomIiPyn1DzhDOMuLeijqip+9atf\n4be//S1UVcUbb7yB/fbbD//973/d6A7VULmL9TCMExER+Ue5i/U0ehh3Nel897vfxQ477IBTTz0V\nq1atwkEHHYQHH3wQ06dPd7NbVA3rZ0gY2S8lzQBiMgiIzA9is0ggpKQLNhESBgATMRkGgMy+MIvu\nk5/MfCg6oMUr3JeIHKXofX5vEFH9q3TFzEKL/jTCtIaun3KcNm0aXnvtNUyfPh3Lly/HjBk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hj3X0XkEgETPZeTqp3xJFdI6NmFfwCuwElEROQldodwS6MMU2EQJ3sI+0O4hWGciIjIe2oVwi2N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\n"
          }
        }
      ],
      "source": [
        "# visualizing the mode simulation\n",
        "mode_solver = mode_solver_substrate_loss(\n",
        "    resolution=20,\n",
        "    npml=9,\n",
        "    delta_override=None,\n",
        ")\n",
        "\n",
        "mode_solver.plot()\n",
        "\n",
        "plt.show()"
      ],
      "id": "38181cb4"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next, we run the mode simulation to analyze the modes:"
      ],
      "id": "a5ef7025-f07d-440d-bc59-1df1852f0689"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:04:55 UTC </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'mode_2026-07-12_14-04-55'</span> with resource_id           \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'mos-21712121-210e-429a-8c68-e036960319b7'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'MODE'</span>.   \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"9bf02a51b07b4b08ac4a51175717fc16\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:04:57 UTC </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.004</span>. For this solver type, the        \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>estimate is the final billed cost.                                 \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:04:58 UTC </span>status = success                                                   \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"e7658844f1934ffeb88b816ee984ced8\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:04:59 UTC </span>Loading results from simulation_data.hdf5                          \n",
              "</pre>"
            ]
          }
        }
      ],
      "source": [
        "# run the mode simulation\n",
        "mode_sim_data = web.run(mode_solver)\n",
        "mode_data = mode_sim_data.modes"
      ],
      "id": "715881fd"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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jvLw8zZo1S8ccc0xU142Hq6++WhdeeKE+/vhjffvtt1q7dq0qVKigJk2a6JRT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\nZhrMY85QF0430LneQJEmikclk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1oHg//mN7/BxRdfDKCxrGl1dTUA4JVXXsmWq7z33nsx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\nbbk8ClaBAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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33+jXX3/V/v37FRMTo0aNGqlfv37q2bOnVxXqLrnkEkfRkIYNGwZs3LLqz5PK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\nNGlSWflnzJgRTps2LZw2bVq4bt262DzPPvtsmEgki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          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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+Qa0Ydvrpp3sWi2jZsqVj7YarvqrUrVtXl156qd5++20tXLhQK1euVIcOHYK6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\noUMHSdLRo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          }
        }
      ],
      "source": [
        "# plot the fields\n",
        "for i in range(mode_solver.mode_spec.num_modes):\n",
        "    mode_sim_data.plot_field(\"E\", \"abs\", mode_index=i)\n",
        "\n",
        "plt.show()"
      ],
      "id": "6590a4d4"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As one can note, the use of PMLs can lead to non-physical solutions. In\n",
        "this particular case, the physical mode is only the third one. Hence,\n",
        "when dealing with lossy structures, where PMLs are needed, it is\n",
        "important to carefully analyze the fields to exclude the non-physical\n",
        "ones. One way to achieve this is by looking at the effective index,\n",
        "which is approximately 2.4 for the real mode. Hence, we can just look at\n",
        "the mode closest to this value:"
      ],
      "id": "f4bd5097-9a00-41a7-a0d0-bc423c367023"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "mode_data.to_dataframe()"
      ],
      "id": "691577e9"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "In most cases, the effective index is not known beforehand. To\n",
        "automatically filter the correct mode, we will create an auxiliary\n",
        "function that will compares the field energy around a given radius at\n",
        "the center of the simulation plane with the fields outside it, and\n",
        "return `True` if the field energy inside is higher than the energy\n",
        "outside, and `False` otherwise. Also, we will define a function to\n",
        "iterate through the modes and return the first valid mode."
      ],
      "id": "6ac791fd-49ac-430d-935b-e2571551c395"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "# function to decide if a mode is a valid solution\n",
        "def isMode(mode_data, mode_index, radius=1, freq_index=0):\n",
        "    E = abs(mode_data.Ex**2 + mode_data.Ey**2 + mode_data.Ez**2)[0, :, :, freq_index, mode_index]\n",
        "    center = (\n",
        "        E.y.min() + (E.y.max() - E.y.min()) / 2,\n",
        "        E.z.min() + (E.z.max() - E.z.min()) / 2,\n",
        "    )\n",
        "\n",
        "    bmInside = (abs(E.y) < (center[0] + radius)) & (abs(E.z) < (center[1] + radius))\n",
        "\n",
        "    if E.values[bmInside].sum() > E.values[~bmInside].sum():\n",
        "        return True\n",
        "    else:\n",
        "        return False\n",
        "\n",
        "\n",
        "# function to find the first valid mode\n",
        "def findMode(mode_data, radius=1):\n",
        "    for i in range(mode_data.Ex.shape[-1]):\n",
        "        if isMode(mode_data, i, radius):\n",
        "            return i\n",
        "    return None"
      ],
      "id": "36682d48"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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+Qa0Ydvrpp3sWi2jZsqVj7YarvqrUrVtXl156qd5++20tXLhQK1euVIcOHYK6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\nAAAAAElFTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "# testing\n",
        "idx = findMode(mode_data)\n",
        "mode_sim_data.plot_field(\"E\", \"abs\", mode_index=idx)\n",
        "plt.show()"
      ],
      "id": "00411125"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Convergence tests\n",
        "\n",
        "First, we will analyze the convergence of the effective index as a\n",
        "function of the plane size:"
      ],
      "id": "e8bc5746-44e6-4854-b7b6-7726854f7f6b"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"3725c285bf7a4d9e98284621077a2133\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:05:05 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">7</span> tasks.                       \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:05:11 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.034</span> for the whole batch.                \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"f9e262a9e7d24c359d379eca1ec572fb\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:05:14 UTC </span>Batch complete.                                                    \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        }
      ],
      "source": [
        "sizes = np.arange(1, 4.5, 0.5)\n",
        "\n",
        "# create a dictionary with the mode simulation objects\n",
        "mode_solvers = {}\n",
        "for s in sizes:\n",
        "    mode_solver = mode_solver_substrate_loss(\n",
        "        resolution=30,\n",
        "        npml=9,\n",
        "        delta_override=None,\n",
        "        size=(s, s + 1.3),\n",
        "    )\n",
        "    mode_solvers[str(s)] = mode_solver\n",
        "\n",
        "batch_data = web.run(\n",
        "    simulation=mode_solvers,\n",
        "    folder_name=\"radiative_losses\",\n",
        "    path=\"radiative_losses_size_sweep\",\n",
        ")"
      ],
      "id": "43b4b003"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        }
      ],
      "source": [
        "# analyzing the results\n",
        "Real = []\n",
        "Imag = []\n",
        "\n",
        "for sim_data in batch_data.values():\n",
        "    mode_data = sim_data.modes\n",
        "    idx = findMode(mode_data)\n",
        "\n",
        "    Real.append(float(mode_data.n_complex.sel(f=mode_solver.freqs[0], mode_index=idx).real))\n",
        "    Imag.append(float(mode_data.n_complex.sel(f=mode_solver.freqs[0], mode_index=idx).imag))\n",
        "\n",
        "fig, ax = plt.subplots(2, 1)\n",
        "ax[0].plot(sizes, Imag, \"o\")\n",
        "ax[0].set_ylabel(\"k\")\n",
        "ax[0].set_yscale(\"log\")\n",
        "\n",
        "ax[1].plot(sizes, Real, \"o\")\n",
        "ax[1].set_ylabel(\"n\")\n",
        "ax[1].set_xlabel(r\"Size ($\\mu$m)\")\n",
        "\n",
        "plt.show()"
      ],
      "id": "59e2a261"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "It is possible to note that the simulation size makes little difference\n",
        "in the results for the real part of the effective index. However, to\n",
        "achieve precise results for the imaginary part, it is important to\n",
        "fine-tune the mode plane size.\n",
        "\n",
        "Next, we will run a sweep varying the resolution, analyze the behavior\n",
        "of both the real and imaginary parts of the effective index, and compare\n",
        "the results with the most precise values reported in the reference\n",
        "paper."
      ],
      "id": "92f37306-c995-4584-98c0-8d5dab4bd5f4"
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"459b641552b247368da2507495ab31cd\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:05:22 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6</span> tasks.                       \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:05:27 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.273</span> for the whole batch.                \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"4ddc24bae79a46728ea1b3b941ca7324\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:05:30 UTC </span>Batch complete.                                                    \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        }
      ],
      "source": [
        "resolution = [20, 60, 100, 140, 180, 200]\n",
        "mode_solvers = {}\n",
        "for r in resolution:\n",
        "    mode_solver = mode_solver_substrate_loss(\n",
        "        resolution=r, npml=9, delta_override=None, size=(4, 5.3)\n",
        "    )\n",
        "    mode_solvers[str(r)] = mode_solver\n",
        "\n",
        "batch_data = web.run(\n",
        "    simulation=mode_solvers,\n",
        "    folder_name=\"radiative_losses\",\n",
        "    path=\"radiative_losses_resolution_sweep\",\n",
        ")"
      ],
      "id": "fd49342d"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "It is notable that the results converge well toward the most precise\n",
        "values reported in the paper, although high resolution is needed for\n",
        "optimal accuracy."
      ],
      "id": "2f0bdaae-efee-4da2-9043-1e3b4e1e98cc"
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        }
      ],
      "source": [
        "Real = []\n",
        "Imag = []\n",
        "\n",
        "\n",
        "for sim_data in batch_data.values():\n",
        "    mode_data = sim_data.modes\n",
        "    idx = findMode(mode_data)\n",
        "\n",
        "    Real.append(float(mode_data.n_complex.sel(f=mode_solver.freqs[0], mode_index=idx).real))\n",
        "    Imag.append(float(mode_data.n_complex.sel(f=mode_solver.freqs[0], mode_index=idx).imag))\n",
        "\n",
        "\n",
        "fig, ax = plt.subplots(2, 1)\n",
        "ax[0].plot(resolution, Imag, \"o\")\n",
        "ax[0].hlines(2.913e-8, xmin=0, xmax=300, color=\"black\", ls=\"--\", lw=0.4)\n",
        "ax[0].set_xlim(15, 205)\n",
        "ax[0].set_ylabel(\"k\")\n",
        "\n",
        "\n",
        "ax[1].plot(resolution, Real, \"o\")\n",
        "ax[1].hlines(2.41237, xmin=0, xmax=300, color=\"black\", ls=\"--\", lw=0.4)\n",
        "ax[1].set_xlim(15, 205)\n",
        "ax[1].set_ylabel(\"n\")\n",
        "ax[1].set_xlabel(\"resolution\")\n",
        "\n",
        "plt.show()"
      ],
      "id": "36d137f4"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Real part\n",
        "\n",
        "One can note that the imaginary part of the effective index converges\n",
        "better than the real part in the plot shown above. It is worth\n",
        "mentioning that, for calculating the real part, placing a mesh override\n",
        "region around the waveguide improves the convergence speed without\n",
        "requiring a high mesh density across the entire simulation plane.\n",
        "However, in this case, the imaginary part may exhibit greater error."
      ],
      "id": "16e90c4e-aef7-46a0-aaad-9b66dbac1e41"
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"0debee21d7bc4650b317c2bce790b0a3\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:09:55 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">5</span> tasks.                       \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:10:00 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.051</span> for the whole batch.                \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"50905e1e15d5474c95c5bc5e5635a7c5\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:10:02 UTC </span>Batch complete.                                                    \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        }
      ],
      "source": [
        "grid_step = [0.1, 0.05, 0.01, 0.005, 0.002]\n",
        "mode_solvers = {}\n",
        "for dl in grid_step:\n",
        "    mode_solver = mode_solver_substrate_loss(\n",
        "        resolution=20,\n",
        "        npml=9,\n",
        "        delta_override=dl,\n",
        "        size=(4, 5.3),\n",
        "    )\n",
        "    mode_solvers[str(dl)] = mode_solver\n",
        "\n",
        "batch_data = web.run(\n",
        "    simulation=mode_solvers,\n",
        "    folder_name=\"radiative_losses\",\n",
        "    path=\"radiative_losses_grid_step_sweep\",\n",
        ")"
      ],
      "id": "ccb6fb6a"
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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AAAAAlyD0gs8g9AIA17M77Pp2y0pNXBSr4ydP6B8d++je1nepWGhRT7cGAAAA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\nhx6SJD377LP5DtiyY6YXAAC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keB1OPK4jScd1JPHc48OJ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\n586pTJnEb0qLjY1Vz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          }
        }
      ],
      "source": [
        "real = []\n",
        "imag = []\n",
        "\n",
        "for sim_data in batch_data.values():\n",
        "    mode_data = sim_data.modes\n",
        "    idx = findMode(mode_data)\n",
        "\n",
        "    real.append(float(mode_data.n_complex.sel(f=mode_solver.freqs[0], mode_index=idx).real))\n",
        "    imag.append(float(mode_data.n_complex.sel(f=mode_solver.freqs[0], mode_index=idx).imag))\n",
        "\n",
        "fig, ax = plt.subplots(2, 1)\n",
        "ax[0].plot(grid_step, imag, \"-o\", lw=0.4)\n",
        "ax[0].hlines(2.913e-8, xmin=0, xmax=300, color=\"black\", ls=\"--\", lw=0.4)\n",
        "ax[0].set_xlim(0.11, 0.0019)\n",
        "ax[0].set_xscale(\"log\")\n",
        "ax[0].set_ylabel(\"k\")\n",
        "\n",
        "ax[1].plot(grid_step, real, \"-o\", lw=0.4)\n",
        "ax[1].hlines(2.41237, xmin=0, xmax=300, color=\"black\", ls=\"--\", lw=0.4)\n",
        "ax[1].set_xlim(0.11, 0.0019)\n",
        "ax[1].set_xscale(\"log\")\n",
        "ax[1].set_ylabel(\"n\")\n",
        "ax[1].set_xlabel(\"grid step\")\n",
        "\n",
        "plt.show()"
      ],
      "id": "0348ef5b"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Bent SiN waveguide\n",
        "\n",
        "Next, we will study radiative losses in a bent SiN waveguide."
      ],
      "id": "72247175-b722-425e-87a4-d905a7f33a3a"
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [],
      "source": [
        "# function to define the mode simulation\n",
        "def mode_solver_SiN_wvg(\n",
        "    resolution,\n",
        "    npml,\n",
        "    delta_override=None,\n",
        "    size=(20, 15),\n",
        "    nun_modes=10,\n",
        "    target_neff=1.547,\n",
        "    bend_radius=None,\n",
        "    bend_axis=1,\n",
        "    symmetry=(0, 0, 1),\n",
        "    fields=[\"Ex\", \"Ey\", \"Ez\"],\n",
        "):\n",
        "    siN = td.Medium(permittivity=2**2)\n",
        "    sio2 = td.Medium(permittivity=1.444**2)\n",
        "\n",
        "    structures = [td.Structure(geometry=td.Box(size=(100, 0.6, 0.4)), medium=siN)]\n",
        "\n",
        "    mode_spec = td.ModeSpec(\n",
        "        num_modes=nun_modes,\n",
        "        target_neff=target_neff,\n",
        "        precision=\"double\",\n",
        "        bend_radius=bend_radius,\n",
        "        bend_axis=bend_axis,\n",
        "        num_pml=(npml, npml),\n",
        "    )\n",
        "\n",
        "    if delta_override:\n",
        "        mesh_override = [\n",
        "            td.MeshOverrideStructure(\n",
        "                geometry=td.Box(center=(0, 0, 0), size=(0, 2 * 0.6, 2 * 0.22)),\n",
        "                dl=(delta_override,) * 3,\n",
        "            )\n",
        "        ]\n",
        "    else:\n",
        "        mesh_override = []\n",
        "\n",
        "    grid_spec = td.GridSpec.auto(\n",
        "        min_steps_per_wvl=resolution, wavelength=1.55, override_structures=mesh_override\n",
        "    )\n",
        "\n",
        "    sim = td.Simulation(\n",
        "        size=(10, size[0], size[1]),\n",
        "        center=(0, 0, 0),\n",
        "        grid_spec=grid_spec,\n",
        "        structures=structures,\n",
        "        sources=[],\n",
        "        monitors=[],\n",
        "        run_time=1e-12,\n",
        "        boundary_spec=td.BoundarySpec.all_sides(boundary=td.PML()),\n",
        "        symmetry=symmetry,\n",
        "        medium=sio2,\n",
        "    )\n",
        "\n",
        "    plane = td.Box(center=(0, 0, 0), size=(0, size[0], size[1]))\n",
        "\n",
        "    mode_solver = td.ModeSimulation.from_simulation(\n",
        "        simulation=sim,\n",
        "        plane=plane,\n",
        "        mode_spec=mode_spec,\n",
        "        freqs=[td.C_0 / 1.55],\n",
        "        fields=fields,\n",
        "    )\n",
        "\n",
        "    return mode_solver"
      ],
      "id": "cbf2c1c9"
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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G6Oqrr9Y//vEPPfzww/rK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p110JWrP/FugZEkW4o1t8iMxgvuXyYzGlesyXJjna/ReP70vxCneHZnDtnSlrrSZVapDMQTTzzx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\n8id/8id/V63zb/bxb72gyIa6VO0OxjVSO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          }
        }
      ],
      "source": [
        "# visualizing the mode simulation\n",
        "ms = mode_solver_SiN_wvg(10, 12)\n",
        "ms.plot()\n",
        "plt.show()"
      ],
      "id": "e8cf8965"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Plane Size\n",
        "\n",
        "Due to the relatively low index contrast between core and clad, the\n",
        "evanescent fields are long, so it is necessary to carefully define the\n",
        "simulation size. Evanescent fields in the [PML can lead to artificial\n",
        "gain](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.PML.html)\n",
        "and yield inaccurate results. This issue becomes more significant for\n",
        "larger bend radii, as the losses are smaller.\n",
        "\n",
        "To study this issue, we will test the plane size for several bend radii\n",
        "and choose the minimum value that yields positive results, meaning that\n",
        "the PML error contribution becomes smaller than the physical losses."
      ],
      "id": "1d1d0198-7abb-405a-ab6f-775153621d2a"
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:11:10 UTC </span><span style=\"color: #800000; text-decoration-color: #800000\">WARNING: </span><span style=\"color: #008000; text-decoration-color: #008000\">'ModeSolver'</span><span style=\"color: #800000; text-decoration-color: #800000\">: The mode solver pml in tangential axis </span><span style=\"color: #008000; text-decoration-color: #008000\">'0'</span><span style=\"color: #800000; text-decoration-color: #800000\">  </span>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #800000; text-decoration-color: #800000\">covers more than </span><span style=\"color: #008000; text-decoration-color: #008000\">'50%'</span><span style=\"color: #800000; text-decoration-color: #800000\"> of the mode plane cells. Consider using a   </span>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #800000; text-decoration-color: #800000\">larger mode plane or smaller </span><span style=\"color: #008000; text-decoration-color: #008000\">'num_pml'</span><span style=\"color: #800000; text-decoration-color: #800000\">.                            </span>\n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #800000; text-decoration-color: #800000\">WARNING: </span><span style=\"color: #008000; text-decoration-color: #008000\">'ModeSolver'</span><span style=\"color: #800000; text-decoration-color: #800000\">: The mode solver pml in tangential axis </span><span style=\"color: #008000; text-decoration-color: #008000\">'1'</span><span style=\"color: #800000; text-decoration-color: #800000\">  </span>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #800000; text-decoration-color: #800000\">covers more than </span><span style=\"color: #008000; text-decoration-color: #008000\">'50%'</span><span style=\"color: #800000; text-decoration-color: #800000\"> of the mode plane cells. Consider using a   </span>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #800000; text-decoration-color: #800000\">larger mode plane or smaller </span><span style=\"color: #008000; text-decoration-color: #008000\">'num_pml'</span><span style=\"color: #800000; text-decoration-color: #800000\">.                            </span>\n",
              "</pre>"
            ]
          }
        }
      ],
      "source": [
        "td.config.logging.warn_once = True\n",
        "\n",
        "radius = np.arange(20, 130, 20)\n",
        "sizes = []\n",
        "loss = []\n",
        "\n",
        "for r in radius:\n",
        "    l = -1\n",
        "    size = 1\n",
        "    while l < 0:\n",
        "        size += 2\n",
        "        mode_solver = mode_solver_SiN_wvg(\n",
        "            resolution=10,\n",
        "            npml=12,\n",
        "            nun_modes=5,\n",
        "            bend_radius=r,\n",
        "            bend_axis=1,\n",
        "            size=(size, size),\n",
        "        )\n",
        "\n",
        "        mode_data = web.run(mode_solver, verbose=False).modes\n",
        "\n",
        "        idx = findMode(mode_data, 0.4)\n",
        "\n",
        "        l = mode_data.to_dataframe().iloc[idx][\"loss (dB/cm)\"]\n",
        "\n",
        "    loss.append(l)\n",
        "    sizes.append(size)"
      ],
      "id": "9686b890"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As we can see, the plane size needed for physical results increases\n",
        "approximately linearly with the bend radius.\n",
        "\n",
        "For simplicity, we conducted the tests with the same size for the y and\n",
        "z dimensions. However, since the bend is in the y dimension, the size in\n",
        "the z dimension can be smaller."
      ],
      "id": "87839e9f-9c9e-444f-894c-c4a7927baf5e"
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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uadbW79M8VjxfYY1o1VsdajaXm6sh/6oHIBtwMTrAv+rUqaMNGzao\nT58+unTpknLlymV0JAAAAABwKE+WrKinyltu/1E0b0FN7PGOdn70vTrXaUWJBMCmTGaz2Wx0iPvF\nxMSoWLFiSkxM1JUrV+Tt7W10JIcSFhYmf39/SVJoaKj8/PwMTgQAAADA2mLiY5XDwyvNY4fPB6vl\nuD4q7Jdfw1q+rM51WsnDzd3OCQE4C2v3CA5zR9K/cuTIoWbNmik8PFybN282Og4AAAAA2E14VITG\n/TpTVUc/p/O3Lqc5p1qJ8lrw2njt/vhH9WjQjhIJgF055D2P+fPnlyRduHDB2CAAAAAAYAcRMZGa\nuWWZZm5ZpoiYSEnSxLVzNfWl99Oc36xSA3vGA4AUNi+SgoODZTab9fjjj8vVNWNvDLh27ZokycfH\nx5bRAAAAAMBQkbFRmr31B32zeYnuRt+zOPbTvvUa2qKXShcoblA6AEjN5kXSwoULNW7cOOXIkUOV\nKlVS1apVVa1aNVWrVk0VK1aUh4eHxfyrV69q9erVcnFxUZMmTWwdDwAAAADsLio2WnO2Ldf0TYsU\nFhWR5pw83rl1PuQKRRIAh2K3R9tiYmK0b98+7du3L2XM3d1d5cuXV9WqVVWmTBndvn1bixcvVkxM\njD7//HMFBQXZKx4AAAAA2Fx0fKzmbftJ0zYuVGhkeJpz/Lxz67WmL6p3447y9spp34AA8B9s/ta2\nu3fv6tChQzpy5IiOHj2qo0eP6uTJk0pMTEz3nHz58qlp06aqWLGiKlWqpEqVKqlo0aK2jOk0eGsb\nAAAA4Hxi4mO1YPvPmrZxoUIiQtOc45szl159ppv6PNVJuXLw9moA1mHtHsHmRVJaYmNj9ddff+no\n0aMpBdOxY8cUGRmZ7jl+fn6qWLGiKlasqF69eqlGjRp2TOw4KJIAAAAA5xJ85Yy6TR2um3dvp3k8\nl5e3BjzTVf2bdFHuHOwTC8C6rN0jGPLWNi8vLz355JN68sknU8bMZrPOnDljUS4dOXJEN2/elPTP\nD759+3Zt375dRYoUybZFEgAAAADnUip/MZlkSjXu45VT/Z7uogFNuiiPd24DkgFA5hlSJKXFZDKp\nbNmyKlu2rDp16pQyfvPmTR05csTi0biMvv0NAAAAAIzm5e6poc/20lvLvpQk5fTMob5PddIrz3ST\nv4+vwekAIHMMebQND49H2wAAAADHk5CUqJ8PbNRz1ZvIy90z1fG4hHg9M6aHmlVqoFebdle+XPwe\nD8A+HPbRtps3byp//vzWWs6C2WxWSEiIAgMDbbI+AAAAADyMxKRE/bR/gyaumaOLt68qIiZSfZ/q\nlGqep7uHfntvsdxcHeahEAB4KC7WWmjSpEmqXbu2Nm3aZK0lJUkrV65U1apVNWfOHKuuCwAAAAAP\nKyk5ST/tW6+GH3XV0Pmf6OLtq5Kkr9bNV0x8bJrnUCIByAqsViTlzJlT+/btU7NmzVS7dm3NnDlT\n4eHhD7VWSEiIpk6dqipVqqhdu3b6448/lDNnTmtFBQAAAICHkpycrF8ObFLjj7tp4NwPde7WZYvj\ntyLuaMH2nw1KBwC2Z7U9kpKTkzV//ny98847un79uiTJ09NTzZs3V/369VWrVi1VrVpVuXLlSnVu\neHi4Dh8+rL1792rnzp3atGmTEhMTJUlBQUEaO3asunTpYo2YTo89kgAAAAD7S05O1poj2/Tlmtk6\nde1cmnPcXFzVrd5zGvJsLxXxL2DnhACQNmv3CFbfbDsqKkoTJkzQN998oxs3bqQ67uXlJX9/f+XK\nlUsRERG6c+eO4uPjU80rXry4Bg0apMGDB8vTM/VmddkVRRIAAABgP2azWeuO/q4vV8/W8at/pznH\n1cVVXeq00tBnX1KxfIXsnBAAHszhi6R/JSQk6Oeff9bs2bO1fft2xcXF/ec5Pj4+evrpp9WvXz+1\nbNlSLi5We/Iuy6BIAgAAAGzPbDZr0587NX7VLP15+XSac1xMLnqh9rMa3vJlBQUUsXNCAMgYpymS\n7hcbG6t9+/Zpz549unr1qkJCQhQREaE8efIoICBARYsWVf369fXkk0/KzY0N6B6EIgkAAACwvYu3\nr6nu+y8oKTkp1TEXk4va12yuES1fVsn8xQxIBwAZZ+0ewS6tjZeXlxo1aqRGjRrZ43IAAAAA8EiK\n5yukjrVa6Ps9a1LGTCaT2j3ZVCNa9VaZAkHGhQMAA3H7DwAAAACkYUTL3lq+b72SkpP0XPUmGtGq\nj8oVKml0LAAwVLYvkhITExUeHi7pnzunfHx8HnqthIQE3b17N+Wzv78/+zwBAAAADmr36cP6YtUs\nvfv8a3qyZMVUx4sHFNbYLiP1ZMkKeqJIGQMSAoDjyXYtx8WLF7Vs2TINHz5c9erVU+7cuRUQEKCA\ngAANGzbskdYeMGBAyloBAQG6dOmSdUIDAAAAsJp9fx9Vh0kD1X7ia9p75ojGr5qV7tyeDZ+nRAKA\n+2S7O5K6d++uXbt2pXx2dXW1yrobN27U3LlzrbIWAAAAAOs7eO5PjV81S7+f2G8x/vuJ/dp75qhq\nl6liTDAAcCLZrkgKCgpSkSJFVLNmTdWsWVPly5dP2b38Yd27d0/9+vWTJJUvX17BwcHWiAoAAADA\nCg6fD9b41bP0W/DedOdsDd5DkQQAGZDtiqRFixZZfI6NjX3kNd944w1dunRJbdu2Vbly5SiSAAAA\nAAdw7NJJjV81S5v+3JXunIblamhUm36qUaqSHZMBgPPKdkWStW3btk0zZsxQrly5NG3aNE2bNs3o\nSAAAAEC29tfl0/py9Wyt/2N7unPqlq2mUW36qU6ZqnZMBgDOjyLpEURHR6tPnz4ym80aM2aMihQp\nYnQkAAAAINu6G31PIxZ+pjVHfkt3Tq3SlTWqTX/Vf6y6HZMBQNZBkfQI3nrrLZ07d041a9bUwIED\njY4DAAAAZGu5vLx19mbab05+smRFvdGmnxqUqyGTyWTnZACQdbgYHcBZ7dq1S9OmTZObm5tmzpwp\nFxf+owQAAACM5OLiolFt+lqMVQ16QksGT9KqUTPV8PGalEgA8IgMuSMpIiJCV69eVUREhIoWLapC\nhQoZEeOhxcbGqnfv3kpOTtbIkSNVuXJlq64fFhaW7rHw8HCrXgsAAABwNudvXZaft6/yeOdOdezZ\nyo1UoWhZuZhMGtWmv56pUJfyCACsyK630fzwww+qXbu2/Pz89MQTT6h27dpasGCBxZx169apS5cu\nWrhwoT2jZcr777+v06dPq0SJEvrggw+svr6/v3+6XyVLlrT69QAAAABncDHkqoYt+FT1P+yibzYt\nTnOOi4uLlg6epA1vzVPTivUokQDAyuxyR1JycrJeeumlDJVDgYGB+v7773XhwgX16NHDDuky58CB\nA5o4caIk6ZtvvlHOnDkNTgQAAABkbZfvXNfktXP1/Z41SkxOkiTN+u0H9X+mq/L65Ek1PyB3Xjsn\nBIDswy53JH3yyScpJVLHjh31448/6sUXX0xzbrVq1ZQ/f34dPHjwgY94GSE+Pl4vv/yykpKS1K1b\nNzVv3twm1wkNDU3369y5cza5JgAAAOBorobe1BtLxqnu+y9o8a5fU0okSYqOi9H0jYsMTAcA2ZPN\n70gKCwvT+PHjJUlTpkzRkCFDJEkHDx5Mc77JZFLFihW1efNmHTp0SM8884ytI2bY4sWLFRwcLB8f\nH73zzju6fft2qjkxMTEp34eFhcnHx0cuLi7y9/fP8HX8/PyskhcAAABwRtfDbumr9Qu0eNdKxScm\npDmnVP5iqlL8CTsnAwDYvEjasmWLoqKiVL169ZQSSdIDn1XOnz+/JOn8+fO2jpcpUVFRkqTIyEiV\nL1/+P+dXq1ZNkpQ3b940SycAAAAA/+fW3TuaumGBFmz/WXGJ8WnOCQoootdb9dHzNZrKzdWQdwcB\nQLZm83/ynjlzRpIydWdRYGCgpH/e7uZIcuTIobx5H/y8dXR0dMpdSX5+fnJxcfnPcwAAAIDsLCQi\nVNM2LtSC31coJiEuzTnF8hXSiJa91bFWCwokADCQzf8JHBsbK0ny9va2GH/QHUnR0dGS/iluHEmf\nPn3Up0+fB84ZPXq0xo0bJ0k6fPiwgoKC7JAMAAAAcE7xiQl6+tMXFRIRmubxwv4FNKLly+pUp5Xc\nKZAAwHA2/ydxQECAJOnixYsZPufo0aOSpIIFC9oiEgAAAAAH4eHmrq512+ir9fMtxgv5BWrosy+p\na9028nBzNygdAOB/2bxIqlmzpiRpzZo1iouLk6enp6T070j6448/tH//fklS3bp1rZ4nLi5O9+7d\ns/h8//f372VkMpl4LA0AAACwsVee6aY5235UZGy0CvgGaMizvdS93nPydPcwOhoA4H/YvEh68skn\nVbZsWZ0+fVpDhgzRt99+m26JdP36dXXr1k1ms1ktWrRI2XTbmhYuXKh+/fqleWzRokVatOj/XiHq\n7e2tyMhIq2cAAAAAspOImEjN2vq9KhUrp6YV66U67u/jq1Gt+8nF5KIXG7RVDg8vA1ICADLC5kWS\ni4uLvvzyS7Vt21YzZ87UiRMnNHDgQIWEhEiS7t27p/3792v9+vX66quvdOfOHXl6euqzzz6zSR4v\nL68M32Xk4+OT6fW9vb1T1nd1dc30+QAAAEBWERkbpdlbf9C3m5cqPDpCTxQurSbl68jFxSXV3AHP\ndDUgIQAgs0xms9lsjwtNnjxZr7/+upKTkx84z8PDQ/Pnz1eXLl3sEcvphIWFyd/fX5IUGhoqPz8/\ngxMBAAAAlqJiozXn9+X6ZuNihUbdtTg2q99nalP9aYOSAUD2Y+0eIfVfBdjIsGHDtHXrVtWrl/pW\n1n/Vr19fO3bsoEQCAAAAnFB0fKymb1ysmu910Jifp6cqkSTpu99+MCAZAMBa7Pr+zEaNGmnnzp26\ndOmS9u7dq5s3byo5OVmBgYGqU6eOgoKC7BkHAAAAgBXExMdq4Y5fNHXDAoVEhKY5J3cOH73yTDf1\ne7qzndMBAKzJrkXSv4oVK6ZixYoZcWkAAAAAVhKbEKdFO1dq6voFunn3dppzcnl5q3+TLurfpIt8\nc+ayc0IAgLXZvEiKjY1VbGys3NzcMrx59b/n5MiRQ56enjZOCAAAACAzzGaz5m9foSnr5ul6eEia\nc7w9c6rf05004Jmu8vP2tXNCAICt2HyPpA8//FB+fn7y8/PTrFmzMnXOpEmTbJwOAAAAQGaZTCat\nPbItzRIph4eXBjfvqf1jVmh021cokQAgi7Hbo22JiYnq37+/Tp06pS+++CLNV34CAAAAcA6j2vTT\n9pMHUj7ncPfUS4076rWm3RWQ29/AZAAAW7Jbm5MnTx5J0oQJE9S+fXtFRUXZ69IAAAAAHkJiUqIi\nYiLTPFajVCU99URtebl7qv/TXbTv0xX6oMNgSiQAyOLsdkfSqFGjFBoaqgkTJmjlypVq0KCBVq1a\npcKFC9srAgAAAIAMSEpO0sqDmzVhzXeqUaqSJvd8N815n3V5XTk8vFQgT4CdEwIAjGK3O5JcXFz0\n5ZdfasaMGXJzc9ORI0dUs2ZNHT582F4RAAAAADxAcnKyfjm4SY0/7q7X5nygszcv6ce963Tu5qU0\n55cILEqJBADZjN03Kurfv7/Wr1+vPHny6Nq1a2rYsKF++eUXe8cAAAAA8P8lJydr9eGtevrTHnpl\n9ns6c+NCyrGk5CRNXDvXuHAAAIdiyI7XTZo00Z49e1SyZElFRUWpQ4cO+vLLL42IAgAAAGRbZrNZ\n647+rqaf9VLfmW/r5LWzqea4urjKy91DZrPZgIQAAEdjtz2S/le5cuW0b98+Pf/889q5c6dGjRql\nU6dOafr06UZFAgAAALIFs9msTX/u1JerZ+vYpVNpznExuahjrRYa0aq3ggKK2DkhAMBRGVYkSVK+\nfPm0efNm9e3bV4sWLdLs2bN1/vx5lS5d2shYAAAAQJZkNpu1NXiPvlg1S39cPJHmHJPJpA41m2t4\ny94qlb+YnRMCABydoUWSJHl6emrhwoUqW7asPvjgA23ZskVbtmwxOhYAAACQ5fSZMVprj/6e5jGT\nyaS21Z/RiFa9VbZgCTsnAwA4C0P2SErLe++9pyVLlsjLy8voKAAAAECWVLdstTTH21Rrot/eW6xv\n+35CiQQAeCCb35H07LPPKk+ePGrcuPF/zu3SpYuCgoI0YsQIxcfHq2DBgraOBwAAAGQbLzZop2kb\nFunG3RBJUssqjTSydV89UaSMwckAAM7CZOb1C04lLCxM/v7+kqTQ0FD5+fkZnAgAAACOZP/ffyg8\n+p6aVaqf5vG525Zr2/F9Gtm6ryoWe8zO6QAA9mbtHsHwPZIAAAAAPLpD5/7S+NWztO34PhXME6CG\nj9eQl7tnqnkvNeqglxt3NCAhACAroEgCAAAAnNjRiyc0ftUsbflrd8rY9fAQLdq5Un2f6pRqvslk\nsmc8AEAWY7Ui6ZdfftH69eslSc8//7yaN2+eajyz7l8HAAAAwP/589IpjV89SxuP7Uzz+NT1C9Sj\nfjt5unvYORkAICuzWpG0d+9ezZgxQ5IUFBSUUgDdP55Z968DAAAAQDp+5Yy+XD1ba4/+nu6c2mWq\n6o02/SiRAABWZ7UiqUCBAipfvrwkKSAgIM3xzLp/HQAAACA7O3H1rCas+U6rD29Nd07NUpX0Rpv+\nqvdYdR5hAwDYBG9tczK8tQ0AACB7OX39vCaumaOVhzYrvV/dq5eooDfa9FPDx2tSIAEALPDWNgAA\nACAb+Wr9fP1ycFOax6oUf0Kj2vTV0+XrUCABAOyCIgkAAABwYCNa9tbPBzYpKTkpZaxi0bIa1aa/\nmlasR4EEALArhyiSLl++rHXr1ikyMlLVqlVT48aNjY4EAAAA2FVycrJcXFxSjZfMX0wdajbXD3vX\nqnyRMhrVup+aV25AgQQAMIRdiqSJEydq+/btev3119WgQQOLYytWrFC3bt0UFxeXMvbcc8/pxx9/\nlIcHb5kAAABA1nYl9IamrJunkIhQzXv1izTnvN6qj5pVqq+WVRqnWTYBAGAvNt9sOzExUQULFtTd\nu3d148aNlA2eJOnOnTsqUaKE7t27l+q8t956S5999pktozklNtsGAADIGq6F3dJX6+dr8c6VSkhK\nlCSteWO2qpesYHAyAEBW4nSbbe/cuVO3b99WkyZNLEokSZo3b57u3bsnd3d3LV26VI0aNdKUKVP0\n6aefaurUqXrvvfeUI0cOW0cEAAAAMsVsNmvX6cNatnu1LoRcUWRstHy8cioooIi61m2tumWrpfvo\n2c27t/XV+vlatGOl4hLjLY6NXz1Ly4ZMscePAADAQ7F5kXT+/HlJUsmSJVMdW716tSSpU6dO6tCh\ngyTp448/1uLFi3X+/Hnt3btXTz31lK0jAgAAABliNpu1eOdKzdiyTGduXEh1/OC5P7V83zqVKRCk\nAU26qHv9timFUkjEHU3bsFDzt/+s2IS4VOdK0oWQqwqLuis/b19b/hgAADw0mxdJ165dkyQVKlTI\nYjwhIUH79u2TJLVu3Tpl3GQyqUGDBjp//rzOnDlDkQQAAACHkJCUqBELP9OPe9f+59wzNy5o5OLP\nte/sMb3d7lXN2rJMc7ctV0w6BVLRvAU1olUfdazVQu6uDvE+HAAA0mTzP6Xi4/+5XTc2NtZi/ODB\ng4qJiZEk1a9f3+JY3rx5JSnNvZMAAAAAezObzRkuke734961WrF/g5KSk9I8Xti/gIY/+5I61Wkl\nDzd3a0QFAMCmbF4kBQYGSpJOnz5tMb5hwwZJUlBQkIoUKWJxLCwsTJJS7akEAAAAGGHxzpWZLpH+\nlVaJVDBPgIY++5K61m0jT3feVAwAcB42L5Jq1KghSVq7dq1OnDihxx9/XHfv3tV3330nSWratGmq\nc65fvy4p9eNwAAAAgL2ZzWbN2LLUKmvl982nIS16qXv95+Tl7mmVNQEAsCebF0k1a9ZUhQoV9Ndf\nf6lWrVqqV6+e/vrrL125ckWS1Lt371TnnDhxQpJUoQKvPgUAAICxdp0+rDM3Lj7yOi836qD3OwxW\nDg8vK6QCAMAYLva4yPz58+Xr66t79+5p/fr1KSXS0KFDVbt2bYu5x48f16VLl1ShQgUVLlzYHvEA\nAACAdC3bvdoq60TGxVAiAQCcnl1eCVGtWjUFBwdrxowZOnHihAICAtSqVSu1atUq1dzg4GBVr15d\nnTt3tkc0AAAA4IEuhFyxzjq3LltlHQAAjGS3d4sWLlxYH3/88X/Oe+GFF/TCCy/YIREAAADw3yJj\no62zTpx11gEAwEh2ebQNAAAAcFY5Pa3zOJqPZ06rrAMAgJHsdkcSAAAA4EziEuK1eNevOn7lb6us\nFxRY1CrrAABgJIokAAAA4D7xiQlatnu1pqybp6thN622bpc6qfcHBQDA2VAkAQAAAJISkhL14961\nmrhmjq6E3rDq2mUKBKlu2WpWXRMAACNQJAEAAACSpm1YoHG/zkzzmJurmxKTEh967QFNushkMj30\n+QAAOAo22wYAAAAk9WjwvHJ65rAY83TzUL+nO+vgmJ/1Qu2WD7Vup9ot1b1+W2tEBADAcNyRBAAA\nAEjKl8tPfRq/oKkbFsjDzV0v1m+rwc17qqBfoCRpYo+3JUk/7l2b4TU71W6pCT3e5m4kAECWQZEE\nAACAbCE5OVmrDm/VuqO/65s+H6dZ7rzatLui4qI1sFkPFfbPb3HM3dVNX/V6T7VKVdKMLct05saF\ndK9VpkCQBjTpou7121IiAQCyFJPZbDYbHQIZFxYWJn9/f0lSaGio/Pz8DE4EAADg2JKTk7X26DZ9\nufo7nbx2VpI095VxerZKo4de02w2a/fpw1q2Z40u3LqsyLho+XjmVFBgUXWt21p1ylSlQAIAOARr\n9wiG3pGUlJQkFxcX/pAFAACA1ZnNZm34Y4fGr56l4CtnLI59uXq2mldqIBeXh9sy1GQyqd5j1VXv\nserWiAoAgNOw62bbp06d0qBBg/T444/L29tbbm5uGjdunMWc/fv368svv9SOHTvsGQ0AAABZhNls\n1sZjO9V87Et66ds3UpVIknTi6ln9cemkAekAAHBudrsjacqUKRo5cqQSEx/82tTIyEiNGjVKTZs2\n1caNG+2UDgAAAM7ObDbrt+N79cWvs3T04vE055hMJj3/ZFONaNVHpQsUt3NCAACcn12KpMWLF2vY\nsGGSpNKlS6tDhw46dOiQNm/enGpugwYNlCtXLu3YsUOxsbHy8vKyR0QAAAA4KbPZrO0n9mv86tk6\neO7PdOe1ffIZjWjZR48VKmHHdAAAZC02f7QtNjZWI0eOlCT17t1bJ06c0Oeff67q1dN+ntzd3V3V\nqlVTbGysDh48aOt4AAAAcGJHL55QuwmvqPNXQ9MtkVpVfUq/vbdIM/p+SokEAMAjsvkdSb///rtu\n3LihEiVK6Ntvv5Wb2z+XfNAG2/nz//Oq1b///lv169e3dUQAAAA4qZj4WO37+480j7Wo3FAjW/dV\nhaJl7ZwKAICsy+ZF0rFjxyRJbdq0kbu7e4bOKVCggKR/XlEHAAAApKdOmapqUO5J7Tj5f3eyN61Y\nTyNb91Pl4uUMTAYAQNZk8yIpIiJCkhQQEGAx/qA7kpKSkiRJrq6utgsGAAAAp3H5znUVzVswzWOj\nWvfTjpMH9VT52hrVup+qlShv53QAAGQfNi+S/Pz8JEm3bt3K8DmnTp2SlLp8AgAAQPbyx8WTGr96\nlrYF79Wuj39U8XyFUs2pWbqytr2/ROUKlTQgIQAA2YvNN9uuVKmSJGnjxo0W4+ndkXT9+nVt375d\nklSzZk3bhgMAAIBD+vPSKfWaPkrNx76kzX/uUmJykiavnZvufEokAADsw+ZFUoMGDZQvXz6dOnVK\nU6dOfeDc+Ph49enTR/Hx8apSpYpKlSpl63gAAABwICeu/q0+M0ar6We9tOHYDotjP+xdq/O3LhuU\nDAAASHYokjw9PfXee+9JkoYOHaphw4bp7NmzFnPi4+O1du1a1atXT+vWrZMkffLJJ7aOBgAAAAdx\n8to59Zv5jp765EWtObItzTlVg55QdHysfYMBAAALJrPZbLbHhXr27KmFCxemfHZxcVFycrJy586t\n6OhoJSYmphx7++23NWbMGHvEcjphYWHy9/eXJIWGhqbsQQUAAOCMzty4oIlr5uiXg5uU3q+lVYOe\n0Btt+qvxE7Ue+MIWAACQmrV7BJtvtv2v+fPnq1q1avrkk08UGhqq5ORkSf/3VjdJypcvn8aOHau+\nffvaKxYAAAAMcO7mJU1cO0cr9m9Usjk5zTmVipXTG236q0mFOhRIAAA4CLvdkfSvqKgobdiwQXv3\n7tXNmzeVnJyswMBA1alTR88++6y8vb3tGcfpcEcSAABwdluD96jH1yOVlJyU5vEKRctqVOu+alap\nAQUSAACPyNo9gt2LJDwaiiQAAODsouNjVevd9gqJCLUYf7xwKY1q3U8tKjeUi4vNt/IEACBbsHaP\nwJ/QAAAAsKucHl4a0rxXyueyBUtoZr8x2vLOQrWs2pgSCQAAB2a3PZIAAACQfVwPu6W5v/+kka37\nysPNPdXxFxu01YZjO/Ri/bZqU/1pubq4GpASAABkll2LpCNHjmjVqlUKDg5WWFiY4uPjHzi/f//+\n6tatm53SAQAA4FHdvHtbU9cv0MIdvyguMV6F/fOrV8P2qebl8PDS8uHTDEgIAAAehV2KpIiICPXs\n2VMrV67M1HktWrSwUSIAAABYU0jEHU3bsFDzt/+s2IS4lPEp6+apc51W8nL3NDAdAACwFrsUSZ06\nddKGDRskSe7u7qpcubIKFiwoDw+PB55Xrlw5e8QDAADAQ7p9L0zTNy7S3G3LFXNfgfSva2G3tHzv\nOr3YoJ39wwEAAKuzeZG0b9++lBKpd+/e+uKLL5Q3b15bXxYAAAA2FBp5V99uXqLZv/2g6LiYNOcU\n9suvYS1fVqc6reycDgAA2IrNi6SdO3dKkmrUqKHZs2fLZDLZ+pIAAACwkfCoCM3YslSztn6vyNjo\nNOcUzBOgIS16qVu95+Tp/uA70AEAgHOxeZF07949SVLz5s0pkQAAAJxUREykZm5Zphmbl+pebFSa\ncwJz59WQZ3vpxfpt2RMJAIAsyuZFUtGiRSVJZrPZ1pcCAACAjdwID9GENd+l+Ttdvlx+Gty8p3o2\nfF45PLwMSAcAAOzF5kVSmzZt5OnpmfKIGwAAAJxP2YIl1L5GM/20f0PKmL9PHg1q1kO9GrWXt2cO\nA9MBAAB7cbH1BQIDA/XJJ5/o999/188//2zrywEAAOARxCcmpHtsRKs+cjG5yM87t95p95oOfLpC\nrzXrTokEAEA2YvM7kiRp1KhRSk5OVo8ePfT666/rlVdeUcGCBe1x6f+UmJio8PBwSZKXl5d8fHwy\nvUZMzD9vKsmRg1+iAACAc4qJj9WC7T9r2saFWjhwgqoUfzzVnFL5i2nOgM9V77HqypXD24CUAADA\naCazjTcvmjx5smbPni1JunLliu7evStJKlSokPLkyfPADbiHDx+uPn36WDXPxYsXtWfPHu3bt0/7\n9+/XkSNHUoqgPn36pGRNz40bN7RlyxZt27ZNe/bs0dWrV1OKqNy5c6t27drq3bu3OnXqZJPNxcPC\nwuTv7y9JCg0NlZ+fn9WvAQAAso/YhDgt2rlSX62br1sRdyRJTSrU1eJBEw1OBgAArMHaPYLN70i6\nceOGgoODU41fu3ZN165de+C5ISEhVs/TvXt37dq1K+Wzq6trps4fPXq05s+fbzHm5eUlk8mkiIgI\nbdy4URs3btTs2bO1YsUK5cqVyyq5AQAArCkuIV5Ldv2qr9bP1/Vwy9+5tvy1W4fO/aXqJSsYlA4A\nADgqmxdJNWvWfOi7iipXrmzlNFJQUJCKFCmimjVrqmbNmipfvnxKM5cZNWrU0IABA9S8eXMVKVJE\nkvTnn3/qvffe08qVK7V582Z17dpVq1evtvaPAAAA8NDiExP0/Z41mrx2rq6G3UxzTk7PHPr75kWK\nJAAAkIrNH21zdLGxsSl7G2Xk0bZx48apSpUqat68eZrHzWaz2rZtq1WrVkmStm/frgYNGlgtL4+2\nAQCAh5GQlKgf967TpLVzdPnO9TTn5PDwUu/GHfVq0+7Kl4vfMQAAyAqc7tG2rObNN9984HGTyaR3\n3303pUjasGGDVYskAACAzEhMStRP+zdo4po5unj7appzvNw91atRew1q9qICcue1c0IAAOBMKJJs\noFSpUinfX7+e9t/4AQAA2NrlO9fVecoQnbt1Oc3jnm4e6tGgnQa36Kn8vvnsnA4AADgjiiQbuHz5\n/35Zy5Mnj3FBAABAtlbIL1CuLqlfLOLh5q7u9dpqSIueKugXaEAyAADgrOxaJMXHx2vdunXat2+f\nrl69qnv37ik5OTnd+T179lT79u3tmNA6Fi1alPJ9/fr1DUwCAACyM1cXV41s3VcDZr8rSXJ3dVPX\num005NleKuJfwOB0AADAGdmtSPrpp580cOBA3byZ9ttB0lK7dm0bJrKNkydPatq0aZL+ecStdevW\nmV4jLCws3WPh4eEPGw0AAGRBZrNZ647+rnqPVZdvzlypjrep9rSmFS2rSsXKaeizL6lYvkIGpAQA\nAFmFXYqkFStW6IUXXpDZbJabm5sqVqyo0NBQXbx4UaVKlVLevHkVHBysqKgo5c+fXxUq/POq2aCg\nIHvEs5rIyEh17NhRcXFxMplM+vrrr+Xu7p7pdf7dTR0AACA9ZrNZG4/t0JerZ+vPy6f1eqs+GtWm\nX6p5Li4uWjt6jtxd2dEAAAA8OhdbXyA+Pl5Dhw6V2WxW/fr1df78eR0+fFhdunSRJPXt21f79u1T\naGioJk+erIiICNWoUUObN29OmeMMEhMT1bVrVwUHB0uSRo8erebNmxucCgAAZDVms1mb/9ytFp/3\nVq9v3tCfl09LkmZuWaawqLtpnkOJBAAArMXmv1Xs3LlTV65cUY4cObR06VIVKVIkzXkeHh4aOnSo\nAgIC1L17d/n6+mr06NG2jmcVZrNZffr00erVqyVJvXr10pgxYx56vdDQ0HSPhYeHq2TJkg+9NgAA\ncE5ms1nbju/T+NWzdPh8cKrj92KjNGPzUo1u+4oB6QAAQHZh8yLp6NGjkqRWrVqlWSL972bb3bp1\n09ixY/Xpp59q4MCBypUr9bP+jmbw4MFasGCBJKlDhw767rvvZDKZHno9Pz8/a0UDAABOzmw2a+ep\ng/ri15k6cO7PdOc9V72Jnq/B3dAAAMC2bF4k/bs5dJkyZSwv7PbPpWNjY1OdU79+ff3111/asmWL\n2rVrZ+uIj+TNN9/U119/LUlq2bKllixZIlfX1K/ZBQAAyKzdpw/ri1WztPfMkXTntKr6lEa27qPH\nC5e2YzIAAJBd2bxI8vX1TXP83zuNbty4kerYvxtUX7582XbBrODjjz/WF198IUlq0qSJfvrpJ3l4\neBicCgAAOLt9fx/V+FWztfPUwXTntKjcUCNb91WFomXtmAwAAGR3Ni+SChX65xWz165dsxgvVaqU\nJOnw4cOpzvl3w+pHeTzM1iZMmKAPPvhAktSgQQP9+uuv8vLyMjgVAABwduFREeoyZahiEuLSPP5M\nxXoa1bqfKhcvZ+dkAAAAdnhrW6VKlSRJZ86csRivV6+eTCaTDh06pC1btqSMb9q0Sb/99psk6Ykn\nnrB1vIcyY8YMjRw5UpJUu3ZtrVmzRjlz5jQ4FQAAyAryeOfWS407php/qnxtrX3zOy0aOIESCQAA\nGMbmdySVL19exYoV0969e3Xr1i0FBgZKkgoWLKhWrVpp9erVevbZZ9WkSRMlJCTo999/l9lsVlBQ\nkBo2bGj1PHFxcbp3757F5/u/v337dspnk8mkvHnzWpy/ZMkSvfbaa5Kkxx57TIsWLVJcXJzFOvfz\n8PBQ7ty5rfkjAACALG5gsxc1f/sKRcfFqGG5GhrVpp9qlKpkdCwAAACZzGaz2dYXmThxorZu3apR\no0apUaNGKeOXLl1SvXr1dOXKFYv53t7eWr9+verXr2/1LLNnz1a/fv0yNNfb21uRkZEWY40bN9bv\nv/+e4es1adJEmzdvzlTGBwkLC5O/v78kKTQ0lDe8AQDghIKvnNGXq2ara702alYp7d93luxapRKB\nRVSnTFU7pwMAAFmJtXsEm9+RJEkjRozQiBEjUo0XK1ZMf/zxh6ZOnardu3crPj5elSpV0pAhQ1L2\nULI2Ly+vVHcZpcfHxyfVmK+vb4bP/3c+AACAJJ24elYT1nyn1Ye3SpKuhF5X04r10twXslu9NvaO\nBwAA8J/sckcSrIc7kgAAcD6nr5/XhDXf6ddDW/S/v3rNfWWcnq3SKJ0zAQAAHo1T3pEEAACQHZ29\neUkT13ynFQc2piqQ/rX+j+0USQAAwGlQJAEAAFjZ+VuXNXHtXP20b72SzclpzqlU7DGNatNfz1So\na+d0AAAAD89qRVJISIju3LljreUkSYGBgSm3XwEAADi6i7evafLaufph71olJSelOad8kTIa1bqf\nmldukObeSAAAAI7MakXShAkTNG7cOGstJ0kaO3asRo8ebdU1AQAArC0uIV7vfD9By3avVmI6BVK5\nQqU0qk1fPVu5kVxcXOycEAAAwDp4tA0AAOARebi56+zNS2mWSGUKBGlk675qU+1pCiQAAOD0rFYk\n9e3bV88884y1lpMklSlTxqrrAQAA2ILJZNKoNv3UfuJrKWOl8hfTyNZ99Vz1JnJ1cTUwHQAAgPVY\nrUgqXbq0Spcuba3lAAAAHM6tu3dkMkkBufOmOla3bDXVf+xJXQ29oRGt+uj5Gk3l5srN3wAAIGvh\ntxsAAID/EBIRqmkbF2rB7yvUsfazGt897T0cp/f+SP4+vhRIAAAgy+K3HAAAgHTciQzX9I2LNGfb\ncsXEx0qSlu5apUHNe6p4vkKp5gf6pr5TCQAAICuxa5GUmJioX3/9Vb/++quOHj2qO3fuyGQyKV++\nfKpWrZratWunli1bshElAAAwVFjUXX27aYlm//ajouKiLY4lJidp8tq5mtTzHYPSAQAAGMduRdKB\nAwfUs2dPnTx5MtWxy5cv68iRI/ruu+9UuXJlLVy4UBUrVrRXNAAAAEnS3eh7mrFlmWZuWarI2Og0\n5xTwDVCVoMftnAwAAMAx2KVI2rNnj5o2baqoqChJUt68eVWjRg0VKFBAZrNZ165d04EDBxQeHq4/\n/vhDDRs21LZt21S5cmV7xAMAANlcREykZm39XjM2L1VETGSacwJy+2tI8156sUFb5fDwsnNCAAAA\nx2DzIikhIUE9evRQVFSU/P39NWXKFHXp0kVubpaXjouL07x58/T6668rPDxcvXr10pEjR2QymWwd\nEQAAZFORsVH67rcf9c2mJQqPjkhzTt5cfhrcvId6NmyvnBRIAAAgm7N5kbRlyxadPXtW7u7u2rRp\nk6pVq5bmPE9PTw0YMEBly5ZVkyZN9Mcff2jfvn2qXbu2rSMCAIBsyGw269nP++jMjQtpHvf39tVr\nzV7Uy407ytszh33DAQAAOCib72p99OhRSVLbtm3TLZHu99RTT+npp5+WJP3xxx+2jAYAALIxk8mk\nbvXapBrPkzO33m73qvaPWaFBzXtQIgEAANzH5kVSYmKiJKlChQoZPuffuf+eCwAAYAu9GnVQQG5/\nSZJvzlx6o01/HRjzs4a06CUfL2+D0wEAADgemz/aVrp0aUlSeHh4hs8JCwuTJJUpU8YWkQAAQDYR\nmxCnRTtXKl8uP7V7smmq4zk9vPRGm/66ER6i/k26yDdnLgNSAgAAOA+T2Ww22/ICUVFRKlq0qHx9\nfXXy5El5eno+cP69e/dUqlQpeXl56dy5c6k25c7uwsLC5O//z9+choaGys/Pz+BEAAA4nriEeC3d\nvUpT1s3T9fAQFfYvoD0f/ygPN3ejowEAANiVtXsEmz/a5u3trQULFujy5cvq3bu3YmNj05177949\nde3aVREREVq8eDElEgAAyJSEpEQt2vGL6n7QSaOXjtf18BBJ0tXQG1q6e5XB6QAAAJyfzZuakJAQ\nlS5dWrNmzdLIkSNVrlw5vfzyy6pbt67y588vs9ms69eva8eOHZo7d66Sk5M1b948BQQE6OTJk2mu\nGRgYmNKmAQAAJCQl6se96zRp7RxdvnM9zTkztyxTzwbPy2Qy2TkdAABA1mHzR9tGjx6tcePGWXXN\nsWPHavTo0VZd01nwaBsAAP8nMSlRKw5s1MQ1c3Qh5Eqac7zcPdWzwfMa1LyHAn3z2jkhAACAsazd\nI/DsGAAAcDpJyUn65cAmTVjznc7dupzmHA83d/Vo0E6Dm/dUgTwBdk4IAACQNdm8SOrdu7caN25s\n1TUfe+wxq64HAACcx6+Htmj8qpk6c+NimsfdXd3Urd5zGvrsSyrkF2jndAAAAFmbzYuksmXLqmzZ\nsra+DAAAyCbWHtmWZonk5uKqrvXaaEiLXiqat6AByQAAALI+Hm0DAABO5fXWffTroS1KNidLklxd\nXNWpdksNa/myiucrZHA6AACArI0iCQAAOByz2azI2GjlyuGd6liZAkF6vkZT/XxgkzrWaqHhLV9W\nicCiBqQEAADIfmz+1jZYF29tAwBkZWazWVuD9+iLVbNUwDef5r82Ps15l+9cV3xigkrlL2bnhAAA\nAM6Ft7YBAIAsx2w26/cT+zV+1SwdOv+XJOkPSUcvnlCV4o+nms8eSAAAAMagSAIAAI/MbDZr1+nD\nWrZ7tS6EXFFkbLR8vHIqKKCIutZtrbplq8lkMqV93qlD+mLVTO0/eyzV8S9Xz9aigRPs8SMAAAAg\nAyiSAADAQzObzVq8c6VmbFmmMzcupDp+8NyfWr5vncoUCNKAJl3UvX7blEJp9+nDGr9qlvacOZLu\n+u4ubopLiJenu4etfgQAAABkAkUSAAB4KAlJiRqx8DP9uHftf849c+OCRi7+XPvOHlPXOq01ce0c\n7Tx1MN35zSrV18jWfVWpWDlrRgYAAMAjYrNtJ8Nm2wAAR2A2mzVk/icZKpEy4+nydTSqTT9VDXrC\nqusCAABkV2y2DQAADLd450qrlkiNn6ilUa37qXrJClZbEwAAANZHkQQAADLFbDZrxpalVlmr/mNP\nalSbvqpVuopV1gMAAIBtUSQBAIBM2XX6sM7cuPjI63z8wjD1b9LFCokAAABgL3Ytkn7//XetXr1a\nx48fV1hYmOLj4x84f/DgwerVq5ed0gEAgIxYtnu1Vdb58/Jpq6wDAAAA+7FLkXTz5k116tRJ27dv\nz9R5169ft1EiAADwsC6EXLHOOrcuW2UdAAAA2I/Ni6SkpCS1atVKhw4dkiTlypVL1apVU/78+eXu\n7v7AcytUYMNNAAAcTWRstHXWibPOOgAAALAfmxdJGzduTCmRPvroI7355pvy9PS09WUBAICN+Hjl\ntM46ntZZBwAAAPbjYusL/FsitWzZUu+//z4lEgAATi4ooIh11gksapV1AAAAYD82L5L+fXytVq1a\ntr4UAACwgy51W1tnnTqtrLIOAAAA7MfmRdLjjz8uSQoNDbX1pQAAgB3UK1tNAbn9H2mNMgWCVLds\nNSslAgAAgL3YvEhq2bKlihUrppUrVyo+Pt7WlwMAADa2aOdKhUQ82l8QDWjSRSaTyUqJAAAAYC82\nL5Lc3Ny0ZMkS3bp1S71791ZsbKytLwkAAGxkya5fNWrx54+0RqfaLdW9flsrJQIAAIA92fytbZJU\nr149/fbbb+rTp4/KlSunnj17qlq1avL19X3g30aWLFlSxYoVs0dEAADwH5btXq3XF421GHMxmZRs\nNmd4jU61W2pCj7e5GwkAAMBJ2aVIkqTcuXOrcuXKWrx4sT755JMMnTN27FiNHj3axskAAMB/+XHv\nOg1fOEbm+0ojd1c3ze4/ViERdzRjyzKduXEh3fPLFAjSgCZd1L1+W0okAAAAJ2aXImn16tXq1KmT\nYmJi7HE5AABgRVdCb2jE/5RIbi6umt3/MzWv3ECS1L1+W+0+fVjL9qzRhVuXFRkXLR/PnAoKLKqu\ndVurTpmqFEgAAABZgMlszsT96A8hLCxMJUuWVHh4uPLly6f+/furbt26CgwMlLu7+wPPLVSokAID\nA20Zz+mEhYXJ3/+fN+WEhobKz8/P4EQAgOzgl4ObNHDOh0pKTpKbi6tm9hujllUbGx0LAAAA/8Ha\nPYLN70j69ddfU0qkI0eOqEiRIra+JAAAsLJ2TzaVi8lFQ+Z9rGkvf0CJBAAAkE3ZvEi6cOGCJKlr\n166USAAAOLHnqjdRrdKVld83n9FRAAAAYBAXW18gX75/ftnMmzevrS8FAABsjBIJAAAge7N5kdSk\nSROZTCYFBwfb+lIAAOARbfpzl95YMk7JyclGRwEAAIADsvmjbeXKlVPPnj21ZMkSHTlyRFWrVrX1\nJQEAwEPY8tdu9ZkxWvGJCYqNj9Oknu/I1cXV6FgAAABwIDa/I0mSZs6cqRdeeEFNmzbVkiVLlJiY\naI/LAgCADNp2fJ96f/tPiSRJP+xdq2ELxsjGL3cFAACAk7H5HUkLFy7UTz/9lPK5e/fuGjhwoCpX\nrixfX1+ZTKZ0z+3Zs6fat29v64gAAGRr20/s10vfvKG4xHiL8ZqlKj3wz2kAAABkPzYvkoKDg7Vy\n5UqLsfDwcP3+++//eW7t2rVtFQsAAEjaefKgek0fpdiEOIvxz7uOUo8G7YwJBQAAAIdl8yKpZMmS\natSo0UOdW6xYMSunAQAA/9p9+rB6TB+pmP8pkcZ0fl0vNepgUCoAAAA4MpOZzQ+cSlhYmPz9/SVJ\noaGh8vPzMzgRAMAZ7T1zVN2mDVd0XIzF+McvDFP/Jl0MSgUAAABrs3aPYJfNtgEAgOM4cPaYuk8b\nkapE+qDDYEokAAAAPBBFEgAA2cihc3+p69RhioqLthh/9/mBerVpd4NSAQAAwFlQJAEAkE0cPh+s\nLl8NVWSsZYn0drtXNah5D4NSAQAAwJnYfLPttWvXauvWrQ91bqtWrfTUU09ZOREAANlPZGyUXvz6\ndd2LjbIYf6NNfw1p0cugVAAAAHA2Ni+Stm/frgkTJjzUufny5aNIAgDACny8vPVFtzf0yuz3lJic\nJEl6vVUfjWjV2+BkAAAAcCY2L5L8/PxUvHjxdI8nJycrLCxMkZGRkqTcuXOn7CDu6+tr63gAAGQb\nras9rZn9XNR/1jsa1LyHRrbua3QkAAAAOBmT2Ww2Gx3CbDbr+PHjmjRpkn744QdNmzZNPXv2NDqW\nQ7L2a/sAANnPqWvnVbZgkEwmk9FRAAAAYGPW7hFsfkdSRphMJpUvX16zZ89W+fLl1atXL7m5ualb\nt25GRwMAIMt5rFAJoyMAAADASTncW9uGDRumcuXKafDgwYqOjv7vEwAAgIXT18/rgx8nK+n/74UE\nAAAAWIvDFUkmk0mNGzdWaGioNm7caHQcAACcyt83LqrjpEGasWWZhs7/hDIJAAAAVuVwRZIkeXh4\nSJIuXrxocBIAAJzHuZuX1GHSQN2KuCNJWr5vvQbN/UiJSYkGJwMAAEBW4XBFktls1rZt2yRJPj4+\nxoYBAMBJXAi5og6TBurm3dsW47m8vOVicrg/7gEAAOCkHOo3y8jISL322ms6duyYJKlOnToGJwIA\nwPFdvH1NHSYO1PXwEIvx7vWe0+ddR8nFxaH+uAcAAIATs/lb21asWKG1a9c+cE58fLyuXr2qvXv3\npmyw/fzzz+uJJ56wdTwAAJzapdvX1GHia7oadtNivEvd1hrffTQlEgAAAKzK5kXS/v379d1332Xq\nnNatW2vBggU2SgQAQNZwJfSGOk4epCuhNyzGX6jdUhNefIsSCQAAAFZn8yKpUKFCqly58gPneHp6\nyt/fXxUrVlS7du1Ut25dW8cCAMCpXQu7pQ4TB+rS7WsW4x1qNtfknu/I1cXVoGQAAADIykxms9ls\ndAgjJSYmKjw8XJLk5eX10Bt8R0dHy8PDQ25utu3mwsLC5O/vL0kKDQ2Vn5+fTa8HAHA8N8JD9PyE\nV3U+5IrFeLsnm2rayx/IzdXmf08EAAAAJ2HtHiHb3fN+8eJFLVu2TMOHD1e9evWUO3duBQQEKCAg\nQMOGDcvUWsHBwerZs6fy5s0rb29veXp6qlSpUnrnnXcUERFhmx8AAJCt3bx7Wx0mDUxVIrWp1oQS\nCQAAADaX7X7b7N69u3bt2pXy2dX14W79//7779WrVy/FxcVJ+udupoSEBJ07d06fffaZFi9erK1b\nt6pkyZJWyQ0AQGJSorp+NUxnb16yGG9VtbGm9/mIEgkAAAA2l+3uSAoKClLnzp01YcIE7dixQyEh\nIf990v84dOiQevbsqbi4OJUvX1579+5VTEyMoqOjNXfuXHl7e+vixYtq2bJlStEEAMCjcnN106g2\n/eR+X2HUonJDfdPnE4sxAAAAwFbs9ltnQkKCfvjhB61evVrHjx9XWFiY4uPjH3jOu+++q0GDBlk1\nx6JFiyw+x8bGZnqNkSNHKj4+Xn5+ftq0aZMKFiwoSfLw8NBLL70kHx8fvfDCCzp16pS+/vprjRgx\nwirZAQB4tkojfTdgrPrOfFuNn6ilmf3GyMPN3ehYAAAAyCbsUiSdOXNGzz33nE6ePJmp8yIjI22U\n6OGdPHlS27ZtkyQNHDgwpUS6X8eOHVWpUiUdO3ZM33zzDUUSAMCqmlVqoBUjpqti0ccokQAAAGBX\nNi+S4uLi1KpVK505c0aSVLJkSdWpU0f58+eXu/uDf/mtU6eOreNl2sqVK1O+79ChQ7rzOnbsqGPH\njunvv//W8ePH9cQTT9gjHgAgm3iyZEWjIwAAACAbsnmRtGbNGp05c0YuLi6aNWuWevfubetL2tTh\nw4cl/bO5dsWK6f8SX6tWLYtzKJIAAJlxN/qeZm39XsOefYlNtAEAAOAwbP6b6V9//SXpn7t3nL1E\nkqRTp05JkooXL/7AN74FBQWlfJ/ZR/oAANlbREykOk8ZqqMXj+vvGxc17eUPKJMAAADgEGz+W2nO\nnDkl6YF37ziTO3fuSJICAgIeOO/+46GhoZm6RlhYWLrHwsPDM7UWAMC53IuJUtevhunoxeOSpF8O\nblJScrKm9/mIN7MBAADAcDb/jbRSpUqSpBs3btj6UnYRFRUl6Z9H2x4kR44cKd9ndtNwf3//zAcD\nADi9yNgodZs6TIfO/2UxHhJxR/GJCRRJAAAAMJyLrS/QtGlTPf7441qxYoVDvoUts0wmkyTJbDY/\ncN79x11cbP4fMwDAyUXFRqv7tBE6cO5Pi/GapSpp0aAJ8vbMkc6ZAAAAgP3YvOEwmUxavny5EhIS\n1L59+5RHw5yVj4+PJCkmJuaB8+4//u85GRUaGpru17lz5zIfGgDg0KLiYtT969e17+8/LMarl6ig\nxYMmycfL26BkAAAAgCW73CP/xBNPaN++fRowYIBKlSql9u3bq1q1avL19U25wyctVatWVfny5e0R\nMcMCAwN16dKl/3xU7/r16ynf/9d+Sv/Lz8/vobIBAJxPdHysek4fqb1njliMVw16QkuHTFauHJRI\nAAAAcBx222zh6tWrkqS7d+9q7ty5mjt37n+eM3bsWIcrksqVK6eDBw/q8uXLio+Pl4eHR5rz7r9z\n6PHHH7dXPACAE4mJj9VL00dp16lDFuOVipXTsiFTlDtH5u5oBQAAAGzNLpv3zJ07V08//bS2bNli\nj8vZVK1atSRJCQkJOnjwYLrzdu3alfJ9zZo1bZ4LAOBcYhPi9PK3b2r7yQMW4xWLltX3Q6fIN2cu\ng5IBAAAA6bP5HUnXr1/XoEGDlJSUpNKlS2vEiBGqW7euAgMD5e7u/sBzvb0d73b+du3aaciQITKb\nzVqyZInq1q2bak5ycrK+//57SVKVKlUUFBRk55QAAEcWlxCv3t+O1rbj+yzGyxcpo++HTpWft69B\nyQAAAIAHs3mRtGbNGkVHR6to0aI6cOCA8uTJY+tL2lSRIkXUsWNH/fjjj5o9e7ZeffXVVI/fTZky\nRRcuXJAkjRgxwoCUAABH9tqcD7Q1eI/F2OOFS+mHYVPl70OJBAAAAMdl80fb/t0bqVOnTg5RIsXF\nxen27dspX/e/Re5Bx+43btw4+fv7Ky4uTk8//bTmz5+vixcv6vjx43rrrbc0cuRISVKjRo3UvXt3\nu/xcAADn0blOK3m4/d9duY8VKqkfh01TXp88xoUCAAAAMsDmdyQVLFhQkuTj4xgbhi5cuFD9+vVL\n89iiRYu0aNGilM/e3t6KjIxMNa9EiRJatWqVOnTooBs3buill15KNadevXpasWKFXFzssg0VAMCJ\nNKtUX3MGjFOfGaNVLF8hLR82Vfly8cZOAAAAOD6bF0nNmzeXq6vrAzemticvLy/lzZs3Q3MfVH7V\nrVtXf/31l7799lutXbtWly9flqenp8qWLavOnTvrxRdfpEQCAKTrmYp1tXjwJJUpUFwBuTP25xIA\nAABgNJPZbDbb+iKjRo3ShAkTtGnTJjVp0sTWl8vSwsLC5O/vL0kKDQ2Vnx9/gw0AAAAAANJm7R7B\nLrfMjBs3TqNGjVK7du30xRdfKCwszB6XBQDAUEnJSZqzbbkSkhKNjgIAAABYhc3vSJo2bZrmzZsn\nSTp79qzCw8Pl4uKiEiVKyNfXVyaTKd1zBw8erF69etkyntPhjiQAcA5JyUkaOv8TLd+3Xq2qPqVv\n+34id1ebP1EOAAAAWLB2j2Dz32ivXLmiQ4cOWYwlJyfr7Nmz/3nu9evXbRULAACbSU5O1vAFY7R8\n33pJ0pojv2nArHf0bd9PLd7WBgAAADgbmxdJVatWVffu3R/q3AoVKlg5DQAAtpWcnKzXF43VD3vX\nWoz/cemU7twLU0G/QIOSAQAAAI/OLpttw3p4tA0AHFdycrLeWDJOi3autBgv5Beon0d8o+IBhQ1K\nBgAAgOzKKTfbBgAgqzObzXpr2ZepSqQCvgH6afjXlEgAAADIEiiSAAB4RGazWe98P0Hzt6+wGM/v\nm08/jfhaJQKLGpQMAAAAsC6KJAAAHoHZbNb7P07WnG3LLcYDcvtr+fBpKpW/mEHJAAAAAOuz2mbb\nv//+u/bs2SNJaty4sWrXrp1qPLPuXwcAAEdjNpv14U9fadbW7y3G8+Xy0/JhX6tMgSBjggEAAAA2\nYrUiad26dRo3bpwkaezYsSkF0P3jmXX/OgAAOBKz2axPf/5aMzYvtRj398mjH4dN02OFShiUDAAA\nALAdqxVJnp6e8vb2liR5eHikOZ5Z968DAIAjGb96tr7euMhizN/bV8uHTdXjhUsZlAoAAACwLZPZ\nbDYbHQIZZ+3X9gEAHs7mP3erz4zRikuMlyTlyZlby4dPU4WiZQ1OBgAAAPwfa/cIbLYNAMBDeKZi\nXc179Qt5uXvKN2cu/TDsK0okAAAAZHlWe7QNAIDs5qnytbXgtfHKnTOXKhUrZ3QcAAAAwOYokgAA\neAQNH69pdAQAAADAbuxeJJ0+fVrBwcEKCwtTfHz8A+fWrl1bVapUsU8wAADSsf7odj1doY483NyN\njgIAAAAYym5F0rJly/TBBx/o9OnTGT5n7NixFEkAAEPN2LxUHyyfohaVG2pmvzGUSQAAAMjW7LLZ\n9vjx49W1a9dMlUgAABht9m8/6IPlUyRJ6//Yrr4z31JcwoPvpgUAAACyMpvfkXT16lW9++67kqTi\nxYvr7bffVpMmTVSwYEF5eHg88FxXV1dbxwMAIE1zty3Xu99PtBjbceKATl0/x8baAAAAyLZsXiSt\nW7dO8fHxCgwM1P79+xUYGGjrSwIA8EgWbP9Zby370mLMy91TCwZ+SYkEAACAbM3mj7ZdvnxZktS5\nc2dKJACAw1u8c6XeWDLOYszTzUPzXv1CDcrVMCgVAAAA4BhsXiT5+/tLkvLly2frSwEA8EiW7l6t\nkYs/txjzcHPX3FfHqfETtQxKBQAAADgOmxdJ9erVkyQ22gYAOLQf9q7ViIVjZDabU8bcXd303YDP\n9XT5OgYmAwAAAByHzYukJ598Ui1bttQvv/yS8pgbAACO5Kd96zV0/idplEhj1bRiPQOTAQAAAI7F\n5kWSJC1evFjly5dXixYtFBwcbI9LAgCQIb8c2KTB8z62KJHcXFw1s98YNavUwMBkAAAAgOOx+Vvb\nfvvtN+3atUstWrTQ9OnTVbFiRTVs2FDVq1dXnjx5ZDKZ0j336aefVt26dW0dEQCQTf16aIsGzv1Q\nyebklDFXF1d92/cTPVulkYHJAAAAAMdk8yJpw4YNGjfO8u03v//+u37//ff/PNfNzY0iCQBgM7lz\n+Mjd1U1JyUmS/imRpvf+SK2rPW1wMgAAAMAx2bxI8vT0lLe390Od6+HhYeU0AAD8n8ZP1NKC18ar\n1/RRiktM0LSXP1DbJ58xOhYAAADgsEzm+zeFgMMLCwuTv7+/JCk0NFR+fn4GJwIA57fz1CHdDA9R\nh1otjI4CAAAAWJW1ewSb35EEAICjq/9YdaMjAAAAAE7BLm9tAwDAaEcuHFd8YoLRMQAAAACnRpEE\nAMjytp/Yr3ZfvqI+M0YrLiHe6DgAAACA07Lao20hISG6c+eOJCkwMDDl+bv7xzPr/nUAAHgYO08e\nVM/poxSXGK9Nf+7Sy9++qTmvfC4vd0+jowEAAABOx2pF0oQJEzRu3DhJ0tixYzV69OhU45l1/zoA\nAGTW7tOH1ePr1xWbEJcytjV4j7YF71OLKg0NTAYAAAA4Jx5tAwBkSXvPHFX3aSMUc1+JJEmfdhpO\niQQAAAA8JKvdkdS3b18988wzkqQyZcqkOZ5Z968DAEBG7f/7D3WbNlwx8bEW4x91HKq+T3c2KBUA\nAADg/KxWJJUuXVqlS5fO8DgAALZw6Nxf6jZtuKLjYizG32s/SAOe6WpQKgAAACBr4NE2AECWcfh8\nsLp8NVSRsdEW4++0e00Dm71oUCoAAAAg66BIAgBkCUcvnlCXr4bqXmyUxfibz/XX4BY9DUoFAAAA\nZC1We7Qto8xms65cuaKwsDDFx8c/cG6RIkVUoEABOyUDADirY5dOqvOUIYqIibQYH9m6r4a37G1Q\nKgAAACDrsVuRdOzYMY0dO1Zr165VREREhs4ZO3asRo8ebeNkAABnFnzljDpPGaK70fcsxoe3fFmv\nt+pjUCoAAAAga7JLkfT999/rxRdfVGJioj0uBwDIRsKiIhQbH2cxNqRFL73Rpr9MJpNBqQAAAICs\nyeZF0s2bN9WnTx8lJiYqV65ceumll1S3bl3lz59f7u7uDzw3KCjI1vEAAE6u/mPVtWjQRL349euK\niY/Va0276622r1AiAQAAADZg8yLp119/VVRUlPLkyaODBw+qVKlStr4kACCbqfdYdS0ZPEnbgvdq\nNCUSAAAAYDM2L5KuXLkiSXrxxRcpkQAANlOnTFXVKVPV6BgAAABAluZi6wvkz59fkhQQEGDrSwEA\nsrjLd64rLuHBb/wEAAAAYDs2L5IaNmwoSTp+/LitLwUAyMLO37qsNl/018vfvqnYhLj/PgEAAACA\n1dm8SKpQoYI6duyon3/+WcHBwba+HAAgC7oYclUdJg3Ujbsh2hq8Ry9/86Zi4mONjgUAAABkOzYv\nkiRp/vz5qlOnjp555hn98ssvMpvN9rgsACALuHT7mtpPGqhrYbdSxn47vlcLd/xiXCgAAAAgm7L5\nZtuSlDNnTm3ZskUffvihnn/+eeXPn19VqlSRr6/vA9+s061bNz333HP2iAgAcECX71xXh0kDdTX0\nhsV4p9ot1fepTgalAgAAALIvuxRJycnJeu+99/TVV19Jkm7evKkNGzb853lVqlShSAKAbOpq6E11\nmDRQl+9ctxjvWKuFJvV8Ry4udrmpFgAAAMB97FIkvfzyy1qwYEHK5yJFiigwMFDu7u4PPK9w4cK2\njgYAcEDXw26pw6SBunT7msX48zWaaUqv9+Tq4mpQMgAAACB7s3mRdOjQoZQS6aWXXtLHH3+sokWL\n2vqyAAAndSM8RB0mDdSFkCsW489Vb6KpL71PiQQAAAAYyOZF0s6dOyVJderU0dy5c219OQCAE7t1\n9446Thqkc7cuW4y3qvqUvu79kdxc7XIjLQAAAIB02HyDiXv37kmSmjZtautLAQCcWEjEHXWYNFB/\n37xoMd6ySiN92/cTuVMiAQAAAIazeZFUunRpSVJsbKytLwUAcFK374Wp4+TBOnPjgsV480oN9G3f\nTymRAAAAAAdh8yKpTZs2ypMnj9avXy+z2WzrywEAnNCFkCup3s72TMV6mtlvjDzcHvxiBgAAAAD2\nY/MiydvbW/Pnz9dff/2l9957z9aXAwA4oSdLVtTSwZPk7ZlTkvRU+dqa3f8zebp7GJwMAAAAwP1M\nZhvfJhQZGanIyEht27ZNAwcOVPny5TVgwABVr15dvr6+MplM6Z6bK1cueXt72zKe0wkLC5O/v78k\nKTQ0VH5+fgYnAgDrOXD2mGZsWaZpL38gL3dPo+MAAAAATs/aPYLNi6TRo0dr3LhxD3Xu2LFj/197\n9xkeVbW/ffye9EYSQu+9SbVQRQGp0kQBAbsUsQIKYj8H9ZzjURARwQaCHmmCgoqIUkRq6GgQQpMS\nQgkEAqS3Wc8Lnsw/QyZhEiaZBL6f6+Jy2GvtNb+JO8Pkzlpr6+WXX3ZxRSUbQRIAAAAAAHCWq3OE\nQl/aBgBAdvHJiUpJT3V3GQAAAAAKoNBvg/PAAw+oRYsWBTq3efPmri0GAOBWCSmJGvLRGAX6+uvL\np96Tv4+fu0sCAAAAkA+FvrQNrsXSNgAlVWJKkoZ8NEZb/46QJN3R8DZ99fQkBRAmAQAAAIWGpW0A\ngBInMTVZD04fawuRJGn9vu1694dP3VgVAAAAgPwiSAIAFKqktBQ9PH2sNh/cZXf8llqNNa73CDdV\nBQAAAKAgCJIAAIUmOS1Fj348TpsO7LQ73rxGI81/bopK+Qe6qTIAAAAABUGQBAAoFCnpqXrsk/Fa\nv2+73fFm1Rvom1EfKiSglJsqAwAAAFBQBEkAAJdLSU/V45++pLWRW+2ON6lWX9+MnqrQwGA3VQYA\nAADgWhAkAQBcKjU9TcM/f1Vr9my2O35TlbpaOPojlQ4McVNlAAAAAK4VQRIAwGXSMtI1YsarWrV7\no93xhpXraOGYjxQWRIgEAAAAlGQESQAAl0jPzNDIGa9rRcQGu+P1K9XSojEfqWyp0m6qDAAAAICr\nECQBAFzi0OljWrdvm92xehVr6Nsx01QuOMxNVQEAAABwJYIkAIBLNKpSR9+M/lBBfgGSpDoVquvb\n56erfEgZN1cGAAAAwFUIkgAALnNb7aZaOHqqmtdopG/HTFOFkLLuLgkAAACAC3m5u4DrgTFG8fHx\n8vb2lr+/v7vLAQC3uqVWE/3y8ixZLBZ3lwIAAADAxZiRVECXLl3Sv//9b916663y9fVVSEiIAgIC\nFBoaqm7dumn+/Pkyxri7TAAoFFarVSnpqbm2EyIBAAAA1yeLIe3Itz179qh79+46ceKE7Zifn5/S\n09OVmZlpO9a9e3ctXrxYAQEBLnvuuLg4hYVd3rT2/PnzKl2auyABKFpWq1Vj57yj4+dO6X/PTFKA\nj5+7SwIAAACQC1fnCMxIyqf09HTdd999thBp7NixioqKUnJyspKTk7VlyxZ17NhRkvTrr7/q5Zdf\ndmO1AOBaVqtV4+e9q/mblmrD/u16aNoLSkxNdndZAAAAAIoIQVI+/f777zpw4IAkaeTIkZo0aZKq\nVasmSfL29larVq20bNky1a1bV5I0e/Zspaenu61eAHAVY4xeXjBRczb8YDu26cBOjf36P26sCgAA\nAEBRIkjKp7///tv2uF+/fg77BAQEqFu3bpKkhIQEnTlzpihKA4BCY4zRqwve1//WLbE7XiGkrMb3\nGeGmqgAAAAAUNYKkfKpcubLtcWpq7hvNZrV5eXmpXLlyhV4XABQWY4zeWPiBZq/91u54ueAwfff8\ndNWuUN1NlQEAAAAoagRJ+XTnnXeqTJkykqSvvvrKYZ+zZ89q2bJlkqRevXrJx8enyOoDAFcyxmjC\ntx9q5pqFdsfLliqt756frroVa7ipMgAAAADuQJCUT6GhoZo1a5b8/f21ZMkS9evXT6tXr9axY8cU\nGRmpOXPm6I477tDp06dVv359TZ061d0lA0CBGGP09uJp+mz1ArvjYUGh+vb56apfqZabKgMAAADg\nLhZjjHF3ESXR3r179eGHH+qLL75QZmamXVu5cuU0atQoPffccwoJCcn32HFxcbm2XbhwQbVr15bk\nmtv2AYAjxhj95/tP9NGv/7M7HhYYou9emK5GVeq6qTIAAAAA+REXF6ewsDBJrskRvFxR1I1oxYoV\n+vXXX20hUlBQkNLT05WamqqzZ89q+fLluv3229WpU6d8j531PxgA3MEYo/eWfp4jRCodGKxFz08j\nRAIAAABuYCxtK4BHH31Uzz//vI4fP66XXnpJJ06cUHx8vJKTk7Vjxw716NFDmzZtUvfu3bVgwYKr\nDwgAxcikn2bqg59n2x0LCSilb0ZPVeOq9dxUFQAAAIDigKVt+TRv3jw9+OCDkqR33nlHL7/8co4+\nmZmZ6ty5s9auXavAwEAdOXIkX3duY2kbAHc5GXdGd745WAkpSbZjwf5BWjjmI7Wo0ciNlQEAAAAo\nCFcvbWNGUj59+eWXkqSAgACNGTPGYR9PT0+98sorkqTExER9++23DvvlpnTp0rn+CQ0NvYbqASBv\nlUuX18LRUxXsHyRJKuUXqAWjPiREAgAAACCJICnfDhw4IEmqV6+e/Pz8cu3XvHnzHOcAQElwS60m\nWjjmI1UJq6gFoz7ULbUau7skAAAAAMUEm23nk5fX5S/ZlXdqu1JGRkaOcwCgpGhRo5HC31okHy9v\nd5cCAAAAoBhhRlI+1alTR5K0f/9+XbhwIdd+mzZtsj3O2tMIAIqbTGvuoTghEgAAAIArESTlU58+\nfSRJ6enpeu211xz2SUhI0FtvvSXp8n5JPXv2LLL6AMBZs37/VgOnPKfEbBtrAwAAAEBeCJLyafjw\n4WrYsKEk6eOPP9a9996r3377TSdOnNCRI0c0b948tWrVSnv27JEkPffcc6pRo4Y7SwaAHL5at1iv\nLpikTQd26sFpLyghJdHdJQEAAAAoASzGGOPuIkqaY8eO6b777tPOnTvz7PfEE0/o448/lqenp8ue\n29W37QNw45mz/nuNm/tfu2N3NLxNC0d/JIvF4qaqAAAAABQGV+cI7AJdADVq1NCWLVu0ZMkSLVmy\nRBERETp//ry8vLxUqVIltW7dWo8++qhuvfVWd5cKAHbmbVyaI0Ty8fLWU10fJEQCAAAAcFX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          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.plot(radius, sizes, \"--o\")\n",
        "ax.set_xlabel(\"bend radius ($\\\\mu$m)\")\n",
        "ax.set_ylabel(\"minimum plane size ($\\\\mu$m)\")\n",
        "\n",
        "plt.show()"
      ],
      "id": "4abeb2b9"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "After defining an appropriate plane size that can handle large bend\n",
        "radii, we will analyze the losses as a function of the bend radius using\n",
        "two different resolution parameters: 10 and 50."
      ],
      "id": "660ed29b-a803-4e92-8df3-f9cf5d94f4b5"
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"b0fa608451ba4133a352ea38250f6a14\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:14:36 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6</span> tasks.                       \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:14:41 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.032</span> for the whole batch.                \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"73d9d20e69f049e1a9dd5443d4aeb20a\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:14:44 UTC </span>Batch complete.                                                    \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        }
      ],
      "source": [
        "# creating the mode simulation objects and running them\n",
        "mode_solvers = {}\n",
        "for r in radius:\n",
        "    mode_solver = mode_solver_SiN_wvg(\n",
        "        resolution=10,\n",
        "        npml=12,\n",
        "        nun_modes=5,\n",
        "        bend_radius=r,\n",
        "        bend_axis=1,\n",
        "        size=(20, 15),\n",
        "    )\n",
        "\n",
        "    mode_solvers[str(r)] = mode_solver\n",
        "\n",
        "batch_data = web.run(\n",
        "    simulation=mode_solvers,\n",
        "    folder_name=\"radiative_losses\",\n",
        "    path=\"radiative_losses_sin_radius_res10\",\n",
        ")"
      ],
      "id": "63218d0f"
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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OOCKHHnpohgwZkkmTJlXjpQGAzcStj93T5OBqhd+MfCC3PnZPhTsCAKAaaooq\n/hpywYIFOe200/Lggw8mSdq3b58OHTqs85hhw4Zlv/32q0Z7rEVdXV1qa2uTJDNnzkyXLl2auSMA\ntjRFUeQ9VwzOuGn/ets1+nTrlUf/+zb7XwEAbGSVzhGqsmF7kjz22GM57bTTMn369IbnFi5cmIUL\nF67zuKVLl27s1gCAkhvx0pgNCq6St/bAevylMTli94Mq1BUAANVQlfDqtddey7HHHpuFCxemRYsW\n6devX/bdd9906dIlLVqs+8rFHj16VKNFAKDEbn/8vsrUeeJ+4RUAwCamKuHV9773vSxcuDDdu3fP\n0KFDXQYIADTJhDcqs1fmhOkTK1IHAIDqqcqG7c8++2yS5IorrhBcAQBNNm/RgsrUWVyZOgAAVE9V\nwquWLVsmSfbee+9qvBwAsJnp2G7dN3hpdJ22lakDAED1VCW8WrHaatq0adV4OQBgM9Ora8/K1Nl+\nx4rUAQCgeqoSXl144YVp165dfvnLX1bj5QCAzczgw0+oTJ3Djq9IHQAAqqcq4VXv3r1z880358EH\nH8yXv/zlLFu2rBovCwBsJo7oe2D6dNt5g2r06dYrh/c9sEIdAQBQLVW52+DQoUOzePHiXHTRRbn2\n2mtzxx135NRTT83uu++eDh3WvffEoEGDUltbW402AYCSqqmpyYUDzs4lt179tmtcOGBwampqKtgV\nAADVUFMURbGxX+Tggw/O008//baOffLJJ3PwwQdXuCOaoq6uriFAnDlzZrp06dLMHQGwJSqKIhfd\n9I3cOfKBJh97Zr9B+f6HLxdeAQBUQaVzhKpcNggAsKFqamoy5LzLcka/QU067sx+g/Kd8y4TXAEA\nbKKqctngsGHDsnTp0rd1bOfOnSvbDACwyWrdslWu+/DlObT3vrl+2O0ZN23CWuf26dYrFw4YnHP6\nnyy4AgDYhFXlskE2bS4bBKCMiqLI4y+Nye1P3J8J0ydm3uIF6di2Q3ptv2POPvyEHNbnAKEVAEAz\nqHSOUJWVVwAAlVZTU5Mjdj8oR+x+UHO3AgDARmTPKwAAAABKq2rh1X/+53/mvPPOy5w5c9Y79/vf\n/37OPffct32HQgAAAAA2D1UJr0aPHp3/+7//y0svvZRtttlmvfO33nrr3HrrrfnJT35She4AAAAA\nKKuqhFe/+93vkiSnnnpqo+afdtppqxwHAAAAwJapKuHVK6+8kiTp06dPo+Z36tQp2223XWbOnJlZ\ns2ZtxM4AAAAAKLOqhFdTpkxJknTr1q3Rx3Tv3n2VYwEAAADY8lQlvOrQoUOSpK6urtHHzJw5M0nS\npk2bjdITAAAAAOVXlfCqV69eSZJHHnmkUfNfeumlTJ48Oa1atUqPHj02YmcAAAAAlFlVwquBAwcm\nSX76059mwoQJ65xbFEUuvfTSJMlhhx3WsGoLAAAAgC1PVcKrD3zgA9lxxx0zd+7cHH300Xn00UfX\nOG/GjBn50Ic+1HCXwc997nPVaA8AAACAkmpVjRdp06ZNfvGLX+S4447Lq6++miOPPDJ77713+vXr\nl2233TaLFi3KCy+8kOHDh2fRokVJkrPPPjsf+MAHqtEeAAAAACVVUxRFUa0X+8Mf/pAPfehDmT17\n9jrnXXDBBfnBD36Qtm3bVqkz1qWuri61tbVJ3tpIv0uXLs3cEQAAAFBWlc4RqnLZ4AonnXRSXnnl\nlVxxxRU55JBDGvazatWqVXr16pWPfOQjGTlyZH76058KrgAAAACo7sqrNVmyZElat26dmpqa5myD\ndbDyCgAAAGis0q+8uu222/LCCy80en6bNm0EVwAAAACsUcXDq+985zvZc889s8cee+TLX/5yRo4c\nmWZe3AUAAADAJqri4dVee+2VFi1a5MUXX8y3vvWtHHbYYenRo0cuvPDCDB06NEuWLKn0SwIAAACw\nmdooe15Nnz49f/jDH3L33Xdn2LBhWbRoUcPY1ltvnfe///05+eSTc/zxx6dTp06VfnkqzJ5XAAAA\nQGNVOkfY6Bu2z58/Pw8++GDuvvvu3H///amrq2sYa926dY466qiccsopOfnkk/OOd7xjY7bC2yS8\nAgAAABprkwuvVrZs2bIMHz4899xzT+6555689tpr/6+RmpocfPDBOfnkk3PKKafkne98Z7XaYj2E\nVwAAAEBjbdLh1b8bM2ZM7r777tx999157rnnVhnbbbfdcsopp+SUU07JYYcdlhYtKr49F40kvAIA\nAAAaa7MKr1b26quvNgRZI0aMyPLlyxvGtt9++/z1r39N3759m7HDcli+fHn+/Oc/57bbbsuYMWMy\nceLEdOrUKf369cvnPve5vOtd76r4awqvAAAAgMbabMOrlc2YMSP33ntv7r777jz88MNZuHBhnnzy\nyRx88MHN3Vqzu/766/PJT35yjWMtWrTIr3/965x11lkVfU3hFQAAANBYlc4RSnkt3nbbbZfzzz8/\n99xzT2bMmJHf//736dGjR3O3VQotW7bMsccemxtvvDF/+9vfMn369Dz55JM54YQTUl9fn0996lNZ\nsmRJc7cJAAAAUBGlXHlF0y1dujR77rlnXnnllTzzzDPZd999K1bbyisAAACgsTbLlVfLli3LnDlz\nIkd7+1q3bp0999wzSdKxY8dm7gYAAACgMjZqeDVnzpyMGjUqf/vb3zJ37tzVxu+4444cdthhad++\nfTp16pT27dtn4MCB+dOf/rTRelq6dGmeeuqp/OhHP8qHP/zh7LnnnuncuXM6d+6ciy66qEm1pk+f\nnq9//es59NBD8453vCO77rprjjvuuPzyl79MfX39RnoHa1ZXV5fHHnss+++/f3bdddeqvjYAAADA\nxtJqYxRdtmxZLrnkkvz4xz9u2H+pbdu2ueiii/Ktb30rNTU1ufzyy3PllVeuctzixYszbNiwDBs2\nLEOGDMnnPve5ivc2cODAPProo2scW7BgQaPr/OUvf8kZZ5yRGTNmrPL8q6++moceeig/+9nPct99\n91XlErv6+vqcf/75mT9/fn784x9v9NcDAAAAqJaNsvLqP/7jP/L9739/lY3DFy9enGuuuSZXXXVV\nHnjggYbgaquttsohhxySd7/73dlxxx0b5l9yySV58sknK95by5Ytc9BBB+VTn/pUbrzxxowZM6bJ\nNcaNG5dTTjklM2bMSPfu3XPrrbdm4sSJeeGFF3LppZemRYsWefzxx/OBD3xgjZdCfuMb30jHjh0b\n/XXrrbeutZf6+vpccMEFuffee/Pzn/88/fr1a/L7AQAAACiriq+8Gjt2bG644YYkyU477ZTBgwen\nS5cuefTRRzN06ND8+Mc/zn777Zckueyyy/LVr3417du3bzj+z3/+cz74wQ/m9ddfzzXXXJPf/OY3\nFe3vT3/6U1q0+H+Z3aJFi5pc45JLLsns2bPTvn37PPLII9l9990bxq666qpst912ufjiizN8+PDc\neuutOffcc1c5fvHixZk/f36jX2/p0qVrff7cc8/NXXfdlRtvvDHnnXdek98LAAAAQJlV/G6DV1xx\nRb7+9a9n5513zpgxYxp2l0+SL3zhC7n22muTJMcff3zuu+++Nda45557csopp2SbbbbJrFmzUlNT\nU8kWV7Fo0aKG8OxjH/tYQ/C2Nq+++mrDnlKf+9znMmTIkNXm1NfXZ5dddslrr72Wgw46KE899dQq\n40uWLFllVdr6tGvXLq1arZozzp8/P6eddlr+9Kc/5aabbso555zT6HpN5W6DAAAAQGOV/m6Df/vb\n35Ik//mf/7lKcJUkl156aUMIc/bZZ6+1xoknnpitt946c+bMyaRJkyrd4ga5++67Gx6v7T20aNEi\nZ511VpLk6aefzsSJE1cZb9OmTZMuG/z34Kquri4DBw7MsGHDcuutt27U4AoAAACgOVU8vFqxgfne\ne++92lhtbW26d++eJNlll13W3lSLFtl5552TvBXUlMno0aOTvLUa6oADDljrvMMPP7zhcSX37po2\nbVqOPPLIPP3007n99tsbQrINVVdXt9avWbNmVeQ1AAAAAJqq4uHV4sWLkyRdu3Zd4/iK59u0abPO\nOm3btk2SJl1eVw3PP/98kmTnnXdebUXUylZcWrjyMZVw/fXX57nnnsvy5cvz4Q9/eI0rtR588MEm\n162trV3r18rvBQAAAKCaKr5h+/q20NqY+1dVwxtvvJEk2WGHHdY5r1u3bqsdUwkr/vvW19evddP3\nZcuWVez1AAAAAJpTxcOrzd3cuXOTZJU7JK7JyuMrjqmEyy67LJdcckmjX7uxZs6cudaxWbNmWX0F\nAAAANAvh1du0vhVkK49X8oaObdq0We8ll2+HOwgCAAAAZbTRwqvzzz8/W2211WrPv/DCC+sc//d5\nZbPVVltl7ty5WbRo0TrnLVy4sOFxx44dN3ZbAAAAAJuljRZe/eMf/9ig8bLadtttM23atPXuY7Xy\n+Lbbbrux2wIAAADYLFU8vOrRo0dmzJhRsXor7jpYFnvssUfGjh2bCRMmpL6+Pi1arPmGja+++uoq\nxwAAAADQdBUPr/7whz9UumSpHHjggfntb3+b+fPnZ+zYsdlnn33WOG/UqFENjw844IBqtQcAAACw\nWVnzsiHW6uSTT254fNddd6113oqxPffcM3379t3ofQEAAABsjoRXTfTOd74z73nPe5IkP/zhDzNt\n2rTV5vz617/O888/nyT5j//4j6r2BwAAALA5EV69Dd/5znfSpk2bzJw5MwMGDMjjjz+eoiiycOHC\n/PSnP83HP/7xJMnee++dCy+8sJm7BQAAANh01RRFUVSq2L/+9a8sXLiwUuWSJL169Uq7du0qVu+W\nW27Jf/3Xf63y3OzZs5Mkbdq0Sfv27Rue79ixYyZNmrTGOnfccUc+8pGPZNGiRQ3HLl26NCv+c/bu\n3Tt//vOfs9NOO1Ws9+ZSV1eX2traJMnMmTPTpUuXZu4IAAAAKKtK5wgV3bD9tNNOy9NPP13Jknny\nySdz8MEHV6ze4sWLG8Kqf7dkyZIsWbKk4ftly5attc5ZZ52VffbZJ9/61rcydOjQvPHGG2nZsmV2\n2223DB48OF/4whey1VZbVaxvAAAAgC1Rxe82WHYf+tCHcvrppzdqbk1NzTrH99prr9x0001J3grF\nWrdunRYtXIkJAAAAUCkVDa/+7//+L3PmzFnr+B//+McMGTIkPXv2zFlnnZX9998/Xbp0yaJFi/LK\nK6/koYceyp/+9KccfPDB+drXvpZ27dpl9913r2SLadOmTdq0aVPRmknStm3bitcEAAAA2NJVdM+r\ndfnud7+bz3/+87nkkkty1VVXpXXr1mucN3z48Jx66qnp3bt3HnnkEZfelYA9rwAAAIDGqnSOUJVr\n3P7+97/n4osvzgknnJBrrrlmrcFVkhx55JH55S9/mSeffDKXXnppNdoDAAAAoKSqEl7dcMMNKYoi\n559/fqPmn3DCCenatWt+8YtfrLKBOgAAAABblqqEV88//3ySpFu3bo2aX1NTk27dumX+/Pl57bXX\nNmZrAAAAAJRYVcKr5cuXJ0leeeWVRs1funRp/vWvfyVJ6uvrN1pfAAAAAJRbVcKrvfbaK0ly3XXX\nZdmyZeud/7Of/Sxz5sxJhw4dstNOO23s9gAAAAAoqaqEVx/60IeSJE899VROOumkTJ48eY3zli9f\nnuuuuy6f+cxnkiRnnXVW2rVrV40WAQAAACihmqIoimq80Gc/+9l8//vfT5K0atUqRx55ZPbff/90\n6dIlixYtyquvvpo//elPef3115MkO+20U5588slsv/321WiPdaj0LS4BAACAzVelc4RWlWiqMb77\n3e+mY8eOufrqq7Ns2bIMGzYsw4YNW+PcQw45JLfffrvgCgAAAGALV5XLBpO37iB45ZVXZuzYsfnc\n5z6XfffdN23btn2riRYt0qNHj5x66qm566678vjjj2eXXXapVmsAAAAAlFTVLhtcm8WLF6dNmzap\nqalpzjZYB5cNAgAAAI21yV42uDYrVl8BAAAAwL+r2mWDAAAAANBUwisAAAAASqui4dXXvva1PPPM\nM5UsmSSZO3durrzyyjz//PMVrw0AAABAeVU0vHrggQdywAEH5IwzzsjTTz+9wfVmzJiRb33rW9ll\nl11y+eWXZ/78+RXoEgAAAIBNRUXDq09+8pPp0qVL7rrrrhx88MF55zvfmauvvjovvvhiGntTw7q6\nutx11105+eST06NHj3z5y1/Om2++mTPOOCO77bZbJdsFAAAAoORqisamSo1UV1eXK664Iv/3f/+X\npUuXNjxfW1ubQw45JHvttVe23Xbb1NbWpm3btpk5c2ZmzpyZ1157LaNHj864ceNWCbr69euXIUOG\n5LDDDqtkmzRBpW9xCQAAAGy+Kp0jVDy8WmHy5Mn56U9/mhtuuCFTpkxp0rGtW7fOqaeemk9+8pM5\n6qijNkZ7NIHwCgAAAGisTSa8WmHZsmX505/+lEceeSSPPvpoxowZkyVLlqzaRE1NevXqlSOPPDJH\nHnlkBg0alO23335jtkUTCK8AAACAxtrkwqs1qauryxtvvJElS5Zku+22y3bbbZdWrVpVuw0aSXgF\nAAAANFalc4RmSYy6dOkiAAEAAABgvSp6t0EAAAAAqCThFQAAAAClJbwCAAAAoLSEVwAAAACUlvAK\nAAAAgNISXgEAAABQWsIrAAAAAEpLeAUAAABAaQmvAAAAACgt4RUAAAAApdWquRtYYdmyZXnhhRfS\nqlWr9O3bNy1ayNUAAAAAtnRVS4huvvnm/PCHP8zcuXNXG/vd736XHj16ZJ999smee+6Z3r1759FH\nH61WawAAAACUVE1RFMXGfpHXXnstvXr1yk477ZRXX301NTU1DWPPP/989t9//yxZsmSVYzp27Ji/\n//3v6d2798Zuj/Woq6tLbW1tkmTmzJnp0qVLM3cEAAAAlFWlc4SqrLy68847UxRFzjrrrFWCqyS5\n5pprsmTJkrRv3z7XXHNNfvGLX2SnnXbKvHnz8s1vfrMa7QEAAABQUlUJr/7xj38kSd75zneu8nx9\nfX1+//vfJ0m+8pWv5JJLLsn555+fm2++OUly9913V6M9AAAAAEqqKuHV1KlTkyQ9e/Zc5flnnnkm\ns2bNSpKcccYZDc8feeSRqa2tTV1dXSZPnlyNFgEAAAAooaqEV7Nnz06StGq16s0NR4wYkSTZYYcd\n0rdv31XGunfvniR58803q9AhAAAAAGVUlfCqU6dOSZKJEyeu8vywYcOSJP3791/tmIULFyZJOnTo\nsJG7AwAAAKCsqhJe7b333kmSO+64o+G56dOn58EHH0ySHH300asdM23atCRJjx49qtAhAAAAAGVU\nlfDq9NNPT5Lce++9OfPMMzNkyJAcc8wxWbRoUdq0aZNTTz11lfnTp0/PggUL0r17dyuvAAAAALZg\nVQmv+vXrlw9/+MNJkjvvvDMXX3xxnn322STJJZdckm7duq0y/+GHH06SDBw4sBrtAQAAAFBSrdY/\npTJuuOGG7LHHHrnpppsyderU7LrrrvnEJz6RCy+8cLW5Ky4nfN/73let9gAAAAAooZqiKIrmbuLf\nzZs3L8uWLcvWW2+dli1bNnc7W7y6urrU1tYmSWbOnJkuXbo0c0cAAABAWVU6R6jayqum6NixY3O3\nAAAAAEAJlCa8WrZsWV544YW0atUqffv2TYsWVdmOCwAAAIASq1pCdPPNN+eHP/xh5s6du9rY7373\nu/To0SP77LNP9txzz/Tu3TuPPvpotVoDAAAAoKSqsufVa6+9ll69emWnnXbKq6++mpqamoax559/\nPvvvv3+WLFmyyjEdO3bM3//+9/Tu3Xtjt8d62PMKAAAAaKxK5whVWXl15513piiKnHXWWasEV0ly\nzTXXZMmSJWnfvn2uueaa/OIXv8hOO+2UefPm5Zvf/GY12gMAAACgpKoSXv3jH/9Ikrzzne9c5fn6\n+vr8/ve/T5J85StfySWXXJLzzz8/N998c5Lk7rvvrkZ7AAAAAJRUVcKrqVOnJkl69uy5yvPPPPNM\nZs2alSQ544wzGp4/8sgjU1tbm7q6ukyePLkaLQIAAABQQlUJr2bPnp0kadVq1ZsbjhgxIkmyww47\npG/fvquMde/ePUny5ptvVqFDAAAAAMqoKuFVp06dkiQTJ05c5flhw4YlSfr377/aMQsXLkySdOjQ\nYSN3BwAAAEBZVSW82nvvvZMkd9xxR8Nz06dPz4MPPpgkOfroo1c7Ztq0aUmSHj16VKFDAAAAAMqo\nKuHV6aefniS59957c+aZZ2bIkCE55phjsmjRorRp0yannnrqKvOnT5+eBQsWpHv37lZeAQAAAGzB\nqhJe9evXLx/+8IeTJHfeeWcuvvjiPPvss0mSSy65JN26dVtl/sMPP5wkGThwYDXaAwAAAKCkWq1/\nSmXccMMN2WOPPXLTTTdl6tSp2XXXXfOJT3wiF1544WpzV1xO+L73va9a7QEAAABQQjVFURTN3cS/\nmzdvXpYtW5att946LVu2bO52tnh1dXWpra1NksycOTNdunRp5o4AAACAsqp0jlC1lVdN0bFjx+Zu\nAQAAAIASqMqeVwAAAADwdjTLyqu5c+fmiSeeyAsvvJBZs2alffv26dGjRw477LDsuuuuzdESAAAA\nACVU1fBq9uzZ+cpXvpIbb7wxCxYsWOOc/v3759vf/nYOO+ywarYGAAAAQAlV7bLByZMn58ADD8yP\nfvSjtQZXSfLYY4/lPe95T375y19WqzUAAAAASqoq4VVRFDnttNMyfvz4JMnAgQNz66235oUXXsgb\nb7yRiRMn5pFHHsnFF1+crbbaKsuWLcsFF1yQMWPGVKM9AAAAAEqqpiiKYmO/yP33358TTjghNTU1\nuf7663PBBResde6ECRNyzDHH5OWXX85JJ52Ue+65Z2O3x3pU+haXAAAAwOar0jlCVVZe3XvvvUmS\nD33oQ+sMrpKkV69eufnmm5Mkf/zjH7N48eKN3h8AAAAA5VSV8Orll19Okpx55pmNmn/YYYelZ8+e\nWbRoUSZNmrQxWwMAAACgxKoSXi1cuDBJ0qlTp0Yf07lz5yRZ5+buAAAAAGzeWlXjRbbbbrskydix\nY3PEEUesd/7ChQsbNnfv2rXrRu0NAAA2BUVRZMRLY3L74/dlwhuTMm/RgnRs1yG9uvbM2YefkMP7\nHpiamprmbhMAKq4q4VW/fv3yhz/8IUOGDMk555yTrbbaap3zhwwZkgULFqRXr17p1q1bNVoEAIBS\nKooitz52T64fdnvGTZuw2vhT45/LXaOGpk+3XrlwwOCc0/9kIRYAm5WqXDZ47rnnpm3btnnxxRcz\nYMCA/POf/1zjvAULFuRrX/taLr/88iTJxz/+8Wq0BwAApbR0+bJcdNM3csmtV68xuFrZuGkTcsmt\nV+eim76RpcuXVadBAKiCmqIoimq80Le//e186Utfavj+4IMPzoEHHpguXbpk8eLFefnllzN8+PDM\nnTs3SbLffvvl8ccfT4cOHarRHutQ6VtcAgCwfkVR5KKbvpE7Rz7Q5GPP7Dco3//w5VZgAdAsKp0j\nVOWywST54he/mPr6+lx++eVZtmxZnnrqqTz11FNrnHvUUUfl9ttvF1wBALDFuvWxe95WcJUkvxn5\nQA7pvW/OffcplW0KAJpBVS4bXOHLX/5ynn/++Vx88cXZb7/90q5du7eaaNEiPXr0yGmnnZZ77rkn\nw4YNyw477FDN1gAAoDSKosj1w27boBrXD7s9VbrIAgA2qqqtvFpht912y7XXXtvw/eLFi9OmTRtL\nmgEA4P834qUxGTftXxtUY9y0CXn8pTE5YveDKtQVADSPqq68WpO2bduuMbgaPHhw9t5774wdO7YZ\nugIAgOZz++P3VabOE/dXpA4ANKdmD6/W5uWXX87YsWOzcOHC5m4FAACqasIbkypTZ/rEitQBgOZU\n2vAKAAC2VPMWLahMncWVqQMAzUl4BQAAJdOxXWXuut2xrbt3A7DpE14BAEDJ9OraszJ1tt+xInUA\noDkJrwAAoGQGH35CZeocdnxF6gBAcxJeAQBAyRzR98D06bbzBtXo061XDu97YIU6AoDmI7wCAICS\nqampyYUDzt6gGhcOGJyampoKdQQAzUd4BQAAJXRO/5NzRr9Bb+vYM/sNyjn9T65wRwDQPFpVuuDT\nTz+duXPnbnCdStQAAIBNVU1NTYacd1mS5M6RDzT6uDP7Dcp3zrvMqisANhsVD68uvPDCPP3005Uu\nCwAAW5zWLVvlug9fnkN775vrh92ecdMmrHVun269cuGAwTmn/8mCKwA2KxUPrwAAgMqpqanJue8+\nJef0PzmPvzQmtz9xfyZMn5h5ixekY9sO6bX9jjn78BNyWJ8DhFYAbJYqHl5ddtllmT59esXq7bzz\nht1lBQAANgc1NTU5YveDcsTuBzV3KwBQVRUPr0499dRKlwQAAABgC+VugwAAAACUlvAKAAAAgNIS\nXgEAAABQWsIrAAAAAEpLeAUAAABAaQmvAAAAACgt4RUAAAAApSW8AgAAAKC0hFcAAAAAlJbwCgAA\nAIDSEl4BAAAAUFrCKwAAAABKS3gFAAAAQGkJrwAAAAAoLeEVAAAAAKUlvAIAAACgtIRXAAAAAJSW\n8AoAAACA0hJeAQAAAFBawisAAAAASkt4BQAAAEBpCa8AAAAAKC3hFQAAAAClJbwCAAAAoLSEVwAA\nAACUlvAKAAAAgNISXgEAAABQWsIrAAAAAEpLeAUAAABAaQmvAAAAACgt4dVm4Gc/+1n22GOP7LHH\nHnn11Vebux0AAACAimnV3A2wYSZPnpxLLrkk8+fPz/Lly7N48eLmbgkAAACgYqy82sR9+tOfzi67\n7JKBAwc2dysAAAAAFSe82oTdfffduffee3PDDTekVSuL6AAAAIDNj/BqEzVnzpx8+tOfzmc+85kc\nfPDBzd0OAAAAwEaxRS7XmTZtWkaNGpXRo0dn9OjRmTp1apLktNNOyxVXXNHoOgsWLMivf/3rDB06\nNJMmTUrbtm3Tt2/fDB48eKNfxnfppZemTZs2+cY3vrFRXwcAAACgOW1x4dVJJ52Ue++9d41j/fr1\na3SdZ599NqeddlpefvnlVZ7/61//mp///Oc5/fTTc/PNN6d9+/Yb1O+ajBw5Mj/5yU/y0EMPpUOH\nDhWvDwAAAFAWW1x4NXPmzHTr1i3vete7csghh2T//ffPiSee2KQaU6ZMyXHHHZepU6dm6623zle/\n+tW85z3vyfz583PTTTfllltuyV133ZWiKHLXXXetdvz3v//9/PjHP2706/3v//5vPvCBDyRJli5d\nmgsuuCDnnXeeTdoBAACAzd4WF17de++96dKlS8P3ixYtanKNSy+9NFOnTk2rVq3y8MMP59BDD20Y\nGzBgQHr06JFvfetb+e1vf5v77rsvJ5xwwirHv/HGG3nxxRcb/XqzZ89ueHzNNddk+vTpGTJkSJP7\nBgAAANjU1BRFUTR3E81p0aJFDZf2fexjH8sNN9ywzvlTp05Nz549U19fnwsuuCA//elPV5uzZMmS\n7Ljjjpk+fXre/e5359FHH11lfMaMGZkxY0aje+zevXs6deqUJOnUqVNqamrSrVu3VeZMmjQp8+fP\nzy677JI2bdpk2LBhecc73tHo11iXurq61NbWJnlr5drK4R8AAADAyiqdI2xxK6821N133536+vok\nyXnnnbfGOW3atMlZZ52VH/zgBxkxYkRef/317LDDDg3j2223Xbbbbru39fqLFy/O4sWLV1mNtbJX\nX301yVuXFwIAAABs6oRXTfT4448nSVq3bp1DDjlkrfP69++fH/zgB6mvr8+oUaNy0kknVeT1n332\n2YbwbGWf+tSn8pe//CUPPPBAdtlllyavuqqrq1vr2KxZs5raJgAAAEBFCK+a6Pnnn0+S7LTTTmnb\ntu1a5/Xp02eVYyoVXvXt23eNz2+11VZJkl122SV77LFHk+uuWM4HAAAAUCYtmruBTc20adOSJD16\n9FjnvO7du692DAAAAABNY+VVE82bNy9JGjZ5X5sOHTqsdszG9JOf/CTz5s3Lrrvu+raOnzlz5lrH\nZs2a9bbrAgAAAGwI4VUTLV++PEnSsmXLdc5beXzZsmUbtack6dmz5wYd7w6CAAAAQBm5bLCJVuwt\ntXDhwnXOW3m8Y8eOG7UnAAAAgM2V8KqJVqxQWtdldv8+3rlz543ZEgAAAMBmS3jVRCvu9jdhwoR1\nzlt5fPfdd9+IHQEAAABsvoRXTbT//vsnSebMmZMXX3xxrfNGjx692jEAAAAANI3wqolOPPHEhsf3\n3HPPWuetGOvVq1f23nvvjd4XAAAAwOZIeNVEBx98cA444IAkyfe///3Mnj17tTlDhw7NU089lST5\n+Mc/XtX+AAAAADYnwqu34dprr02LFi0yZcqUnHjiiavsb/XAAw/k3HPPTZLstNNO+exnP9s8TQIA\nAABsBmqKoiiau4lq+t3vfpevfe1rDd8XRZF//vOfSd66k2CPHj0axjp06LDK3lUru+666/LZz342\nRVGkRYsW2WmnnTJ//vy88cYbSZLtttsujzzyyGZxyWBdXV1qa2uTvHUXxRV3XAQAAAD4d5XOEVpV\noqlNycyZMzN27Ng1jtXV1aWurq7h+6222mqtdS666KLst99++Z//+Z/85S9/aVh9tc022+SMM87I\nlVdemW7dulW0dwAAAIAtzRa38qquri6TJ09u1NyWLVtmzz33XO+8RYsWZcqUKWnbtm26deuWli1b\nbmibpWLlFQAAANBYVl5toC5dulQ8fGnXrl123XXXitYEAAAAwIbtAAAAAJSY8AoAAACA0hJeAQAA\nAFBawisAAAAASkt4BQAAAEBpCa8AAAAAKC3hFQAAAAClJbwCAAAAoLSEVwAAAACUlvAKAAAAgNIS\nXgEAAABQWsIrAAAAAEpLeAUAAABAaQmvAAAAACgt4RUAAAAApSW8AgAAAKC0hFcAAAAAlJbwCgAA\nAIDSEl4BAAAAUFrCKwAAAABKS3gFAAAAQGkJrwAAAAAoLeEVAAAAAKUlvAIAAACgtIRXAAAAAJSW\n8AoAAACA0hJeAQAAAFBawisAAAAASkt4BQAAAEBpCa8AAAAAKC3hFQAAAAClJbwCAAAAoLSEVwAA\nAACUlvAKAAAAgNISXgEAAABQWsIrAAAAAEpLeAUAAABAaQmvAAAAACgt4RUAAAAApSW8AgAAAKC0\nhFcAAAAAlJbwCgAAAIDSEl4BAAAAUFrCKwAAAABKS3gFAAAAQGkJrwAAAAAoLeEVAAAAAKUlvAIA\nAACgtIRXAAAAAJSW8AoAAACA0hJeAQAAAFBawisAAAAASkt4BQAAAEBpCa8AAAAAKC3hFQAAAACl\nJbwCAAAAoLSEVwAAAACUVqvmbgAAAADWpCiKjHhpTG5//L5MeGNS5i1akI7tOqRX1545+/ATcnjf\nA1NTU9PcbQIbmfAKAACAUimKIrc+dk+uH3Z7xk2bsNr4U+Ofy12jhqZPt165cMDgnNP/ZCEWbMaE\nVwAAAJTG0uXL8vlbrsqdIx9Y79xx0ybkkluvzqhXns2Q8y5L65b+iQubI3teAQAAUApFUTQ6uFrZ\nnSMfyMW3XJWiKDZSZ0BzEl4BAABQCrc+dk+Tg6sVfjPygdz62D0V7ggoA+EVAAAAza4oilw/7LYN\nqnH9sNutvoLNkPAKAACAZjfipTEZN+1fG1Rj3LQJefylMRXqCCgL4RUAAADN7vbH76tMnSfur0gd\noDyEVwAAADS7CW9Mqkyd6RMrUgcoD+EVAAAAzW7eogWVqbO4MnWA8hBeAQAA0Ow6tutQmTptK1MH\nKA/hFQAAAM2uV9eelamz/Y4VqQOUh/AKAACAZjf48BMqU+ew4ytSBygP4RUAAADN7oi+B6ZPt503\nqEafbr1yeN8DK9QRUBbCKwAAAJpdTU1NLhxw9gbVuHDA4NTU1FSoI6AshFcAAACUwjn9T84Z/Qa9\nrWPP7Dco5/Q/ucIdAWUgvAIAAKAUampqMuS8y5ocYJ3Zb1C+c95lVl3BZqpVczcAAAAAK7Ru2SrX\nffjyHNp731w/7PaMmzZhrXP7dOuVCwcMzjn9TxZcwWaspiiKormboNzq6upSW1ubJJk5c2a6dOnS\nzB0BAABbgqIo8vhLY3L7E/dnwvSJmbd4QTq27ZBe2++Ysw8/IYf1OUBoBSVU6RzByisAAABKqaam\nJkfsflCO2P2g5m4FaEb2vAIAAACgtIRXAAAAAJSW8AoAAACA0hJeAQAAAFBawisAAAAASkt4BQAA\nAEBpCa8AAAAAKC3hFQAAAAClJbwCAAAAoLSEVwAAAACUlvAKAAAAgNISXgEAAABQWsIrAAAAAEpL\neAUAAABAaQmvAAAAACgt4RUAAAAApSW8AgAAAKC0hFcAAAAAlJbwCgAAAIDSEl4BAAAAUFrCKwAA\nAABKS3gFAAAAQGkJrwAAAAAoLeEVAAAAAKUlvAIAAACgtIRXAAAAAJSW8AoAAACA0hJeAQAAAFBa\nwisAAAAASkt4BQAAAEBpCa8AAAAAKC3hFQAAAAClJbwCAAAAoLSEVwAAAACUlvAKAAAAgNISXgEA\nAABQWsIrAAAAAEpLeAUAAABAaQmvAAAAACgt4RUAAAAApSW8AgAAAKC0hFcAAAAAlJbwCgAAAIDS\natXcDbBhli5dmldffTVFUWS33XZLy5Ytm7slAAAAgIqx8moTNX/+/HzhC19I165ds/vuu2ePPfZI\nbW1tLr/88ixdurS52wMAAACoiJqiKIrmboKmWbhwYY455piMGDEiSbLLLrukU6dOeeGFF7Jo0aJM\nnTo13bp1q9jr1dXVpba2Nkkyc+bMdOnSpWK1AQAAgM1LpXMElw1ugv77v/87I0aMSJ8+fXLHHXfk\ngAMOSJLMmzcv1113Xdq0adPMHQIAAABUhpVXm5i5c+eme/fuWbRoUZ599tnstddeG/01rbwCAAAA\nGsvKqwqbPHlypk6dmiTp2rVrdt555ybXmDNnTiZPnpy2bdumZ8+eG3Xl0yOPPJL58+fn/e9/f/ba\na6/MmTMn48ePz3bbbZeePXtutNcFAAAAaA5b3Ibto0aNytVXX50PfOADecc73pGePXvmXe96V971\nrnflG9/4RpNq/fGPf0z//v3TuXPn7LXXXundu3e6dOmSc889N5MmTdoo/f/jH/9IkrznPe/JN7/5\nzeywww454IADsuOOO2afffbJo48+ulFeFwAAAKA5bHErry6++OKGjc6TpHv37g0rr5ri29/+dr70\npS8lSVq1apXevXtn/vz5mTRpUm699dbcf//9+fOf/9ywH9XKJk2a1KRwq3fv3unatWuSt5beJcmD\nDz6Y4cOHZ7vttkufPn0yfvz4/OMf/8ixxx6bxx9/PAceeGCT3xMAAABA2Wxx4VW/fv3Sv3//HHLI\nITnkkEOy3XbbpX379k2q8dBDD+XLX/5ykmTAgAG5+eab06NHjyTJn//85wwePDhvvPFGTjzxxDz/\n/PPZeuutVzn+Jz/5Sb75zW82+vVuvPHGfOQjH0nyVlCWJMOHD8+QIUPy2c9+NjU1NZk3b14+8YlP\n5LbbbssVV1yRe+65p0nvCQAAAKCMtrjw6tprr13l+0WLFjXp+KIo8oUvfCFFUWTHHXfM73//+1XC\nqaOPPjq//vWvc8wxx2Ty5MkZMmRI/vu//3uVGjvuuGMOPfTQRr/milVXSbLtttsmSQ4++OB87nOf\na3i+Y8eO+elPf5rf/OY3eeyxx5r0ngAAAADKaosLrzbU6NGj89xzzyVJPvOZz6y2qipJBg4cmEMP\nPTSjRo3KL37xi9XCqwsvvDAXXnjh23r9FXcXXLHSa2UdO3ZMp06dMm/evLdVGwAAAKBstrgN2zfU\nfffd1/D4pJNOWuu8FWOvvfZann322Yq9/nve8560a9cuI0eOzKxZs1YZGzlyZGbOnJldd921yXXr\n6urW+vXvrwMAAABQLVZeNdEzzzyTJOnUqVP69Omz1nnvete7Vjlm3333rcjrd+zYMZ/4xCdy3XXX\n5aijjsoll1ySd7zjHXn22Wdz1VVXJUnOO++8Jtetra2tSH8AAAAAlSS8aqKXXnopSdKrV691zlt5\nfMUxlXLVVVflySefzBNPPLFaUDVo0KB84QtfqOjrAQAAADQX4VUT1dXVJVn/SqUuXbqsdkylbLXV\nVhk+fHh+8YtfZOjQoZk5c2a6d++ek08+OYMHD06LFk2/GnTmzJlrHZs1a9bbuhQRAAAAYEMJr5po\n/vz5SZJ27dqtc1779u1XO6aSWrduvUEbv/+7lcM2AAAAgLKwYXsTtWr1Vt63fPnydc5beXzFMQAA\nAAA0jfCqiTp27JgkWbBgwTrnrTy+4hgAAAAAmkZ41UQ9evRIkkyZMmWd81Ye7969+0btCQAAAGBz\nJbxqoj333DNJMnHixCxatGit88aNG9fweK+99trofQEAAABsjoRXTXT44YcnSZYuXZpRo0atdd6j\njz6aJGnRokUOPfTQqvQGAAAAsLkRXjXRKaeckpYtWyZJbrrppjXOWbRoUX7zm98kSd797nena9eu\nVesPAAAAYHMivGqiHXbYIR/+8IeTJDfffHMee+yx1eZcdtllmTFjRpLky1/+clX7AwAAANictGru\nBqptxowZmTBhQsP3S5YsWWXsqaeeavi+ZcuWOeCAA1ar8c1vfjMPP/xwJk6cmOOOOy5f/OIXc+SR\nR2bevHm56aabcueddyZJzj777Bx33HEb780AAAAAbOZqiqIomruJarrhhhtywQUXNGruVlttlXnz\n5q1x7Pnnn89pp52W559/fo3j55xzTn7+85+nbdu2b7vXsqirq0ttbW2SZObMmenSpUszdwQAAACU\nVaVzhC1u5VXXrl1z0EEHNWpuhw4d1jq25557ZsyYMbnzzjszdOjQTJo0KW3bts3uu++ewYMHp3//\n/pVqGQAAAGCLtcWtvKLprLwCAAAAGqvSOYIN2wEAAAAoLeEVAAAAAKUlvAIAAACgtIRXAAAAAJSW\n8AoAAACA0hJeAQAAAFBawisAAAAASkt4BQAAAEBpCa8AAAAAKC3hFQAAAAClJbwCAAAAoLSEVwAA\nAACUlvAKAAAAgNISXgEAAABQWsIrAAAAAEpLeAUAAABAaQmvAAAAACgt4RUAAAAApSW8AgAAAKC0\nhFcAAAAAlJbwCgAAAIDSEl4BAAAAUFrCKwAAAABKS3gFAAAAQGkJrwAAAAAoLeEVAAAAAKUlvAIA\nAACgtIRXAAAAAJSW8AoAAACA0hJeAQAAAFBawisAAAAASkt4BQAAAEBpCa8AAAAAKC3hFQAAAACl\nJbwCAAAAoLSEVwAAAACUVqvmbgAAAACApCiKjHhpTG5//L5MeGNS5i1akI7tOqRX1545+/ATcnjf\nA1NTU9PcbVad8AoAAACgGRVFkVsfuyfXD7s946ZNWG38qfHP5a5RQ9OnW69cOGBwzul/8hYVYgmv\nAAAAAJrJ0uXL8vlbrsqdIx9Y79xx0ybkkluvzqhXns2Q8y5L65ZbRqxjzysAAACAZlAURaODq5Xd\nOfKBXHzLVSmKYiN1Vi7CKwAAAIBmcOtj9zQ5uFrhNyMfyK2P3VPhjspJeAUAAABQZUVR5Ppht21Q\njeuH3b5FrL4SXgEAAABU2YiXxmTctH9tUI1x0ybk8ZfGVKij8hJeAQAAAFTZ7Y/fV5k6T9xfkTpl\nJrwCAAAAqLIJb0yqTJ3pEytSp8yEVwAAAABVNm/RgsrUWVyZOmUmvAIAAACoso7tOlSmTtvK1Ckz\n4RUAAABAlfXq2rMydbbfsSJ1ykx4BQAAAFBlgw8/oTJ1Dju+InXKTHgFAAAAUGVH9D0wfbrtvEE1\n+nTrlcP7HlihjspLeAUAAABQZTU1NblwwNkbVOPCAYNTU1NToY7KS3gFAAAA0AzO6X9yzug36G0d\ne2a/QTmn/8kV7qichFcAAAAAzaCmpiZDzrusyQHWmf0G5TvnXbZFrLpKklbN3QAAAADAlqp1y1a5\n7sOX59De++b6Ybdn3LQJa53bp1uvXDhgcM7pf/IWE1wlSU1RFEVzN0G51dXVpba2Nkkyc+bMdOnS\npZk7AgAAgM1PURR5/KUxuf2J+zNh+sTMW7wgHdt2SK/td8zZh5+Qw/ocsEmEVpXOEay8AgAAACiB\nmpqaHLH7QTli94Oau5VSsecVAAAAAKUlvAIAAACgtIRXAAAAAJSW8AoAAACA0hJeAQAAAFBawisA\nAAAASkt4BQAAAEBpCa8AAAAAKC3hFQAAAAClJbwCAAAAoLSEVwAAAACUlvAKAAAAgNISXgEAAABQ\nWsIrAAAAAEpLeAUAAABAaQmvAAAAACgt4RUAAAAApSW8AgAAAKC0hFcAAAAAlJbwCgAAAIDSatXc\nDVB+9fX1DY9nzZrVfI0AAAAApbdydrBypvB2Ca9Yrzlz5jQ83nXXXZuxEwAAAGBTMmfOnGy77bYb\nVMNlgwAAAACUVk1RFEVzN0G5LVu2LBMnTkySbLPNNmnRYtPJPGfNmtWwWmz8+PHp3Llz8zYEVeC8\nZ0vjnGdL45xnS+S8Z0uzqZ/z9fX1DVdx7bjjjmnVasMu/HPZIOvVqlWr7LLLLs3dxgbr3LlzunTp\n0txtQFU579nSOOfZ0jjn2RI579nSbKrn/IZeKriyTWcJDQAAAABbHOEVAAAAAKUlvAIAAACgtIRX\nAAAAAJSW8AoAAACA0hJeAQAAAFBaNUVRFM3dBAAAAACsiZVXAAAAAJSW8AoAAACA0hJeAQAAAFBa\nwisAAAAASkt4BQAAAEBpCa8AAAAAKC3hFQAAAAClJbwCAAAAoLSEVwAAAACUVqvmbgCaor6+Pn//\n+9/zxBNPZNKkSZk6dWrq6+vTrVu39OvXL8cff3zatm3b6HpPPPFE7r///kycODFt2rRJnz59cvrp\np2fXXXfdiO8CNtycOXPyyU9+MkuWLEmSfOADH8g555yz3uOmTZuWO++8M//85z8zb968dO/ePcce\ne2yOPvrotGjh9xmUT319fR5//PE8/PDDmTx5curr67Pzzjvn0EMPzcCBA9Oq1bo/yixdujRDhw7N\n8OHD8/rrr6dTp07Zf//9c9ppp6W2trZK7wIaZ+7cubn33nvz9NNPZ/r06SmKIl27ds0BBxyQk046\nKZ07d25UnX/+85/53e9+l1dffTX19fXp1atXTjnllOy3334b9w3Av3n55ZczevTojBo1KpMnT06S\n9O/fP5/97GebVGf06NG577778tprr6VVq1bZbbfdcvrpp2e33Xarag1Yn7q6ujz55JMZNWpUxo4d\nm2XLliVJbrvttrRu3Xq9x0+dOjWPPvpoXnrppUydOjWzZs1Kp06dsvfee+f4449Pr169Gt3L66+/\nnjvvvDNjx45t+Nw/cODADBgwIC1btny7b7H5FLCJuOaaa4rOnTsXSdb6tf322xe33Xbbemu9/vrr\nxXHHHbfGGi1atCi++MUvFsuWLavCu4K354ILLljlvP3Sl76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          }
        }
      ],
      "source": [
        "loss_10 = []\n",
        "\n",
        "for sim_data in batch_data.values():\n",
        "    mode_data = sim_data.modes\n",
        "    idx = findMode(mode_data, 0.4)\n",
        "    loss_10.append(mode_data.to_dataframe().iloc[idx][\"loss (dB/cm)\"])\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "ax.plot(radius, loss_10, \"o\")\n",
        "ax.set_yscale(\"log\")\n",
        "ax.set_xlabel(\"bend radius ($\\\\mu$m)\")\n",
        "ax.set_ylabel(\"Loss (dB/cm)\")\n",
        "plt.show()"
      ],
      "id": "08159d7a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As we can note, the losses decrease exponentially as a function of the\n",
        "bend radius.\n",
        "\n",
        "Next, we will perform the same analysis using a finer resolution."
      ],
      "id": "51c0e131-4863-4e7a-9225-9f26a984e94a"
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"56726772eea7421090a2ca8659891a0c\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:14:53 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6</span> tasks.                       \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:14:58 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.259</span> for the whole batch.                \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"4daebb184d344438be410f78bb43576e\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:15:02 UTC </span>Batch complete.                                                    \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        }
      ],
      "source": [
        "loss_50 = []\n",
        "\n",
        "mode_solvers = {}\n",
        "for r in radius:\n",
        "    mode_solver = mode_solver_SiN_wvg(\n",
        "        resolution=50,\n",
        "        npml=12,\n",
        "        nun_modes=5,\n",
        "        bend_radius=r,\n",
        "        bend_axis=1,\n",
        "        size=(20, 15),\n",
        "    )\n",
        "\n",
        "    mode_solvers[str(r)] = mode_solver\n",
        "\n",
        "batch_data = web.run(\n",
        "    simulation=mode_solvers,\n",
        "    folder_name=\"radiative_losses\",\n",
        "    path=\"radiative_losses_sin_radius_res50\",\n",
        ")\n",
        "\n",
        "for sim_data in batch_data.values():\n",
        "    mode_data = sim_data.modes\n",
        "    idx = findMode(mode_data, 0.4)\n",
        "    loss_50.append(mode_data.to_dataframe().iloc[idx][\"loss (dB/cm)\"])"
      ],
      "id": "3709acd3"
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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ApSW8AgAAAKC0hFcAAAAAlJbwCgAAAIDSEl4B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\nb7+8L7HtFLCKuPDCC4sePXoUSZb6tcEGGxTXX3/9+9Z6662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6d+PGjeY18/Ly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          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.plot(radius, loss_50, \"o\")\n",
        "ax.set_yscale(\"log\")\n",
        "ax.set_xlabel(\"bend radius ($\\\\mu$m)\")\n",
        "ax.set_ylabel(\"Loss (dB/cm)\")\n",
        "plt.show()"
      ],
      "id": "44b5b64e"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next, we will analyze the deviation between the two resolutions:"
      ],
      "id": "feb8c1d2-3ddd-4f2a-9b1f-9611f8001f81"
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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KNUxKAzgWRRIAAAAAAHl0ICZaS3astZmL4GkkuBCKJAAAAAAA8ujb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          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.plot(\n",
        "    radius,\n",
        "    100 * np.sqrt((np.array(loss_50) - np.array(loss_10)) ** 2) / np.array(loss_50),\n",
        "    \"-o\",\n",
        ")\n",
        "\n",
        "ax.set_xlabel(\"bend radius ($\\\\mu$ m)\")\n",
        "ax.set_ylabel(\"error (%)\")\n",
        "\n",
        "plt.show()"
      ],
      "id": "04f82319"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "It can be noted that the error for the lower resolution can reach up to\n",
        "43% for low losses.\n",
        "\n",
        "To analyze the convergence, we will plot the loss as a function of\n",
        "resolution for a fixed bend radius of 120 μm."
      ],
      "id": "17e998ad-0922-401b-9922-3a4032546499"
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"4c65a483575e454dba2db812867a089c\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:24:21 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6</span> tasks.                       \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:24:26 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.786</span> for the whole batch.                \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"b60da82a867d404d966bcb9265c697a0\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:24:28 UTC </span>Batch complete.                                                    \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        }
      ],
      "source": [
        "loss = []\n",
        "\n",
        "resolution = np.linspace(20, 100, 6)\n",
        "mode_solvers = {}\n",
        "for r in resolution:\n",
        "    mode_solver = mode_solver_SiN_wvg(\n",
        "        bend_radius=120,\n",
        "        npml=12,\n",
        "        bend_axis=1,\n",
        "        resolution=r,\n",
        "        nun_modes=10,\n",
        "        size=(20, 15),\n",
        "    )\n",
        "\n",
        "    mode_solvers[str(r)] = mode_solver\n",
        "\n",
        "batch_data = web.run(\n",
        "    simulation=mode_solvers,\n",
        "    folder_name=\"radiative_losses\",\n",
        "    path=\"radiative_losses_sin_resolution_sweep\",\n",
        ")\n",
        "\n",
        "for sim_data in batch_data.values():\n",
        "    mode_data = sim_data.modes\n",
        "    idx = findMode(mode_data, 0.4)\n",
        "    loss.append(mode_data.to_dataframe().iloc[idx][\"loss (dB/cm)\"])"
      ],
      "id": "0c05bc0b"
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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cQG5uLk6ePKny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\n"
          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.plot(resolution, loss, \"o\")\n",
        "ax.set_xlabel(\"resolution\")\n",
        "ax.set_ylabel(\"loss (dB/cm)\")\n",
        "plt.show()"
      ],
      "id": "a036c544"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As we can see, the loss values converge for high resolutions.\n",
        "\n",
        "In conclusion, the general behavior of the losses can be captured with a\n",
        "reasonable resolution. However, if a very precise result is desired, a\n",
        "very high resolution is required.\n",
        "\n",
        "## Losses in a bent optical fiber\n",
        "\n",
        "Finally, we will estimate the bend losses in an optical fiber."
      ],
      "id": "45e8eaee-e671-43cd-b50b-a3fc02cbdc40"
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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AyYP9/zoOswsAwnG73ZLqNsyG/9Z/HwAAAEDiaG7/v+Gt1xIdR85h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UmTJsrOzta2bdu0cOFCZWRkaOrUqdq9e7cWLVrk1LfrGRkZksr3iKbIyEilpqYqMzPT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\n9uzZo+PHjyskJERt2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          }
        }
      ],
      "source": [
        "def mode_solver_fiber(\n",
        "    resolution,\n",
        "    npml,\n",
        "    delta_override=None,\n",
        "    size=(30, 30),\n",
        "    num_modes=10,\n",
        "    bend_radius=None,\n",
        "    symmetry=(0, 0, 0),\n",
        "    target_neff=1.41,\n",
        "    fiber_radius=4.1,\n",
        "    coreIndex=1.45213,\n",
        "    cladIndex=1.44692,\n",
        "    fields=[\"Ex\", \"Ey\", \"Ez\"],\n",
        "):\n",
        "    fiberDiameter = 2 * fiber_radius\n",
        "\n",
        "    fiber = td.Cylinder(axis=0, radius=fiberDiameter / 2, center=(0, 0, 0), length=td.inf)\n",
        "\n",
        "    structures = [td.Structure(geometry=fiber, medium=td.Medium(permittivity=coreIndex**2))]\n",
        "\n",
        "    mode_spec = td.ModeSpec(\n",
        "        num_modes=num_modes,\n",
        "        target_neff=target_neff,\n",
        "        precision=\"double\",\n",
        "        bend_radius=bend_radius,\n",
        "        bend_axis=1,\n",
        "        num_pml=(npml, npml),\n",
        "    )\n",
        "\n",
        "    if delta_override:\n",
        "        mesh_override = [\n",
        "            td.MeshOverrideStructure(\n",
        "                geometry=td.Box(center=(0, 0, 0), size=(1, 3 * fiber_radius, 3 * fiber_radius)),\n",
        "                dl=(delta_override,) * 3,\n",
        "            )\n",
        "        ]\n",
        "    else:\n",
        "        mesh_override = []\n",
        "\n",
        "    grid_spec = td.GridSpec.auto(\n",
        "        min_steps_per_wvl=resolution, wavelength=1.55, override_structures=mesh_override\n",
        "    )\n",
        "\n",
        "    sim = td.Simulation(\n",
        "        size=(10, size[0], size[1]),\n",
        "        center=(0, 0, 0),\n",
        "        grid_spec=grid_spec,\n",
        "        structures=structures,\n",
        "        sources=[],\n",
        "        monitors=[],\n",
        "        run_time=1e-12,\n",
        "        boundary_spec=td.BoundarySpec.all_sides(boundary=td.Absorber(num_layers=20)),\n",
        "        symmetry=symmetry,\n",
        "        medium=td.Medium(permittivity=cladIndex**2),\n",
        "    )\n",
        "\n",
        "    plane = td.Box(center=(0, 0, 0), size=(0, size[0], size[1]))\n",
        "\n",
        "    mode_solver = td.ModeSimulation.from_simulation(\n",
        "        simulation=sim,\n",
        "        plane=plane,\n",
        "        mode_spec=mode_spec,\n",
        "        freqs=[td.C_0 / 1.55],\n",
        "        fields=fields,\n",
        "    )\n",
        "\n",
        "    return mode_solver\n",
        "\n",
        "\n",
        "ms = mode_solver_fiber(20, 10, delta_override=0.01)\n",
        "ms.plot()\n",
        "plt.show()"
      ],
      "id": "ca4fec08"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Due to the low index contrast, a fiber is more sensitive to losses;\n",
        "hence, larger bend radii can be analyzed.\n",
        "\n",
        "Again, we need to define a proper plane size. To do so, we will\n",
        "benchmark the losses for a 30 mm bend radius as a function of the plane\n",
        "size. As observed, physical values are obtained only for sizes up to 100\n",
        "μm."
      ],
      "id": "a143e80c-8125-47bf-8a7f-30439bc8061f"
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
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        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:30:22 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">5</span> tasks.                       \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:30:26 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.482</span> for the whole batch.                \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"45d6210958524bebbde9bfce47a4e7db\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:32:09 UTC </span>Batch complete.                                                    \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        }
      ],
      "source": [
        "loss = []\n",
        "sizes = [40, 60, 80, 100, 120]\n",
        "mode_solvers = {}\n",
        "for size in sizes:\n",
        "    mode_solver = mode_solver_fiber(\n",
        "        bend_radius=30000,\n",
        "        npml=12,\n",
        "        resolution=10,\n",
        "        size=(size, size),\n",
        "        target_neff=1.449,\n",
        "        symmetry=(0, 0, 1),\n",
        "        delta_override=0.05,\n",
        "        num_modes=10,\n",
        "    )\n",
        "\n",
        "    mode_solvers[str(size)] = mode_solver\n",
        "\n",
        "batch_data = web.run(\n",
        "    simulation=mode_solvers,\n",
        "    folder_name=\"radiative_losses\",\n",
        "    path=\"radiative_losses_fiber_size_sweep\",\n",
        ")\n",
        "\n",
        "for sim_data in batch_data.values():\n",
        "    mode_data = sim_data.modes\n",
        "    idx = findMode(mode_data, 3)\n",
        "    loss.append(mode_data.to_dataframe().iloc[idx][\"loss (dB/cm)\"])"
      ],
      "id": "7ac4b9cc"
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Size (μm)   Loss (dB/cm)\n",
            "40      -0.002133\n",
            "60      -0.000032\n",
            "80      -0.000001\n",
            "100     0.000000\n",
            "120     0.000000"
          ]
        }
      ],
      "source": [
        "# print the results\n",
        "print(\"Size (μm)\\tLoss (dB/cm)\")\n",
        "for i, s in enumerate(sizes):\n",
        "    print(f\"{s}\\t\\t{loss[i]:.6f}\")"
      ],
      "id": "21de6a57"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Finally, we will analyze the imaginary part of the effective index as a\n",
        "function of the bend radius and compare the results with the analytical\n",
        "model developed by Dietrich Marcuse published in the work “Curvature\n",
        "loss formula for optical fibers” [DOI:\n",
        "https://doi.org/10.1364/JOSA.66.000216](https://doi.org/10.1364/JOSA.66.000216).\n",
        "\n",
        "In this model, the loss coefficient $\\alpha$ is given by:\n",
        "\n",
        "$2\\alpha = \\frac{\\sqrt(\\pi)k^2e^{-(2/3)(\\frac{\\gamma^3}{\\beta_g^2})R}}{e_\\nu \\gamma^{3/2}V^2\\sqrt{R}K_{\\nu-1}(\\gamma a)K_{\\nu+1}(\\gamma a)}$\n",
        "\n",
        "where:\n",
        "\n",
        "$k = \\sqrt{(n_1 2\\pi/\\lambda)^2 -\\beta_g^2}$\n",
        "\n",
        "$\\gamma = \\sqrt{(\\beta_g^2-(n_2 2\\pi/\\lambda)^2)}$\n",
        "\n",
        "$e_\\nu = 1$ for $\\nu = 0$ else 2\n",
        "\n",
        "$V^2 = (a 2\\pi/\\lambda)^2(n_1^2-n_2^2)$\n",
        "\n",
        "and $n_1$ is the core index, $n_2$ is the clad index, $a$ is the core\n",
        "radius, $R$ is the bend radius, $\\beta_g$ is the constant of a straight\n",
        "waveguide, and $K_\\nu$ is the modified Hankel function."
      ],
      "id": "0d99acf0-03f8-4391-8b26-b75ed28a84ed"
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"7662b00799f64ca5b294405d4b1d13fa\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:40:00 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6</span> tasks.                       \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:40:05 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.426</span> for the whole batch.                \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"c5c0eb344cb14de5ad19f78f80be2d5d\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:41:06 UTC </span>Batch complete.                                                    \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        }
      ],
      "source": [
        "loss = []\n",
        "keff = []\n",
        "\n",
        "radius = [5000, 10000, 15000, 20000, 25000, 30000]\n",
        "mode_solvers = {}\n",
        "for r in radius:\n",
        "    mode_solver = mode_solver_fiber(\n",
        "        bend_radius=r,\n",
        "        npml=12,\n",
        "        resolution=10,\n",
        "        size=(100, 100),\n",
        "        target_neff=1.449,\n",
        "        symmetry=(0, 0, 1),\n",
        "        delta_override=0.05,\n",
        "        num_modes=5,\n",
        "    )\n",
        "\n",
        "    mode_solvers[str(r)] = mode_solver\n",
        "\n",
        "batch_data = web.run(\n",
        "    simulation=mode_solvers,\n",
        "    folder_name=\"radiative_losses\",\n",
        "    path=\"radiative_losses_fiber_radius_sweep\",\n",
        ")\n",
        "\n",
        "for sim_data in batch_data.values():\n",
        "    mode_data = sim_data.modes\n",
        "    idx = findMode(mode_data, 4)\n",
        "\n",
        "    loss.append(mode_data.to_dataframe().iloc[idx][\"loss (dB/cm)\"])\n",
        "    keff.append(mode_data.to_dataframe().iloc[idx][\"k eff\"])"
      ],
      "id": "23b2b921"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As we can see, the simulated results, with proper simulation size, match\n",
        "very well the analytical results up to $k_{eff}$ at the order of\n",
        "$10^{-12}$"
      ],
      "id": "852a65aa-b2c7-48c7-8804-208eec344049"
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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          }
        }
      ],
      "source": [
        "# function for calculation alpha\n",
        "def alpha(R, a=4.1, nmode=1.449156, n1=1.45213, n2=1.44692, lda0=1.55, mode=0):\n",
        "    beta = 2 * np.pi * nmode / lda0\n",
        "    ev = 2 if mode == 0 else 1\n",
        "    k0 = np.pi * 2 / lda0\n",
        "    gamma = np.sqrt(beta**2 - (n2**2) * (k0**2))\n",
        "    k = np.sqrt((n1**2) * k0**2 - beta**2)\n",
        "    Vsquare = (k0**2) * (a**2) * (n1**2 - n2**2)\n",
        "\n",
        "    from scipy.special import kv\n",
        "\n",
        "    up = np.sqrt(np.pi) * (k**2) * np.exp(-(2 / 3) * ((gamma**3) / (beta**2)) * R)\n",
        "    down = (\n",
        "        ev\n",
        "        * (gamma ** (3 / 2))\n",
        "        * Vsquare\n",
        "        * np.sqrt(R)\n",
        "        * kv(mode - 1, gamma * a)\n",
        "        * kv(mode + 1, gamma * a)\n",
        "    )\n",
        "\n",
        "    return np.real((1 / 2) * (up / down))\n",
        "\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "ax.plot(radius, keff, \"o\", label=\"Simulated\")\n",
        "ax.plot(\n",
        "    radius,\n",
        "    [alpha(r) * 1.55 / (4 * np.pi) for r in radius],\n",
        "    \"*\",\n",
        "    label=\"Analytical model\",\n",
        ")\n",
        "ax.set_yscale(\"log\")\n",
        "ax.set_xlabel(r\"Bend radius ($\\mu$m)\")\n",
        "ax.set_ylabel(\"$k_{eff}$\")\n",
        "ax.legend()\n",
        "\n",
        "plt.show()"
      ],
      "id": "0418ab13"
    }
  ],
  "nbformat": 4,
  "nbformat_minor": 5,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    }
  }
}