{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Layout design using gdstk\n",
        "\n",
        "In Tidy3D, complex structures can be defined via the third-party\n",
        "[gdstk](https://heitzmann.github.io/gdstk/) package. In this tutorial,\n",
        "we will illustrate how to use the package to define an integrated\n",
        "adiabatic coupler. For a tutorial on how to load a previously generated\n",
        "GDS file, please refer to\n",
        "[this](https://www.flexcompute.com/tidy3d/examples/notebooks/GDSImport)\n",
        "example.\n",
        "\n",
        "<img src=\"img/splitter.png\" alt=\"Schematic of the directional coupler\" width=\"400\"/>\n",
        "\n",
        "Note that this tutorial requires gdstk, so grab it with\n",
        "`pip install gdstk` before running the tutorial or uncomment the cell\n",
        "line below.\n",
        "\n",
        "Alternatively, the same layout design can be done using\n",
        "[Photonforge](https://www.flexcompute.com/photonforge/), our photonic\n",
        "design automation tool.\n",
        "\n",
        "We also provide a comprehensive list of other tutorials such as [how to\n",
        "define boundary\n",
        "conditions](https://www.flexcompute.com/tidy3d/examples/notebooks/BoundaryConditions/),\n",
        "[how to compute the S-matrix of a\n",
        "device](https://www.flexcompute.com/tidy3d/examples/notebooks/SMatrix/),\n",
        "[how to interact with tidy3d’s web\n",
        "API](https://www.flexcompute.com/tidy3d/examples/notebooks/WebAPI/), and\n",
        "[how to define self-intersecting\n",
        "polygons](https://www.flexcompute.com/tidy3d/examples/notebooks/SelfIntersectingPolyslab/).\n",
        "\n",
        "If you are new to the finite-difference time-domain (FDTD) method, we\n",
        "highly recommend going through our\n",
        "[FDTD101](https://www.flexcompute.com/fdtd101/) tutorials."
      ],
      "id": "2305c95d-3f36-47ed-9fc3-ec77d0c90f1f"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "# install gdstk\n",
        "# !pip install gdstk\n",
        "\n",
        "# standard python imports\n",
        "import os\n",
        "\n",
        "import gdstk\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# tidy3d import\n",
        "import tidy3d as td"
      ],
      "id": "3858e890"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Creating the geometry with gdstk\n",
        "\n",
        "In this section, we will construct an integrated adiabatic coupler as in\n",
        "the title image in this notebook using `gdstk`. If you are only\n",
        "interested in importing an already existing GDSII file, please refer to\n",
        "[this](https://www.flexcompute.com/tidy3d/examples/notebooks/GDSImport/)\n",
        "tutorial.\n",
        "\n",
        "We create a function that generates the coupler and returns the\n",
        "corresponding cell. The geometry is built by defining the cross-section\n",
        "of the device in the x-y plane. The cross section can be supplied at the\n",
        "`top`, `bottom`, or the `middle` of the device, specified by the\n",
        "parameter `reference_plane`. Here we choose to define the cross section\n",
        "on the base. There, the two arms of the device start at a distance\n",
        "`wg_spacing_in` apart, then come together at a coupling distance\n",
        "`wg_spacing_coup` for a certain length `coup_length`, and then split\n",
        "again into separate ports. In the coupling region, the field overlap\n",
        "results in energy exchange between the two waveguides. The cell also\n",
        "includes a rectangle around the whole device, which we will use as\n",
        "substrate later. The waveguides use GDS layer 1 and the rectangle layer\n",
        "0.\n",
        "\n",
        "Here, we will only see how to define, export, and import such a device\n",
        "using `gdstk`. When importing the device, we can optionally dilate or\n",
        "erode its cross section via `dilation`. In a later example we will\n",
        "simulate the device and study the frequency dependence of the\n",
        "transmission into each of the ports."
      ],
      "id": "8da39559-5b06-4c53-ab54-169c67b55da6"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "def make_coupler(\n",
        "    length: float,\n",
        "    wg_spacing_in: float,\n",
        "    wg_width: float,\n",
        "    wg_spacing_coup: float,\n",
        "    wg_spacing_side: float,\n",
        "    coup_length: float,\n",
        "    bend_length: float,\n",
        ") -> gdstk.Cell:\n",
        "    \"\"\"Make an integrated coupler using the gdstk RobustPath object.\"\"\"\n",
        "    input_length = length / 2 - coup_length / 2 - bend_length\n",
        "    if input_length <= 0:\n",
        "        raise ValueError(\"Device length must be larger than coupling length plus bending regions.\")\n",
        "\n",
        "    delta = (wg_spacing_in - (wg_spacing_coup + wg_width)) / 2\n",
        "    turn_angle = 2 * np.arctan(delta / bend_length)\n",
        "    bend_radius = bend_length / 2 / np.sin(turn_angle)\n",
        "\n",
        "    coup = gdstk.RobustPath(\n",
        "        (-0.5 * length, wg_spacing_in / 2),\n",
        "        wg_width,\n",
        "        simple_path=True,\n",
        "        layer=1,\n",
        "    )\n",
        "    coup.segment((input_length, 0), relative=True)\n",
        "    coup.turn(bend_radius, -turn_angle)\n",
        "    coup.turn(bend_radius, turn_angle)\n",
        "    coup.segment((coup_length, 0), relative=True)\n",
        "    coup.turn(bend_radius, turn_angle)\n",
        "    coup.turn(bend_radius, -turn_angle)\n",
        "    coup.segment((0.5 * length, wg_spacing_in / 2))\n",
        "\n",
        "    arm_cell = gdstk.Cell(\"COUPLER_ARM\")\n",
        "    arm_cell.add(coup)\n",
        "\n",
        "    cell = gdstk.Cell(\"COUPLER\")\n",
        "    cell.add(gdstk.Reference(arm_cell))\n",
        "    cell.add(gdstk.Reference(arm_cell, x_reflection=True))\n",
        "\n",
        "    substrate = gdstk.rectangle(\n",
        "        (-device_length / 2, -(wg_spacing_in + wg_width) / 2 - wg_spacing_side),\n",
        "        (device_length / 2, (wg_spacing_in + wg_width) / 2 + wg_spacing_side),\n",
        "        layer=0,\n",
        "    )\n",
        "    cell.add(substrate)\n",
        "    return cell"
      ],
      "id": "b341934e"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can also define some structural parameters. We consider the sidewall\n",
        "of the device to be slanted, deviating from the vertical sidewall by\n",
        "`sidewall_angle`. Positive `sidewall_angle` values corresponds to a\n",
        "typical fabrication scenario where the base of the device is larger than\n",
        "the top."
      ],
      "id": "8a7e212f-0529-46cd-9668-c70a47b2d735"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "# ## Lengths in micrometers\n",
        "\n",
        "# Waveguide width\n",
        "wg_width = 0.45\n",
        "\n",
        "# Waveguide separation in the beginning/end\n",
        "wg_spacing_in = 4\n",
        "\n",
        "# Length of the coupling region\n",
        "coup_length = 4\n",
        "\n",
        "# Angle of the sidewall deviating from the vertical ones, positive values for the base larger than the top\n",
        "sidewall_angle = np.pi / 6\n",
        "\n",
        "# Reference plane where the cross section of the device is defined\n",
        "reference_plane = \"bottom\"\n",
        "\n",
        "# Length of the bend region\n",
        "bend_length = 6\n",
        "\n",
        "# Waveguide separation in the coupling region\n",
        "wg_spacing_coup = 0.10\n",
        "\n",
        "# Waveguide separation in the coupling region\n",
        "wg_spacing_side = 4.0\n",
        "\n",
        "# Total device length along propagation direction\n",
        "device_length = 25"
      ],
      "id": "b84d74f1"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Create a gds cell to add our structures to\n",
        "coup_cell = make_coupler(\n",
        "    device_length,\n",
        "    wg_spacing_in,\n",
        "    wg_width,\n",
        "    wg_spacing_coup,\n",
        "    wg_spacing_side,\n",
        "    coup_length,\n",
        "    bend_length,\n",
        ")\n",
        "\n",
        "# Create a library for the cell and save it for future use\n",
        "gds_path = \"coupler.gds\"\n",
        "\n",
        "if os.path.exists(gds_path):\n",
        "    os.remove(gds_path)\n",
        "\n",
        "lib = gdstk.Library()\n",
        "lib.add(coup_cell, *coup_cell.dependencies(True))\n",
        "lib.write_gds(gds_path)"
      ],
      "id": "b41eedfb"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Set up Geometries\n",
        "\n",
        "Next, we can construct tidy3d geometries from the GDS cell we just\n",
        "created, along with other information such as the axis, sidewall angle,\n",
        "and bounds of the “slab”. When loading GDS cell as the cross section of\n",
        "the device, we can tune `reference_plane` to set the cross section to\n",
        "lie at `bottom`, `middle`, or `top` of the generated\n",
        "[Polyslab](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.PolySlab.html)\n",
        "with respect to the axis. E.g. if `axis=1`, `bottom` refers to the\n",
        "negative side of the y-axis, and `top` refers to the positive side of\n",
        "the y-axis. Additionally, we can optionally dilate or erode the cross\n",
        "section by setting `dilation`. A negative `dilation` corresponds to\n",
        "erosion.\n",
        "\n",
        "Note, we have to keep track of the `gds_layer` and `gds_dtype` used to\n",
        "define the GDS cell earlier, so we can load the right components."
      ],
      "id": "1eaf7ab2-c4bc-4be4-8684-19488f8779fc"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Define waveguide height\n",
        "wg_height = 0.22\n",
        "dilation = 0.02\n",
        "\n",
        "substrate_geo = td.Geometry.from_gds(\n",
        "    coup_cell,\n",
        "    gds_layer=0,\n",
        "    gds_dtype=0,\n",
        "    axis=2,\n",
        "    slab_bounds=(-4, 0),\n",
        "    reference_plane=reference_plane,\n",
        ")\n",
        "\n",
        "arms_geo = td.Geometry.from_gds(\n",
        "    coup_cell,\n",
        "    gds_layer=1,\n",
        "    gds_dtype=0,\n",
        "    axis=2,\n",
        "    slab_bounds=(0, wg_height),\n",
        "    sidewall_angle=sidewall_angle,\n",
        "    dilation=dilation,\n",
        "    reference_plane=reference_plane,\n",
        ")"
      ],
      "id": "f990254f"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let’s plot the base and the top of the coupler waveguide arms to make\n",
        "sure it looks ok. The base of the device should be larger than the top\n",
        "due to a positive `sidewall_angle`."
      ],
      "id": "a4ab1068-09f8-4514-8b05-5b0e51a0f188"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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33KLS0tJIuzXb1bSYbH6XBFbXLFDRoIaFJfJvqIlqLygo\n0J133qnzzz9fVmtiZ3ABQGdiGIbmzJmjv/3tb/rss8+i+qw5qUobni97n8ykCHaCVW7Vz1svf0ld\npC09PV2TJk3SNddcI4fDkcDqAGDvEUIhJkIoAJ1FQ0ODpkyZogcffDDqSnqO/llKP76PLBnOBFbX\nLLC1UY3flci3tjqqvVevXrrqqqt0xRVXKD8/P0HVAUDHV1tbq5deeknTpk3TkiVLovpsPdKVOryn\n7L26JEX4FPYG1fDtJnmWlkvb3lmZTCaNHz9ekydPVo8ePRJbIADsI0IoxEQIBaCzWbt2rW6++WYV\nFRU1N1pMSh2ap5RhPWW2WRJX3A4ClW41LiqRb3VVVLvFYtFZZ52liRMnavTo0ZyqBwCtYBiGvv32\nW02bNk2vvfaa3G53VL+tZ4bSjsqXLS89KcInI2zIs7RcDd+WyPAFI+0nnHCCHnvsMR199NEJrA4A\n9h8hFGIihALQWc2ePVvXXnutiouLI23mFJvSjusj58Fdk+JNiCQFqz1yLymXd+VWGf5QVF///v31\n+9//XuPHj1dubm6CKgSA5NXQ0KBXXnlF06dP13fffRfdaTbJOSBbrsNyZe+RnpgCY/CX1Kp+3noF\nqzyRtvz8fP3973/XxRdfnDR/nwBgfxBCISZCKACdWTAY1IwZM3TnnXeqsrIy0m7LSVP6z/rKlpOW\nwOqiGYGQvKsr5V5aoeCWxqg+m82m888/XxMmTNDIkSN5gwLggPfDDz9o+vTpevnll1VfH30VUkuG\nQ64huXIN6iazy5agClsK1nnVMH+DfOuaT8d2OBy6+eabdeuttyo1NTWB1QFA2yKEQkyEUAAOBFVV\nVfrrX/+qJ598UqFQ82wj56BuSju2tyyp9gRW11JgS6M8S8vlXVUZdXluSTrkkEM0YcIEXX755ZHf\n3wBwIPB4PPr3v/+tadOm6X//+190p0ly9MuSa0iu7PkZSRXWhwMhuReVqnFxmRRqfvtUWFiohx56\nSP369UtccQAQJ4RQiIkQCsCBZOnSpbruuuv08ccfR9pMNrNSh+crpaCHTJbkWn8p7A/Ku7JSnqUV\nClZFr2/icDh0wQUXaPz48TrxxBO5sh6ATskwDH333Xd6+eWX9cILL6impiaq35xml2twjlyHdE+6\nDxQMw5B35VY1fL1RYXcg0j506FA99thjGjlyZOKKA4A4I4RCTIRQAA40hmHovffe0/XXX6/Vq1dH\n2i0ZDqWN6CNH36yk+gRdaqo5UNEgz9IKeVdXRn2SLkndunXTeeedp8LCQp166qmy2ZLn9BMA2Fvh\ncFjffPONZs6cqaKiIq1bty56gEmy98lUyuAc2XtnymROrt/ZkhSoaFD9V+sVqGiItHXt2lWTJ0/W\nlVdeKYslOS6SAQDxQgiFmAihAByofD6fHnvsMd17771qaGh+k2DvlaH0EX1lzU5JYHW7FvYG5flp\nizzLKhSq8bboz8rK0tlnn63CwkKNHj1aTqczAVUCwN4JhUL66quvVFRUpKKiIpWUlLQYY06xyXVo\njlyHdpcl3ZGAKvcs1OhXwzcb5f1pa6TNYrHoz3/+s+6++25eawM4YBBCISZCKAAHus2bN+v222/X\n888/39xoklyH5SrtqF4yO5PzNDfDMBQob5BvbZW8a6oUbvC3GJOenq4zzzxT48aN0y9/+UulpCRn\nsAbgwBQMBjVnzhwVFRXpzTffVHl5eYsxJqdVjn5ZcvbPblrrKclOm97OCIblLt6sxkUlMgLNa/n9\n4he/0NSpUzVkyJAEVgcA7Y8QCjERQgFAkwULFuiaa66JWuzW5LAq7Zhecg3OScrTPbYzDEPBrY3y\nrqmSb02VQnW+FmNSUlI0duxYFRYW6owzzlB6evJcrhzAgcPv9+vTTz/VzJkz9fbbb0dduXQ7s8sm\nR/8sOfpny94zI+l///rWV6th/oao370DBw7UI488ojPPPDPpTvEGgPZACIWYCKEAoJlhGHrllVd0\nyy23qLS0NNJuzXYpbURfOXp1SWB1rWMYhoJVHvnWVMm7tkqhak+LMQ6HQ2PGjNEvfvELjRw5UkOG\nDOFNEoC4WbdunebMmaNPPvlE7733nmpra1uMMafa5eifJeeAbNly05M6eNouUOlWw/z18pfURdrS\n09M1adIkXXPNNXI4kvOUQQBoD4RQiIkQCgBaamho0JQpU/Tggw/K52v+ZNvWI12pR+Un3eW/dydY\n7ZF3bdMMqWClO+aY7t276+STT9bIkSMJpQDst+2h0/Zt/fr1McdZ0h1y9M+WY0CWbDlpHeb3TmBr\noxq/K5FvbXWkzWQyafz48Zo8ebJ69OiRwOoAIDkQQiEmQigA2LW1a9fq5ptvVlFRUVS7LSdVqUf1\nkr13lw7zpkmSgrXepjWk1lYpWNG4y3GEUgD2RmtDJ0mydHHKOSBbjv7ZsnZL6VC/WwJbGtS4sES+\n9TVR7SeccIIee+wxHX300YkpDACSECEUYiKEAoA9+/LLL3XPPffo448/jmq3dktV6vCecvTL6lBv\npCQp7AnIX1Ynf2m9/KV1MU/b245QCsCO9iZ0MqfZZe+ZEdmS9ap2u+PfXK/G70rk3xh9GuERRxyh\nSZMm6fzzz+d3IgDshBAKMRFCAUDr/e9//9Pf/vY3vf/++1Ht1uyUpjBqQHaHfSOyN6FUt27dNGzY\nMBUUFGjo0KEqKCjQkCFD5HQ627FiAPEWDAb1008/qbi4WMXFxVq8eLG+//57bdy4cZf36Qyh03b+\n0rqm8GmHNZ8k6ZhjjtGkSZNYdBwAdoMQCjERQgHA3lu4cKH+9re/6a233opqt2Q6lTo8X86DunaI\nRXV3Z29CKUkym806+OCDI6HU9q1///4ym5PzkuoAmhiGodLS0kjYtD1wWrZsmfx+/27v25lCJ6np\nZ+EvqVPjwhIFNtdH9Z1wwgmaNGmSxowZQ/gEAHtACIWYCKEAYN8tXrxYkydP1n/+8x/t+CfRkuFo\nCqMGdpXJ0jkCmB1DqcDmegWrPVJ4zy8DUlNTdfjhh0cFUwcddJDy8vJks9naoXIA24VCIVVUVGjd\nunVRgVNxcbGqqqr2vANT05pOtpy0ThM6bWcYhvwba9W4cJMCO62ZN3LkSE2aNEmnnHIK4RMAtBIh\nFGIihAKA/bds2TJNnjxZr776qsLhcKTdnO5Q6pE95TqkW6cJo7YzwoZCtV4FK90KVjVtgSqPwvW+\nPd9ZTVeSysnJUX5+fsytZ8+eys/PV2ZmJm/6gFZoaGhQSUnJLrfS0lKVlZUpFAq1an/mFJus2Smy\nZruavnZNkTXTJZO1k/0uMwz51lWr8btSBbdGh0+jR4/WpEmTdOKJJyaoOgDouAihEBMhFAC0nZUr\nV+r+++/Xiy++GPVGz5xql2tIjlyHdJcl1Z7ACuMv7A8qWOXZtjUHVIavdW98d5aSkhIJpPLz85WT\nkyOXy9XqLSUlJep7Tg1EsgiHw/J6vfJ4PPu0VVZWRoVMdXV1ez5oLFZzJGiy7RA6mV2de6Zi2B+U\nd2Wl3EvKW5xufMYZZ+jOO+/U8ccfn6DqAKDjI4RCTIRQAND21q5dqwceeEDPP/+8AoFAc4dJcvTL\nkmtIruz5GQfMDB/DMBR2B5pmTVV7FGrwKdzoV7jRr1BjQGG3X+IVBRA35hRb05ZqlyXVLnOqXdas\nprDJkuE4YH4XSVJgS6M8S8vlXVUpIxiO6jv33HN155136qijjkpQdQDQeRBCISZCKACIn40bN+rB\nBx/UCy+8oPr66AVuLRkOuQY3zY7q7DMO9sQIGwp7msKoUKNf4cbAtoDKv62t6XvDv2+zqYBOy2re\nFirZZEmxR4VM5lRb022XrdOdDry3jEBI3tWVci+tUHBL9Cl3NptNhYWFuu222zR06NAEVQgAnQ8h\nFGIihAKA+GtoaNCrr76qadOm6bvvvovuNJvkHJAt1+Ac2fLSD6gZCXsrHAjJ8AZlhMIygk2btt8O\nhWUEDRmhsBT5vrlP28cDycRilslqlmn7V6upuW2H9lhtJrulaeN3xi4FKt3yLKuQd+XWFiF2//79\nNWHCBI0fP145OTkJqhAAOi9CKMRECAUA7evbb7/VtGnT9Oqrr8rtdkf1WTKdShmSK+egbjI7rAmq\nEAA6LiMYlndNpTzLKhTY3BDVZ7FYdPbZZ2vChAkaPXo0a8QBQBwRQiEmQigASIza2lq9/PLLmjZt\nmn788cfoTotJzoO6yjUkR7acNGY6AMAeBGs88iyrkGfFVhm+YFRfr169dNVVV+mKK65Qfn5+gioE\ngAMLIRRiIoQCgMQyDEPz58/XtGnT9O9//1s+ny+q39o1Ra5DussxILvTX1kPAPZG2BeUb321vCu2\nyl8afXVAk8mk008/XRMnTtTpp58uq5XZpQDQngihEBMhFAAkj8rKSr344ouaNm2afvrppxb9tpw0\nOQZkyzkgW5Z0RwIqBIDECnsC8q6rlm9NVVPwFI5+O5Kbm6srr7xSV155pfr165eYIgEAhFCIjRAK\nAJKPYRiaM2eOpk+frjfeeEOBQKDFGGu3VDkHZMnRP1vWTFcCqgSA9hFq9Mu3rlreNVUKlNVJMd6B\njBo1ShMnTtTZZ58tm+3AvuIoACQDQijERAgFAMmtsrJS77zzjoqKivTRRx/FDqSyXXL03zZDKsvF\nGlIAOrxQvU/etVXyra1qscC41HS63c9+9jMVFhbq/PPPV58+fRJQJQBgVwihEBMhFAB0HLW1tXrv\nvfc0c+ZMzZo1S16vt8UYS6ZTzv7ZTTOkuqUQSAHoMIK1XvnWVsm7tkrBisYW/WazWSNHjlRhYaHO\nO+885eXlJaBKAEBrEEIhJkIoAOiYGhoa9OGHH2rmzJl6//331djY8g2bJd0hR/9sOfplNl1lz8Ll\nyAEkD8MwFKx0y7ehRr41VQpWuluMsVqtOu200zRu3Didc8456t69ewIqBQDsLUIoxEQIBQAdn8fj\n0X//+18VFRXpnXfeUV1dXctBVrPsuWmy9cyQPS9DtpxUQikA7Wp76OQvrVOgrF7+sjoZvlCLcQ6H\nQ7/4xS9UWFios88+m9enANABEUJ1ILW1tVq3bp38fr969+6tHj16xO1YhFAA0Ln4fD59+umnKioq\n0ltvvaWqqqrYAwmlAMRZa0MnSXK5XBo7dqwKCwt1xhlnKCMjo52rBQC0JUKoDmDZsmW6+eab9d//\n/lfBYDDSftRRR+mee+7R2LFj2/yYhFAA0HkFAgHNnTtXn332mebMmaOvv/466u9LlB1DqZ4ZsnUn\nlAKwd/YmdJKkI444QiNHjtQpp5yiUaNGKTU1tR2rBQDEEyFUkps9e7bGjh0rr9crk8mkwYMHy+l0\nasmSJfL5fJKkv//977r55pvb9LiEUABw4GhsbNT8+fM1Z86cvQul8tJl7Zois93avgUDSGpGMKxg\ntVv+svq9Cp1GjhypE088UV27dm3HagEA7alDhlBz585VXl6eBg4cGM/DJFxFRYUOOeQQ1dTUqF+/\nfnrrrbd0xBFHSJLKy8v161//Wp9++qlMJpM++eQTnXrqqW12bEIoADhw7VUoJcmcZpc1O0XW7BTZ\nuqbImu2SpYuTGVNAJ2cYhkJ1PgWr3Ns2j4JVboVqvdJu3g0QOgHAgatDhlA33XSTHn74YZ188sm6\n8sorVVhYKJfLFc9DJsS1116rxx9/XGazWQsWLNDw4cOj+mtrazVkyBCVlpbqqKOO0rfffttmxyaE\nAgBst7ehlCTJbJI10yVrV1ckoLJmu2ROtctkMrVP4QDaTNgTiAqaAlVuhao8MoLhPd6X0AkAsF2H\nDqG269Kliy655BJdeeWVLYKajioYDCo3N1dVVVU6/fTT9cEHH8QcN3nyZN15552SpB9++EFDhw5t\nk+MTQgEAdmV7KPX111+ruLhYixcv1k8//aRQaNen22xncliiQilrF6fMqXZZUu0y2SztUD2AXTFC\nYYUb/Qo1BhSq80aFTmF3oFX76N+/vwoKCjR06FAdddRRhE4AgCgdMoSqrq7WSy+9pBkzZqi4uDiq\n78gjj9SVV16pX//618rMzIxnGXH1xRdf6OSTT5YkPfnkk/rjH/8Yc9z333+vYcOGSZLuu+8+3Xbb\nbW1yfEIoAMDe8Hq9Wr58eSSUKi4uVnFxsUpLS1u9D5Pdsi2Qssmc0hRMmbdtTbdtMrtszKQC9pJh\nGDJ8QYUaA9tCJr/C27aQu7nN8O5hhuMOsrOzVVBQEAmcCgoKdNhhhyk9PT2OjwQA0NF1yBBqR19/\n/bWeffZZvfbaa2psbIy0O51OnX/++bryyis1cuTIDveC9R//+IeuvvpqSU2P8dhjj405LhwOy+Vy\nye/366KLLtKrr77aJscnhAIAtIXKyspIILXjtuPf7L1iNsmcYpMlZVsolWqX2W6VyWqSLGaZrNu2\nbbcjbTv0NbWZmtpYtwpJyggbMkJhKRiWEQzLCG37GgxLoZ3bjKa27d8HQpHAKexuCpgU2reX53a7\nXUOGDIkETttDp7y8vA73+hoAkHgdPoTarr6+Xq+++qqeffbZFmsjDRgwQL/73e80fvx49ezZs71L\n2yfb14OSpM2bNys3N3eXYwcOHKjVq1dr+PDhWrhwYZscnxAKABAv4XBY69atU3FxsdavX6+SkpIW\nm9vtbp9iTGoKpngzjWRhGDJChhRun5fTdrtdPXv2VH5+ftTWu3dvHX744Tr44INls9napRYAQOfX\naUKoHX3//fd69tln9a9//Uu1tbWRdovFol/+8pe68sordeaZZ8pqTd5LSl9++eV68cUXJUk+n092\nu32XY4855hh9++23Ouigg7Rq1apWH6O6unqXfTU1NRowYIAkQigAQPsyDEO1tbUxw6kdt4qKCiX4\nJQeQ1LKzs1uESztv3bp1Y0YTAKDddMoQajuPx6OpU6fqrrvuarFYas+ePfWnP/1JV199dVKeuz5u\n3DgVFRXJZDIpHN79VUdOPPFEffnll+rRo4fKyspafYzWvuAghAIAJKNAIKDNmzervr5eHo9Hbrdb\ndXV1qq2tVV1dnerr69XQ0BD52tjYqMbGRrndbnk8Hnk8Hnm9Xvl8PsIsJBWHwyGHwyGXyyWXy6WU\nlBSlpqZGtvT09MjWpUsXdenSRRkZGUpJSYmM79GjR6e8ejQAoGOLRwiV8OlFoVBIH3zwgZ599ll9\n8MEHUQFUly5dVFtbq9LSUt1xxx166qmn9O9//1snnHBCAituafu0Z8MwFA6HZTbves2K7ZfJZqo0\nAKCz8Xg8Ki0t3eVsqNLS0kgI5fV69/jBDdBZmUwmOZ1OuVwupaamqkePHrudAZWMH8ICALAvEhZC\nrV27Vs8995yef/75qKvxZGZm6tJLL9XEiRM1aNAgvf/++3ruuef03nvvqaSkROPGjdOqVauUkpKS\nqNJbSEtLi9x2u91R3+9s+7oZuxsTS1VV1S77djwdDwCAeKipqdG6det2e8rd7v5WAWhmGEZkhl9V\nVZU2btyoBQsW7HJ8enr6bkOqPn36KCcnh1P1AABJr11DKL/fr7feekvPPvusPv3006jp9Mcff7wm\nTJigCy+8MGo68jnnnKNzzjlH8+fP12mnnaaysjJ98sknOvvss9uz9N3Kz8+P3C4tLdWgQYN2Obak\npESS9nrRdU6xAwC0B5/Pp+XLl0eujLd48WIVFxdH/n7tK5PTKkuqXSa7JfqKeDteDW/blfD2dOU8\n8T4bSSRyVbyQEbkiXnNbuGXb9vbt4wOhpivjeQLSLs40ra+v1/Lly7V8+fJd1tG1a1cNHTo06sp4\nhx122F5/8AkAQDy1Swi1bNkyzZgxQy+++KK2bt0aac/IyNCvf/1rTZw4UUOHDt3tPkaMGKHCwkK9\n/PLLWrduXZwr3juDBw+O3F6xYsUuQ6iqqipVVlZKkoYMGdIutQEAEIthGNqwYUMkZNq+rVixInLq\neKtYTLKk2mVOscucapcl1bbtq735a4qtKTwCsEtG2FDYE1C40a9Qo3+Hr9va3E1tRiD2aayVlZWa\nPXu2Zs+eHWkzmUwaMGBAVDBVUFCggQMHJvVFfwAAnVfc//pMmTJFt956a1Tb0UcfrQkTJujiiy9W\nampqq/eVm5srqWlGVTL52c9+JpPJJMMw9MUXX+iss86KOe6LL76I3P75z3/eXuUBAA5wDQ0NWrRo\nUdTMph9//FF1dXV7vrPZJGumU9bsFFm6OHcKmGwyOaycAgS0AZO5KdC1pNq1u5VDw/6gwo2BSFAV\nbvQrWOdTsMqtYLVHCjaHVIZhaPXq1Vq9erXeeuutSLvT6dSQIUMiodTQoUM1fPhwde3aNX4PEAAA\ntUMItWXLFklNayBdfPHFmjhxooYPH75P+zr99NOVmZmZdAFOr169dOyxx+rrr7/WK6+8osmTJ8tu\nt7cY98ILL0iSXC6XTj/99HauEgBwoGhoaNC8efM0Z84czZkzRwsWLGjV7CZzml3W7BRZs12yZqfI\n1rUpeGIWE5A8zHarzHarrFktr6ZnGIZCdT4FK91NoVSVW8Eqj0K13qhxXq9X3333nb777ruo9oKC\nAo0cOVIjR47USSedpG7dusX1sQAADjwmI87XOZ4xY4aCwaB+/etfd+ore7z99ts699xzJUk33XST\nHnzwwaj+t956S+edd54k6eabb9bf//73Njt2PC6bCADoOPY2dDLZLZGgqXlzyezg9BygMzICIQVr\nPApWenYIp9wKe3YfThNKAcCBLR5ZQ9xDqAPJRRddpNdff12SdN555+mSSy6Rw+HQp59+qieffFLB\nYFBDhgzR/PnzlZGR0WbHJYQCgAPLXoVOVrPsPdJky8uQrWtT4GROs3MKHQCFPQEFts2aCpTVy19W\nL8O362CKUAoADiyEUEnO6/Vq4sSJ+uc//xmzf8SIEXr99dfVu3fvNj0uIRQAdG77EjrZ8zJk65kh\nW/dUTqcD0CqGYShY5VGgtE7+0jpCKQA4wBFCdRALFizQv//9b61cuVKBQEC9e/fWGWecobFjx8pi\nsbT58QihAKDzqa6u1jvvvKOZM2fqo48+2vVFOQidAMTJ3oRSJpNJP//5zzVu3Didf/756tWrVztX\nCwBoa4RQiIkQCgA6hy1btuitt97SzJkz9dlnn8We7UToBCBBmkIptwKl9dtCqToZvlDMsccff7wK\nCwtVWFio/v37t3OlAIC2QAiFmAihAKDjKi0t1ZtvvqmioiJ9/vnnCofDLcZYc1Ll6JslO6ETgCSy\nPZTyl9TJv7FG/pI6KcY7i+HDh6uwsFDjxo3ToEGD2r9QAMA+IYRCTIRQANCxbNiwQUVFRSoqKtK8\nefMU60+xrUe6HP2z5OyfLUu6IwFVAsDeCXsD8q2rkXdtlfybaqVwy99thx9+eCSQOuyww7hIAgAk\nMUIoxEQIBQDJb/Xq1SoqKtLMmTO1YMGClgNMkj0vQ44B2XL0y5Il1d7+RQJAGwn7gvJtqJFvTZV8\nG2ukUMu3HIMGDdK4ceNUWFioYcOGEUgBQJIhhEJMhFAAkJxqa2v1r3/9SzNmzNCiRYtaDjCbZM/P\nkKN/tpz9smR22dq/SACIs3AgJP+GbTOk1tfICLY87bh///4aP368rrjiCvXs2TMBVQIAdkYIhZgI\noQAguSxcuFDTpk3TK6+8IrfbHd1pMcnRq0vTjKe+WTI7rIkpEgASwAiG5dtUI9+aavnWV8vwRy9s\nbrFYdPbZZ2vixIkaNWqUzGbWwAOARCGEQkyEUACQeA0NDXrttdc0bdo0LVy4MLrTbJKjb6acA7rK\n3idTZrslMUUCQBIxQmH5S+rkXVsl35qqFoHUgAED9Pvf/17jx49XTk5OgqoEgAMXIRRiIoQCgMRZ\nvHixpk+frpdeekn19fVRfZYMh1yDc+Q6pDun2gHAbhiBkLyrK+VeWqHglsaoPpvNpsLCQk2cOFEn\nnXQSa0cBQDshhEJMhFAA0L48Ho/+85//aNq0aZo/f350p0ly9MuSa0iu7PkZvFkCgL0U2NIoz9Jy\neVZVSjutH3XooYdqwoQJuuyyyyKvfwEA8UEIhZgIoQCgfSxfvlzPPPOMXnjhBVVXV0f1mdPskVlP\nXNlu7xhho2mh4lBYRjAsY/vXWG0hQ+KVC5KIyWKSyWqWyWKWrObIbdO227KYZbKamtosrG+0N8K+\noLyrKuVZWq5glSeqz+l06oILLtDEiRN1/PHHE/gDQBwQQiEmQigAiJ9wOKw333xT//jHPzRnzpwW\n/fY+mUoZkiN770yZzLwJMgxDhj+kcKNfoUa/wo0Bhdz+Hb73K+wN7hAuGVKYlyI4QJi0QzBlltlu\nkTnVLnOqXZaUbV9Tbdu+2mVyWglX1PR7JVDeIM+yCnlXV0qh6N8ZQ4cO1R/+8Af99re/ldPpTFCV\nAND5EEIhJkIoAGh7wWBQr7/+uiZPnqxly5ZF9ZlTbHId2l2uQ3NkSXckqMLECAdCClV7FGrwNQVM\njdEBU8gdaHH6DIB9ZDY1B1MpTcFUU2hlkyXVIWuWU2bngbXeXNgblOenLfIsrVCo1hvVl5eXp5tv\nvlkTJkxQSkpKgioEgM6DEAoxEUIBQNsJBAL617/+pcmTJ2vVqlVRffZeGXINzpWjb2anP63GCBsK\n1XoVrHJv2zwKVrkVqvPt8z4tFovy8vLUvXt3paSkyOVytWrbcazT6eSS7UgahmHI6/XK4/Hs01ZZ\nWanS0lL5fPv+/8qcYpM1O6Vp6+pq+prl6vy/owxDgbJ6uZeWy7e2OmpGZffu3XXTTTfpD3/4g9LT\n0xNYJQB0bIRQiIkQCgD2n8/n0z//+U/df//9WrduXXOHSXIe1FWpw3vKmtX5Plk3DENhdyAqaApW\nuRWs9rQ45WV3unTpovz8/BZbz549I7dzcnJksVji+GiAjscwDFVWVqqkpGS3W2VlZet3apIsXZyy\ndk2JBFS2bJfM6Y5OeXpfqNEv9w9lci+riJqJmZ2dreuvv15XX321unTpksAKAaBjIoRCTIRQALDv\nvF6vZsyYoSlTpmjTpk3NHSbJOai7Uof1lLVL51ljJOQOKFBWp8DmBgW2BU6GN7jH+5nNZg0cOFAF\nBQUqKCjQQQcdFBU0paWltUP1wIHL6/WqrKwsEkqtXbtWP/74o4qLi7Vs2TIFAoE97sNkMzeHUjmp\nsvXMkKUTBVNhT0CNi8vkWVIuI9AcRnXp0kXXXHONrrvuOq6oBwB7gRAKMRFCAcDec7vdmj59uh58\n8EGVlZU1d5hNch3SXalH5smS0fHDp+2hk7+0aQvVePd4n9zc3EjYVFBQoKFDh2rIkCFyuVztUDGA\nvRUIBLRixQoVFxdHbevXr9/jfc1pdtnzMmTvmd5pQqmwNyB38Wa5fyyX4Q9F2tPS0vTnP/9ZN9xw\ng7p3757ACgGgYyCEQkyEUADQevX19Xr66af10EMPacuWLc0dFpNch+Y0hU9pHXex8b0JnVwulw47\n7DANHTo0KnTKyclpx4oBxEttbW1ktlRxcbEWL16s4uJi1dbW7vI+nSmUCvuCcv9YLndxmQxfcxiV\nkpKiP/zhD7rpppvUo0ePBFYIAMmNEAoxEUIBwJ7V1tbqiSee0NSpU1VVVdXcYTUrZXCOUo7IkyXV\nnrgC99HehE45OTkaOXKkRo4cqZNOOkmHHnooazQBBxjDMLR+/Xp98cUXmjNnjubMmaO1a9fucnxn\nCKXC/qA8SyrUuLgs6vRjp9Opq666Srfccot69eqVwAoBIDkRQiEmQigA2LVAIKCnn35a/+///T9V\nV1dH2k1Ws1yH5yp1aJ7Mro5ziXPDMBSoaJBvTbV8G6pbHTqNHDlShx56aId78wgg/tavX6/PP/+8\n1aGUo1cXOQZky94zo0Ndhc8IhOReViH3D2UKu5vX0LLb7br++ut1xx13cDU9ANgBIRRiIoQCgNg+\n+ugjXXfddVq2bFmkzWS3KOXwXKUU9JDZ2THCJyNsKLC5Xt61VfKtrVK4MfYCxIROANpCa0Mpk8Mi\nR98sOftny96ri0zWjhFIGcGwPMsr1Ph9adTv0x49euj+++/XZZddJrO5YzwWAIgnQijERAgFANFW\nrVqlG2+8Ue+8805zo9Ws1KF5ShnaQ2aHNXHFtZIRNuQvrZNvbZV8a6sV9rQMnrp27arTTjuN0AlA\nXO0YSn3yySfauHFjizEmm1mOvlly9M+Wo3cXmWzJf6qvEQrLs3yLGr7dFHWa3jHHHKPHH39cxx9/\nfAKrA4DEI4RCTIRQANCkvr5ef/vb3zR16tSoy5U7DspW+nF9ZElP7gXHjVBY/pI6eddUybeuWoYv\n2GJMjx49dN5556mwsFAnn3yyrNbkD9QAdB6GYWjhwoUqKirSzJkztWrVqpaDrGY5eneRc0BX2ftk\nymxP7kAq7Auq8bsSuX8sl8LNb41+85vf6IEHHlB+fn4CqwOAxCGEQkyEUAAOdOFwWC+++KJuu+02\nbd68OdJu7Zai9BP6yp6XkcDqds8IhuXbWNM042l9TdTlxLfr1auXCgsLVVhYqBNOOIHFxAEkBcMw\nVFxcrJkzZ6qoqEhLly5tOchikr1XFzkHZMvRNyupZ6IGazyqn7de/o3NVw9MTU3V7bffrhtuuEFO\npzOB1QFA+yOEQkyEUAAOZPPnz9c111yjb7/9NtJmclqVdmxvuQ7pLpM5OU9PC2xplGdZhbyrtsoI\nhFv09+/fX4WFhRo3bpyOOeYY1icBkPSWLVumoqIiFRUV6fvvv285wGySo2+mXENyZc/PSNrTh30b\nalQ/b71Ctc0XfujXr58efvhhnXfeeUlbNwC0NUIoxEQIBeBAVFJSoltvvVUvv/xyc6PZpJTDc5U6\nPD8pP203AiF5V1fKvbRCwS2NLfoHDRqkcePGady4cTryyCN5owOgw1q9enXklL0FCxa06LdkOOQa\nkivXoG5JeYVSIxSWe0m5GheWRM1QPfXUU/Xoo4+qoKAggdUBQPsghEJMhFAADiQej0ePPPKI7rvv\nPrnd7ki7vU+m0kf0kTXTlcDqYgtWueVeWiHvyq0tTrfr16+fLr/8co0bN06HHXYYwROATmfDhg16\n44039OKLL2rRokXRnWaTnAOy5RqSI1uP9KT7HRhyB9S4YKM8y7dE2sxmsyZOnKh77rlHXbt2TWB1\nABBfhFCIiRAKwIHAMAy98cYbuummm7Ru3bpIu6WLU+kn9JWjT2bCaovFCIblXVslz9IKBTbXR/WZ\nzWadffbZmjBhgn7xi19wqh2AA4JhGFqwYIGmT5+uV199VR6PJ6rfkuVSyuAcOQd1S7rZrIEtjaqf\ntz7q93lWVpb++te/auLEibLZkm82FwDsL0IoxEQIBaCzW7x4sa677jrNnj070mayW5R6VL5SDsuV\nyZI8IU6wxiPPsgp5ftoadclvScrPz9dVV12lK664Qr169UpQhQCQeDU1NXrppZc0ffp0LVmyJLrT\napbzoK5KGZwja05q0syOMgxDvtVVqv/fBoUb/ZH2IUOG6LHHHtOoUaMSWB0AtD1CKMRECAWgs9q6\ndavuuusuTZ8+XeFw8+LdrkO7K+3Y3kmzjogRCsu3rlqeZRXyl9RF9ZlMJv3yl7/UxIkTNXbsWFmt\nyfXpPgAkkmEY+uqrrzRt2jTNnDlTPp8vqt/aNUWuITlyDuwmsz05rgxqBEJq/KFMjd+XSqHmt1Ln\nnHOOHn74YR100EEJrA4A2g4hFGIihALQ2QQCAT399NO6++67VVNTE2m39UhX+gl9ZeuemrjidmAE\nw/Ks2KLG70sVbvBH9eXm5uqKK67QVVddpX79+iWmQADoQLZu3ap//vOfmj59ulauXBnVZ7JblFLQ\nQykFPZLmVL1QvU/1X2+Qb3VVpM1ut+v666/XHXfcofT09ARWBwD7jxAKMRFCAehMPv74Y1133XVa\nunRppM2cZlf6cX3kOCg7KU7LMAIheZZvC5/cgai+0047TRMnTtTZZ58tu92eoAoBoOMyDEOzZ8/W\ntGnT9OabbyoYbD612WQzK+XwbWFUksyG9ZfVqf6r9QpWNl8so0ePHnrggQd06aWXsu4fgA6LEAox\nEUIB6AxWrVqlG2+8Ue+8805zo8Wk1CN7KvWIPJlsiT8NIxwIybOkXO7FZQp7mt8UORwOXXHFFbr2\n2ms1aNCgBFYIAJ3L5s2bNX36dD322GOqrq6OtJusZrmG5CrliB6ypCQ+8DfChjwrtqjhm41R6wEe\ne+yxeuyxx3T88ccnsDoA2DeEUIiJEApAR1ZfX6/Jkydr6tSp8vubT2lzHJSt9OP6yJLuSGB1TcK+\noNxLyuUu3hz15sLlcmnChAm6+eab1bNnzwRWCACdW11dnZ588kk98sgj2rp1a3OHxSTX4BylHtlT\nltTEh1FhX1CNC0vkXlIuhZvfZl166aV64IEH+FsBoEMhhEJMhFAAOqJwOKwXX3xRt912mzZv3hxp\nt3ZNUfrP+sqel5HA6pqEfUG5izc3hU/+UKQ9NTVVf/rTn3TjjTcqJycngRUCwIGlsbFR06ZN04MP\nPqjy8vLmDrNJrkO7N4VRSfDhRbDao/r56+XfWBtpS01N1e23364bbrhBTqczgdUBQOsQQiEmQigA\nHYlhGPrwww91991369tvv420m5xWpR3bW65DustkTuy6T2FPQI2LN8u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GavDEd5GJWSkqJp06bprLPOqvf4AQAIhLVr1+r222/X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\nb8PhUvHWbNnXZciRUeBVZ7Vaddlll+mGG27QOeeco6CgugdcAHCkcLvd+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          }
        }
      ],
      "source": [
        "f, ax = plt.subplots(2, 1, figsize=(15, 6), tight_layout=True)\n",
        "arms_geo.plot(z=0.0, ax=ax[0])\n",
        "arms_geo.plot(z=wg_height, ax=ax[1])\n",
        "\n",
        "ax[0].set_ylim(-5, 5)\n",
        "_ = ax[1].set_ylim(-5, 5)"
      ],
      "id": "471956ba"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Set up Structures\n",
        "\n",
        "To make use of these new geometries, we need to load them into a\n",
        "`td.Simulation` as `td.Structures` with material properties.\n",
        "\n",
        "We’ll define the substrate and waveguide mediums and then link them up\n",
        "with the Polyslabs."
      ],
      "id": "a0c83c2f-78ca-42b3-a773-9a5593aaaf0a"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Permittivity of waveguide and substrate\n",
        "wg_n = 3.48\n",
        "sub_n = 1.45\n",
        "medium_wg = td.Medium(permittivity=wg_n**2)\n",
        "medium_sub = td.Medium(permittivity=sub_n**2)\n",
        "\n",
        "# Substrate\n",
        "substrate = td.Structure(geometry=substrate_geo, medium=medium_sub)\n",
        "\n",
        "# Waveguides\n",
        "arms = td.Structure(geometry=arms_geo, medium=medium_wg)\n",
        "\n",
        "structures = [substrate, arms]"
      ],
      "id": "cbda495c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Set up Simulation\n",
        "\n",
        "Now let’s set up the rest of the Simulation."
      ],
      "id": "100aeefa-3b28-4c07-8ac2-1c065c7f686f"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Spacing between waveguides and PML\n",
        "pml_spacing = 1.0\n",
        "\n",
        "# Simulation size\n",
        "sim_size = list(arms_geo.bounding_box.size)\n",
        "sim_size[0] -= 4 * pml_spacing\n",
        "sim_size[1] += 2 * pml_spacing\n",
        "sim_size[2] = wg_height + 2 * pml_spacing\n",
        "\n",
        "sim_center = list(arms_geo.bounding_box.center)\n",
        "sim_center[2] = 0\n",
        "\n",
        "# grid size in each direction\n",
        "dl = 0.020\n",
        "\n",
        "# ## Initialize and visualize simulation ###\n",
        "sim = td.Simulation(\n",
        "    size=sim_size,\n",
        "    center=sim_center,\n",
        "    grid_spec=td.GridSpec.uniform(dl=dl),\n",
        "    structures=structures,\n",
        "    run_time=2e-12,\n",
        "    boundary_spec=td.BoundarySpec.all_sides(boundary=td.PML()),\n",
        ")"
      ],
      "id": "9eab8bb9"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Note: `Tidy3D` is warning us that our Simulation does not contain\n",
        "sources. In this case, since we are using the simulation as a\n",
        "demonstration and are not running any simulations, we may safely ignore\n",
        "this warning throughout this notebook.\n",
        "\n",
        "### Plot Simulation Geometry\n",
        "\n",
        "Let’s take a look at the simulation all together with the PolySlabs\n",
        "added. Here the angle of the sidewall deviating from the vertical\n",
        "direction is 30 degree."
      ],
      "id": "cd9648c4-bb3b-494e-a997-a59fea17da40"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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TvF2zZs08HlN1mJlHbm6ua7smP+s84czPIM5U/L1ZlbbuvPeKF/Xm5uZWWtgO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\noL6zmR0AAAAon9VqlZ+fn2s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5aYMGEC3n33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\n/weFs8Ust4CfDwAAAABJRU5ErkJggg==\n"
          }
        }
      ],
      "source": [
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(17, 5))\n",
        "\n",
        "sim.plot(z=wg_height / 2, lw=1, edgecolor=\"k\", ax=ax1)\n",
        "sim.plot(x=0.1, lw=1, edgecolor=\"k\", ax=ax2)\n",
        "\n",
        "ax2.set_xlim([-3, 3])\n",
        "_ = ax2.set_ylim([-1, 1])"
      ],
      "id": "6f26aed3"
    }
  ],
  "nbformat": 4,
  "nbformat_minor": 5,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    }
  }
}