{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Uniform linear grating coupler\n",
        "\n",
        "Grating couplers are optical components used to efficiently couple light\n",
        "between optical fibers (or free-space beams) and integrated photonic\n",
        "waveguides. They consist of a periodic structure—typically etched onto\n",
        "the surface of a photonic chip—that diffracts incoming light into the\n",
        "waveguide mode (or vice versa). Grating couplers are widely used in\n",
        "silicon photonics due to their ease of fabrication, compatibility with\n",
        "planar processes, and ability to support wafer-scale testing.\n",
        "\n",
        "The simplest form of the grating coupler is the uniform linear grating\n",
        "coupler. In this notebook, we demonstrate the design workflow of such a\n",
        "device based on the silicon on insulator (SOI) platform. Conventionally,\n",
        "the initial design starts in 2D for faster speed and lower cost. Once\n",
        "the grating coupler is optimized in 2D, we construct the 3D version and\n",
        "can then potentially perform additional optimization to enhance its\n",
        "coupling efficiency.\n",
        "\n",
        "<img src=\"img/grating_coupler_schematic.png\" width=\"400\" alt=\"Schematic of the grating coupler\">\n",
        "\n",
        "More advanced grating coupler designs, such as the [focusing apodized\n",
        "grating\n",
        "coupler](https://www.flexcompute.com/tidy3d/examples/notebooks/FocusedApodGC/)\n",
        "and the [inverse designed grating\n",
        "coupler](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd19ApodizedCoupler/),\n",
        "can be realized to achieve higher performance."
      ],
      "id": "cb0e4b78-e42b-4e06-8bd9-d78d3ea01aa1"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import matplotlib.pylab as plt\n",
        "import numpy as np\n",
        "import tidy3d as td\n",
        "import tidy3d.web as web"
      ],
      "id": "84b55c99"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Initial Design in 2D\n",
        "\n",
        "We start with the 2D design and aim to optimize its coupling efficiency\n",
        "as much as possible. This way, the design process is faster and costs\n",
        "fewer FlexCredits.\n",
        "\n",
        "First define the wavelength range of interest."
      ],
      "id": "e443b70d-eb44-416d-8cda-1d3320f2a741"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "lda0 = 1.55  # central wavelength\n",
        "freq0 = td.C_0 / lda0  # central frequency\n",
        "ldas = np.linspace(1.5, 1.6, 101)  # wavelength range\n",
        "freqs = td.C_0 / ldas  # frequency range\n",
        "fwidth = 0.5 * (np.max(freqs) - np.min(freqs))  # width of the source frequency range"
      ],
      "id": "32e11c45"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Grating couplers are relatively narrow band device. Within the working\n",
        "bandwidth, the refractive indices of silicon and oxide don’t change\n",
        "noticeably. Therefore, for simplicity we will just model them as\n",
        "nondispersive mediums."
      ],
      "id": "616b3607-a7b1-4d89-8044-3f53b5f26877"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "n_si = 3.47\n",
        "si = td.Medium(permittivity=n_si**2)\n",
        "\n",
        "n_sio2 = 1.44\n",
        "sio2 = td.Medium(permittivity=n_sio2**2)"
      ],
      "id": "e702b2b1"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Define geometry parameters. In this case, we have a silicon layer of 260\n",
        "nm thickness. The grating will be partially etched with an etching depth\n",
        "of 160 nm. The filling fraction is set to be 80% in this case. A higher\n",
        "filling fraction will lead to a smaller gap size so this needs to be\n",
        "chosen according to the fabrication. The BOX layer has a thickness of 2\n",
        "μm and the top oxide cladding has a thickness of 680 nm."
      ],
      "id": "f3d8546f-f43e-4f88-9799-c04829d92847"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "t_si = 0.26  # thickness of the silicon layer\n",
        "etch_depth = 0.16  # etching depth\n",
        "ff = 0.8  # filling fraction of the grating\n",
        "t_tox = 0.68  # top oxide layer thickness\n",
        "t_box = 2  # bottom oxide layer thickness\n",
        "n = 20  # number of grating teeth to create"
      ],
      "id": "21a54d45"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The goal is to couple between a single-mode waveguide and a single-mode\n",
        "fiber with a mode field diameter of 10.8 μm at an angle of 14.5 degrees."
      ],
      "id": "c3adf90c-1f85-4de2-9067-49c5bc459ea8"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [],
      "source": [
        "theta = np.deg2rad(14.5)  # fiber tilt angle\n",
        "mfd = 10.8  # mode field diameter\n",
        "\n",
        "inf_eff = 1e3  # effective infinity\n",
        "buffer = 0.6 * lda0  # buffer spacing to pad the simulation domain"
      ],
      "id": "620e1412"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next we define some\n",
        "[Structures](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.Structure.html)\n",
        "that are not changing in the design. This includes the top oxide layer,\n",
        "BOX layer, slab waveguide layer, etc."
      ],
      "id": "216f0b2e-c081-4e56-9865-f8e1f0c90976"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [],
      "source": [
        "# create the top oxide layer\n",
        "tox = td.Structure(\n",
        "    geometry=td.Box.from_bounds(rmin=(-inf_eff, -inf_eff, 0), rmax=(inf_eff, inf_eff, t_tox)),\n",
        "    medium=sio2,\n",
        ")\n",
        "\n",
        "# create the slab waveguide\n",
        "slab_waveguide = td.Structure(\n",
        "    geometry=td.Box.from_bounds(rmin=(-inf_eff, -inf_eff, 0), rmax=(0, inf_eff, t_si)),\n",
        "    medium=si,\n",
        ")\n",
        "\n",
        "# create the etched waveguide\n",
        "etched_waveguide = td.Structure(\n",
        "    geometry=td.Box.from_bounds(rmin=(0, -inf_eff, 0), rmax=(inf_eff, inf_eff, t_si - etch_depth)),\n",
        "    medium=si,\n",
        ")\n",
        "\n",
        "# create the bottom oxide layer\n",
        "box = td.Structure(\n",
        "    geometry=td.Box.from_bounds(rmin=(-inf_eff, -inf_eff, -t_box), rmax=(inf_eff, inf_eff, 0)),\n",
        "    medium=sio2,\n",
        ")\n",
        "\n",
        "# create the silicon substrate layer\n",
        "substrate = td.Structure(\n",
        "    geometry=td.Box.from_bounds(\n",
        "        rmin=(-inf_eff, -inf_eff, -inf_eff), rmax=(inf_eff, inf_eff, -t_box)\n",
        "    ),\n",
        "    medium=si,\n",
        ")"
      ],
      "id": "f684b0f4"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "To enable parameter sweeping in optimizing the design, we define a\n",
        "function that takes the design parameters as arguments and returns a\n",
        "[Simulation](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.Simulation.html)\n",
        "object. In the simulation, we use a\n",
        "[GaussianBeam](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.GaussianBeam.html)\n",
        "source to represent the incident field from the single-mode fiber. A\n",
        "[ModeMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ModeMonitor.html)\n",
        "is added on the waveguide to measure the coupling efficiency, which will\n",
        "be used as the figure of merit for our design optimization.\n",
        "\n",
        "Since this simulation is 2D, the boundary condition is set to periodic\n",
        "in the $y$ direction."
      ],
      "id": "cc3dd96a-493f-4ad4-ac76-9bdcc111b1de"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "def make_2d_sim(p: float, source_x: float) -> td.Simulation:\n",
        "    \"\"\"Function to create a 2D simulation given the grating period and source position\"\"\"\n",
        "\n",
        "    source_gap = 0.5  # gap distance between the source and the top oxide\n",
        "\n",
        "    # define a gaussian beam source\n",
        "    source = td.GaussianBeam(\n",
        "        size=(2 * mfd, td.inf, 0),\n",
        "        center=[source_x, 0, t_tox + source_gap],\n",
        "        source_time=td.GaussianPulse(freq0=freq0, fwidth=fwidth),\n",
        "        angle_theta=theta,\n",
        "        direction=\"-\",\n",
        "        waist_radius=mfd / 2,\n",
        "        pol_angle=np.pi / 2,  # 90 degree polarization angle for TE polarization\n",
        "    )\n",
        "\n",
        "    # define a mode monitor to measure coupling efficiency\n",
        "    mode_monitor = td.ModeMonitor(\n",
        "        center=(-buffer / 2, 0, t_si / 2),\n",
        "        size=(0, td.inf, 6 * t_si),\n",
        "        freqs=freqs,\n",
        "        mode_spec=td.ModeSpec(num_modes=1, target_neff=3.47),\n",
        "        name=\"mode\",\n",
        "    )\n",
        "\n",
        "    l_grating = n * p  # length of the grating region\n",
        "\n",
        "    # create the grating geometries\n",
        "    gratings = 0\n",
        "    for i in range(n):\n",
        "        gratings += td.Box(\n",
        "            center=(ff * p / 2 + i * p, 0, t_si - etch_depth / 2), size=(p * ff, td.inf, etch_depth)\n",
        "        )\n",
        "\n",
        "    # create the grating structure\n",
        "    gratings = td.Structure(geometry=gratings, medium=si)\n",
        "\n",
        "    # create a box to represent the simulation domain box\n",
        "    sim_box = td.Box.from_bounds(\n",
        "        rmin=(-buffer, 0, -t_box - buffer),\n",
        "        rmax=(l_grating + buffer, 0, t_si + t_tox + buffer),\n",
        "    )\n",
        "\n",
        "    run_time = 1e-12  # simulation run time\n",
        "\n",
        "    # construct simulation\n",
        "    sim = td.Simulation(\n",
        "        center=sim_box.center,\n",
        "        size=sim_box.size,\n",
        "        grid_spec=td.GridSpec.auto(\n",
        "            min_steps_per_wvl=25, wavelength=lda0\n",
        "        ),  # use a fine grid to ensure the small features are well resolved\n",
        "        structures=[\n",
        "            tox,\n",
        "            gratings,\n",
        "            etched_waveguide,\n",
        "            slab_waveguide,\n",
        "            box,\n",
        "            substrate,\n",
        "        ],\n",
        "        sources=[source],\n",
        "        monitors=[mode_monitor],\n",
        "        run_time=run_time,\n",
        "        boundary_spec=td.BoundarySpec(\n",
        "            x=td.Boundary.pml(),\n",
        "            y=td.Boundary.periodic(),  # set the boundary to periodic in y since it's a 2D simulation\n",
        "            z=td.Boundary.pml(),\n",
        "        ),\n",
        "    )\n",
        "\n",
        "    return sim"
      ],
      "id": "304877fb"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "To visualize the simulation setup, we can create a dummy simulation and\n",
        "plot it. The plot shows the setup is correct. We have a grating with a\n",
        "tunable period and a Gaussian beam with a tunable position."
      ],
      "id": "b567c3e7-c430-48db-9302-55104578c2cf"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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vf/tbnee54IILNHv2bD377LP65z//qY8//lij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\nVi1atKhZz+3UqZMqKio0c+ZMnX322ZIki6QjurfTGft30ai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          }
        }
      ],
      "source": [
        "sim0 = make_2d_sim(p=0.5, source_x=5)\n",
        "sim0.plot_eps(y=0, freq=freq0)\n",
        "plt.show()"
      ],
      "id": "0ceb40f2"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The next step is to determine the optimal grating period and source\n",
        "position. We can first get an estimate of the optimal grating period by\n",
        "using the grating equation\n",
        "\n",
        "$$\\Lambda = \\frac{\\lambda_0}{n_{\\text{eff}} - n_{\\text{clad}} \\sin \\theta},$$\n",
        "\n",
        "where - $\\Lambda$ = grating period  \n",
        "- $\\lambda_0$ = free-space wavelength of the incident light  \n",
        "- $n_{\\text{eff}}$ = effective index of the guided mode in the\n",
        "waveguide  \n",
        "- $n_{\\text{clad}}$ = refractive index of the cladding - $\\theta$ =\n",
        "angle of incidence\n",
        "\n",
        "$n_{\\text{eff}}$ can be approximated by\n",
        "\n",
        "$$n_{\\text{eff}} = f n_{etched} + (1-f) n_{unetched},$$\n",
        "\n",
        "where $f$ is the filling fraction, $n_{unetched}$ is the effective index\n",
        "of the unetched slab mode, and $n_{etched}$ is the effective index of\n",
        "the etched slab mode. We will calculate $n_{unetched}$ and $n_{etched}$\n",
        "using our mode solver. The most convenient way of doing so would be to\n",
        "construct mode simulations from the dummy FDTD simulation. For the\n",
        "unetched slab mode, we specify the mode solving plane to be on the left\n",
        "side of the grating region. For the etched slab mode, we specify the\n",
        "plane to be on the right side of the grating region."
      ],
      "id": "4e09a293-efcb-4315-ad65-63eb5aeee661"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "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\">04:45:46 UTC </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'unetched'</span> with resource_id                           \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'mos-4ed7ba54-87c6-47e0-95ba-3ba59f398f66'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'MODE'</span>.   \n",
              "</pre>"
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          }
        },
        {
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          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
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        {
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          "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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        {
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          "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\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">04:45:48 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\">04:45:49 UTC </span>status = success                                                   \n",
              "</pre>"
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        {
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          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
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              "</script>"
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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\"></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\">04:45:50 UTC </span>Loading results from simulation_data.hdf5                          \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>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'etched'</span> with resource_id                             \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'mos-c2dacf3d-5eda-425a-90b8-085a2e24c29d'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'MODE'</span>.   \n",
              "</pre>"
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          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"143b545fbf444ee5992a082a85253794\",\"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\">04:45:51 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\">04:45:52 UTC </span>status = success                                                   \n",
              "</pre>"
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        },
        {
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          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
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          "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\">04:45:53 UTC </span>Loading results from simulation_data.hdf5                          \n",
              "</pre>"
            ]
          }
        }
      ],
      "source": [
        "mode_unetched = td.ModeSimulation.from_simulation(\n",
        "    sim0,\n",
        "    mode_spec=td.ModeSpec(num_modes=1, target_neff=3.47),\n",
        "    plane=td.Box(center=(-0.1, 0, 0), size=(0, td.inf, 5 * t_si)),\n",
        "    freqs=[freq0],\n",
        ")\n",
        "data_unetched = web.run(simulation=mode_unetched, task_name=\"unetched\")\n",
        "\n",
        "mode_etched = mode_unetched.updated_copy(\n",
        "    plane=td.Box(center=(n * 0.5 + 0.1, 0, 0), size=(0, td.inf, 5 * t_si))\n",
        ")\n",
        "data_etched = web.run(simulation=mode_etched, task_name=\"etched\")"
      ],
      "id": "c8349342"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "After running the mode solving, we can extract the effective indices and\n",
        "hence calculate the appropriate grating period."
      ],
      "id": "d5658902-5b6e-4f23-9c10-58b69b936c10"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Calculated grating period is 608 nm"
          ]
        }
      ],
      "source": [
        "neff_unetch = (\n",
        "    data_unetched.modes.n_eff.values.item()\n",
        ")  # effective index of the slab mode of the unetched waveguide\n",
        "neff_etch = (\n",
        "    data_etched.modes.n_eff.values.item()\n",
        ")  # effective index of the slab mode of the etched waveguide\n",
        "theta_c = np.sin(theta) / n_sio2  # incident angle in the cladding\n",
        "ff = 0.8  # filling fraction\n",
        "\n",
        "# calculate the grating period\n",
        "p = lda0 / (ff * neff_unetch + (1 - ff) * neff_etch - n_sio2 * np.sin(theta_c))\n",
        "\n",
        "print(f\"Calculated grating period is {p * 1e3:.0f} nm\")"
      ],
      "id": "d07338e6"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "To optimize the design, we can perform a [parameter\n",
        "sweep](https://www.flexcompute.com/tidy3d/examples/notebooks/ParameterScan/)\n",
        "over the grating period and source position. To do so, we create a\n",
        "dictionary of simulations and then a\n",
        "[Batch](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.web.api.container.Batch.html).\n",
        "When running the batch, multiple simulations will be running in\n",
        "parallel, making the sweep very time-efficient."
      ],
      "id": "9fb55fab-c784-4d7d-ac56-9ae0edad0ee0"
    },
    {
      "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\":\"9ee861428e6d4c8a93b63b1633e55953\",\"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\">04:46:21 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">44</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\">04:47:01 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1.100</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\":\"83271bab7e3642abb7fc5a8f0979d34e\",\"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\">04:47:24 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": [
        "p_list = np.linspace(0.60, 0.63, 7)\n",
        "source_x_list = np.linspace(3, 5, 11)\n",
        "\n",
        "sims_2d = {\n",
        "    f\"p={p:.2f};source_x={source_x:.2f}\": make_2d_sim(p, source_x)\n",
        "    for p in p_list\n",
        "    for source_x in source_x_list\n",
        "}\n",
        "\n",
        "batch = web.Batch(simulations=sims_2d)\n",
        "batch_results = batch.run(path_dir=\"data\")"
      ],
      "id": "141d17e8"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "After the sweep is finished, we can extract the coupling efficiency from\n",
        "the monitor data."
      ],
      "id": "5b37ab32-b223-461c-83bd-ea03279cbff5"
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [],
      "source": [
        "ce = np.array(\n",
        "    [\n",
        "        [\n",
        "            np.abs(\n",
        "                batch_results[f\"p={p:.2f};source_x={source_x:.2f}\"][\"mode\"]\n",
        "                .amps.sel(f=freq0, direction=\"-\")\n",
        "                .values.item()\n",
        "            )\n",
        "            ** 2\n",
        "            for source_x in source_x_list\n",
        "        ]\n",
        "        for p in p_list\n",
        "    ]\n",
        ")"
      ],
      "id": "91abc823"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Plot the coupling efficiency as a function of period and source position\n",
        "in a false color map."
      ],
      "id": "46ed2385-00f1-47c6-a9ea-12f596787897"
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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ERERE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\niIiIiIiISMGYvCEiIiIiIiIiUrD/B8L4hYruoRPMAAAAAElFTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "plt.pcolormesh(source_x_list, p_list, ce, cmap=\"bwr\")\n",
        "plt.colorbar()\n",
        "plt.show()"
      ],
      "id": "419bec46"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "From the result we can determine the optimal grating period and source\n",
        "position."
      ],
      "id": "6b700102-0e04-4c7a-b15f-260b4b60cdf7"
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Optimal period is 620.0 nm.\n",
            "Optimal source_x is 3.6 μm.\n",
            "Optimal coupling efficiency is 56.23%, or -2.50 dB."
          ]
        }
      ],
      "source": [
        "i, j = np.unravel_index(np.argmax(ce), ce.shape)\n",
        "best_p = p_list[i]\n",
        "best_source_x = source_x_list[j]\n",
        "best_ce = ce[i, j]\n",
        "\n",
        "print(f\"Optimal period is {best_p * 1e3} nm.\")\n",
        "print(f\"Optimal source_x is {best_source_x} μm.\")\n",
        "print(f\"Optimal coupling efficiency is {best_ce * 1e2:.2f}%, or {10 * np.log10(best_ce):.2f} dB.\")"
      ],
      "id": "ef9827fb"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## 3D Design of the Grating Coupler\n",
        "\n",
        "The 2D design shows promising results. Now we can convert it to 3D for\n",
        "verification and potentially further optimization.\n",
        "\n",
        "The single-mode waveguide has a width of 500 nm. The waveguide and the\n",
        "grating are connected via a linear taper. The longer the taper, the\n",
        "lower the loss in the taper region but the larger the footprint. Here we\n",
        "use a 50 μm linear taper with reasonably low loss.\n",
        "\n",
        "To enable additional optimization, we create a function similar to\n",
        "before."
      ],
      "id": "43d3d89b-6f80-4b09-95fe-21ed708f87f1"
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [],
      "source": [
        "w_wg = 0.5  # waveguide width\n",
        "w_grating = mfd  # grating width is set to the mode field diameter\n",
        "l_taper = 50  # length of the linear taper\n",
        "\n",
        "\n",
        "def make_3d_sim(p: float, source_x: float) -> td.Simulation:\n",
        "    \"\"\"Function to create a 2D simulation given the grating period and source position\"\"\"\n",
        "\n",
        "    source_gap = 0.5\n",
        "\n",
        "    # define a gaussian beam source\n",
        "    source = td.GaussianBeam(\n",
        "        size=(2 * mfd, 2 * mfd, 0),\n",
        "        center=[source_x, 0, t_tox + source_gap],\n",
        "        source_time=td.GaussianPulse(freq0=freq0, fwidth=fwidth),\n",
        "        angle_theta=theta,\n",
        "        direction=\"-\",\n",
        "        waist_radius=mfd / 2,\n",
        "        pol_angle=np.pi / 2,  # 90 degree polarization angle for TE polarization\n",
        "    )\n",
        "\n",
        "    # define a mode monitor\n",
        "    mode_monitor = td.ModeMonitor(\n",
        "        center=(-l_taper - buffer / 2, 0, t_si / 2),\n",
        "        size=(0, 4 * w_wg, 6 * t_si),\n",
        "        freqs=freqs,\n",
        "        mode_spec=td.ModeSpec(num_modes=1, target_neff=3.47),\n",
        "        name=\"mode\",\n",
        "    )\n",
        "\n",
        "    l_grating = n * p  # length of the grating region\n",
        "\n",
        "    gratings = 0\n",
        "    for i in range(n):\n",
        "        gratings += td.Box(\n",
        "            center=(ff * p / 2 + i * p, 0, t_si - etch_depth / 2),\n",
        "            size=(p * ff, w_grating, etch_depth),\n",
        "        )\n",
        "\n",
        "    # create the grating structure\n",
        "    gratings = td.Structure(geometry=gratings, medium=si)\n",
        "\n",
        "    vertices = [\n",
        "        (0, w_grating / 2),\n",
        "        (0, -w_grating / 2),\n",
        "        (-l_taper, -w_wg / 2),\n",
        "        (-l_taper - 2 * buffer, -w_wg / 2),\n",
        "        (-l_taper - 2 * buffer, w_wg / 2),\n",
        "        (-l_taper, w_wg / 2),\n",
        "    ]\n",
        "    taper = td.Structure(\n",
        "        geometry=td.PolySlab(vertices=vertices, axis=2, slab_bounds=(0, t_si)), medium=si\n",
        "    )\n",
        "\n",
        "    # create a box to represent the simulation domain box\n",
        "    sim_box = td.Box.from_bounds(\n",
        "        rmin=(-buffer - l_taper, -w_grating / 2 - buffer, -t_box - buffer),\n",
        "        rmax=(l_grating + buffer, w_grating / 2 + buffer, t_si + t_tox + buffer),\n",
        "    )\n",
        "\n",
        "    run_time = 2e-12  # simulation run time\n",
        "\n",
        "    # construct simulation\n",
        "    sim = td.Simulation(\n",
        "        center=sim_box.center,\n",
        "        size=sim_box.size,\n",
        "        grid_spec=td.GridSpec.auto(\n",
        "            min_steps_per_wvl=15, wavelength=lda0\n",
        "        ),  # use a fine grid to ensure the small features are well resolved\n",
        "        structures=[\n",
        "            tox,\n",
        "            gratings,\n",
        "            etched_waveguide,\n",
        "            taper,\n",
        "            box,\n",
        "            substrate,\n",
        "        ],\n",
        "        sources=[source],\n",
        "        monitors=[mode_monitor],\n",
        "        run_time=run_time,\n",
        "        symmetry=(0, -1, 0),\n",
        "    )\n",
        "\n",
        "    return sim"
      ],
      "id": "3316b8f1"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Generate the simulation using the optimal parameters from the 2D design."
      ],
      "id": "2f59ccff-47a5-4e50-82f4-1778043f6ac2"
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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69OihgQMHqqSkJOV7b7/9dvXv3z8bzUQmmNzMvhu+7ivt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\nGC5VdbhAUs3PMJalSlOi1d6WOW0fAABoohS5zegydMfzFKj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          }
        }
      ],
      "source": [
        "sim_3d = make_3d_sim(p=best_p, source_x=best_source_x)\n",
        "sim_3d.plot(z=t_si)\n",
        "plt.show()"
      ],
      "id": "06542b2c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Run the 3D simulation."
      ],
      "id": "7ae81d1e-ee90-4034-8ead-9d64182c10f3"
    },
    {
      "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\">04:47:26 UTC </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'3D_GC'</span> with resource_id                              \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-02de62f9-0dd6-4826-95fe-a7b4fdd237d1'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</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>View task using web UI at                                          \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-02de62f9-0dd6-4826-95fe-a7b4fdd237d1\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-02de62f9-0dd</span></a>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-02de62f9-0dd6-4826-95fe-a7b4fdd237d1\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">6-4826-95fe-a7b4fdd237d1'</span></a>.                                         \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>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/9b36e144-ddb6-41f8-8dd8-30b62b26a870\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"8ab70d16e6424989af4760cc1fc56f84\",\"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\">04:47:28 UTC </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.686</span>. This assumes the FDTD solver runs\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>for the full simulation time; if early shutoff is reached, the     \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>billed cost can be lower. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the  \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>billed FlexCredit cost after a simulation run.                     \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\">04:47:29 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\":\"5722cf7a1d4341dfb2d43d4adf76153c\",\"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\">04:47:30 UTC </span>Loading results from simulation_data.hdf5                          \n",
              "</pre>"
            ]
          }
        }
      ],
      "source": [
        "sim_data = web.run(simulation=sim_3d, task_name=\"3D_GC\")"
      ],
      "id": "525d05ab"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Plot the coupling efficiency as a function of wavelength. Compared to\n",
        "2D, the coupling efficiency of -4 dB is slightly lower in 3D. This is\n",
        "because of two factors: 1. the taper introduces some loss during the\n",
        "mode size conversion down to the single-mode waveguide; 2. The optimal\n",
        "parameters in 2D can differ slightly from the optimal parameters in 3D.\n",
        "\n",
        "One can perform a parameter sweep similar to the 2D case to further\n",
        "optimize the design. For simplicity, we skip this part in this notebook."
      ],
      "id": "61317723-b425-45e7-964a-8b46c1b3d7a5"
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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16lWdOXMmFSsDAMBDORzSn3+aZuhFi5rlOydOJH1upUqm39SmTVKz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Q9wtiJFiqhq1arau3ev3TW/fft2SVJAQIBGjhzpcP/0p+PExMRYv8ls3Lix\nXnrpJRdGDdyca9/rM484rFWrlvV1diMR0+vPnDmjM2fOOD9IwImy+3wTHh6upKQkSVLnzp2z7MPT\n01MdO3bUp59+qv379ys6Oto6KhHIS7Vq1dLOnTslZf8+nbnu2vfpGjVq6Ny5czb3qo4UhHtZklRw\nK5mHP/r4+NjU1atXTz/++KMuXbqkw4cP23yoyyz9JkdKG50F5GfZXfOZJScnq1+/flqxYoUkaeTI\nkZo0aZLL4wNcIf26z+qaP378+HW/kEhISNDixYslSfHx8c4NEHCy7N7r69evb32dmJiYbT/p9Tzp\nDPlddtd85sWgM38h7UhAQIDNfiSpYIb69evr22+/lZT9+3Tmumvfp+vVq6ctW7bo6NGjdoMxMisI\n97IkqeA2DMPQxo0bJaWt5ePr62tT37VrV+tjbpcvX57lt+y//PKLpLT/1O68804XRgzcvA0bNlhf\nZ/VtSWpqqgYOHKglS5ZIkh5//HHruj5AQRMVFaUjR45Isr/mR44ced11qMaOHat9+/YpICDAui5P\nuXLlXBIr4Czp7/Wenp52a3Q2a9ZMwcHBOn/+vHbt2pVlHwkJCTp06JCktG/kgfwsu883ZcqUsb6+\n3qiSo0ePSkqb/hccHOzECIGc6969u8aMGSNJ2rVrl9q0aeOwXeb38Gvfp7t27arZs2crNTVVK1as\nsE4Dv1b6vWyNGjWyfDKm2UhSwW3MnTtXhw8fliT17NnTrr558+a65ZZbdOjQIc2cOVOPP/64ihYt\natNmz5491pEm/fv3z3JdByA/OHPmjKZNmyYpbc55Vv/hPfHEE1qwYIGktPV80hfPBQqiV155RYZh\nSLJ/r2/SpImaNGmS7f4ffPCBpLRvKB0tXArkN+vXr9eyZcskSa1bt7YZGSKlLaj70EMPacaMGVq2\nbJkiIiJUpUoVu37+97//WRfUveeee1weN3Cjrly5onHjxkmSPDw81L17d5v6Jk2ayMfHR4mJiZo/\nf76effZZh5/ZT506Zf3dueOOO2wWrwbyUoMGDdSgQQPt3LlTn376qYYNGyYvL/tUzUcffWR9fe11\n36VLF5UpU0Znz57Ve++9pz59+sjDw3YJ8j/++MO67uzDDz/sgjNxDhZOR4EwevRo9e7d2/okj2vN\nnz9f33//vS5fvmxXd/XqVb3zzjvWBaT9/f0drrNjsVis05uOHDmigQMH2vT3zz//qE+fPkpJSVHx\n4sWt2W7AFZYtW6bevXurd+/e1hGAmR04cEDTpk3TP//843D/9evXq02bNtb56q+//rrDD1+jRo2y\njhbp37+/5s6dm+VTpABXunLlivWaz2oB28mTJ2vNmjVKTk62qztz5owGDRqkzz//XFLa0Pl+/fq5\nMmTgpr377rvW6/7ChQt29cuXL9e8efN0/vx5u7qUlBTNmzdPPXr0kGEY8vT0zPJ3Z8yYMQoMDFRC\nQoJ69epl93/HTz/9pOeee06SVKlSJQ0ZMsQJZwfY+/PPP63XfPqU6swuXLigCRMmaPfu3Q7337Nn\njzp27GgdUTJ06FBVr17dpo2fn58GDx4sSdq3b5/69+9v9zt06NAh3XPPPbpy5YokZTmDAnCGQYMG\nqXfv3nrqqaeybDNlyhRJadf4wIEDFRcXZ61LTk7WuHHjtGjRIklpC6hnnsotSb6+vho7dqyktHXZ\nRowYYTM9cNeuXdbEVNmyZTVq1CjnnJwLWIz0rxsBF1mzZo31m2kpbdrd999/L0mqUqWKGjdubK3z\n8fGxjujIrG7dutq7d6/8/Pxs5pmne+ihh/TVV1/Jx8dHlStXVkhIiIKDgxUdHa3t27db9wkICNCS\nJUvUtm3bLON9/vnnNXXqVElSYGCgmjZtqqtXr2rTpk1KTk6Wl5eXlixZwreMyFbfvn2VkpJi3d62\nbZt1yPl9991nkwgaOXKk9cmT6aZPn279z2PhwoV2N9tr1qxRu3btJKVNXy1XrpxCQkKUmpqq/fv3\n69ixY9a2I0aMcPgks2XLllmvYw8PD/Xo0cPhtzaZffDBBwoJCbne6cMNffzxx1q1apV1+99//9W6\ndeskSY0aNVLVqlWtdfXq1dPrr79us39MTIx1LZDOnTtbR61mVrVqVUVERMjf31+VKlVSSEiIihcv\nrlOnTmnnzp3W5FVoaKhWrlypihUr5vo82rZtq7Vr16ps2bI6ffp0rveH+zh8+LD1ceDpVqxYocuX\nLysoKMj6Hp1u1qxZKl26tE1Z5hv1EydO2F2zEyZM0GuvvSZPT0/rNV+mTBldvnxZO3futN54+/j4\naPbs2dl+M7527Vp16dJF8fHx8vLyUtOmTVWqVCkdOnRIBw4ckJT2pMDffvtNd9xxx439UFDojRw5\nUpGRkdbtAwcOWB840alTJ/n7+1vr7r//ft1///02+//888/q0aOHJGn8+PF2X/qePHlSlSpVkiSV\nKlVKFSpUUEhIiLy8vHTkyBHrtSqljZb99ttvHa4/eOnSJXXo0EFbtmyRJBUtWlRNmjRRUFCQIiMj\ntX37dqWmpkqSBg8erM8+++yGfyYo3H744Qd9+eWX1u2rV69q+fLlktIW8K9bt661rkyZMjajndKV\nKlVK58+fV40aNfT3339neay3337b+qCWEiVKqFmzZvL29tb27dutn0kaNmyo1atX242aTTdgwABr\nvGXLltUdd9yhmJgYbdmyRampqfL19dXvv/+ev5etMQAX+9///mdIytGfIkWKOOyjTp06hiTDz8/P\nYf3KlSuNfv36GcHBwQ77DQgIMIYNG2acPHkyxzFXqVLFrp9mzZoZW7ZsueGfBdyHp6dnjq/7+fPn\n2+0/bdo0a/3ChQvt6k+fPm0899xzRt26dR326eHhYbRt29ZYtmxZljEuXLgwxzGm/zl8+LBTf04o\nPAYPHpzj66h9+/Z2+0dHR1vrO3fu7PAYn376qdG5c2fD19fXYb9VqlQxxo8fb1y5cuWGz6NNmzaG\nJKNs2bI33AfcQ1hYWK7eP48ePWrXx3//+19r/YkTJ+zqt2/fbgwePNioWLGiwz59fX2Nfv36Gbt3\n785RzPv27TM6depkeHh42PTj7e1t9OvXzzh27NjN/lhQyNWuXTvH1/zYsWPt9l+6dKm1fvz48Xb1\nV65cMcaOHWs0bdrU7jpN/9OoUSNj3rx51401Pj7eGDdunBESEuKwnzp16hhffPGFM34sKMQmTZqU\n42u+SpUqDvtIv0etUaPGdY+3dOlSh5/vAwICjJdffvm6n3FSU1ONadOm2V33FovFuPvuu419+/bd\nyI8hTzGSCi4XERGhrVu35qitp6en7r33XrvylStXKjY2Vl5eXtkuepuamqrjx4/r1KlTOnfunHx9\nfVWxYkXVrl3bbk7u9RiGob179+rEiRPy9vZWrVq1HK7hADjy/fffW7+hu56mTZvaPW7277//tj6K\ntnnz5tmOCDl//rxOnDihqKgopaSkqFSpUqpbt66KFy+e7XFPnjypzZs35yjGdF27dpWfn1+u9oF7\n+PPPP60L0F5P2bJl7UYPJiUl6ccff5QkhYSEqFWrVlnun5CQoIiICJ06dUqxsbHy9/dXzZo1s31s\nc06tXbtW//77r4oWLcqIWWTrwoULWr16dY7bd+vWzW7a9ebNm3Xy5ElJaeuLXPtQl8wiIyMVGRmp\nM2fOyNvbWyEhIapTp84NrY959uxZHThwQDExMQoKClKDBg2u+38GIEm//fabLl68mKO2t912m267\n7TabstOnT1sXPa9bt65CQ0Oz3P/ixYvWz/UJCQkKDAzUbbfdpqCgoFzFbBiGDh06pIiICF25ckUl\nSpRQaGioypcvn6t+4J4OHjyY5fTTa/n5+alr16525UuXLlVCQoKKFy+uLl265KivI0eO6J9//lFC\nQoLKlSun+vXrX3fGQ2apqanatWuXIiMjVaxYMYWGhhaYB8GQpAIAAAAAAIDpWDgdAAAAAAAApiNJ\nBQAAAAAAANORpAIAAAAAAIDpSFIBAAAAAADAdCSpAAAAAAAAYDqSVAAAAAAAADAdSSoAAAAAAACY\njiQVAAAAAAAATEeSCgAAAAAAAKYjSQUAAAAAAADTkaQCAAAAAACA6UhSAQAAAAAAwHQkqQAAAAAA\nAGA6klQAAAAAAAAwHUkqAAAAAAAAmI4kFQAAQD6waNEiDRkyRK+88orZoeQrn376qYYMGaJJkybl\n2THj4+M1fPhwPfbYY4qOjs6z47rChAkTNGTIEP35559mhwIAwHWRpAIAAE63atUqDRkyREOGDNGB\nAweybfu///3P2vbHH3/Mtu2mTZusbQvbTXdYWJjmzJmjb775xuxQ8pXVq1drzpw51702nGnatGma\nNWuWzpw5o8DAwDw7riuEhIRozpw5GjFihNmhAABwXV5mBwAAAAofHx8fzZkzR5JUu3ZthYaGZtl2\n2rRp2r17tyQpKipKvXr1yrLt119/be331VdfdWLEyEtffPGF1q9frwoVKujNN980OxwbZ8+e1aRJ\nk2SxWPJdbDfikUce0aRJk7R582Z9/fXX6tevn9khAQCQJUZSAQAAp2vWrJmKFi0qSVq3bl2W7S5c\nuKA9e/ZYtzdu3KjU1NQs26f3ValSJVWrVs1J0SKvrV+/XnPmzNHixYvNDsXO+PHjFRcXp27duqlh\nw4Zmh3PTvLy89MILL0iSXn75ZaWkpJgcEQAAWSNJBQAAnK5IkSJq1qyZJGnDhg1ZJp7Wr18vwzBU\ns2ZNlS5dWrGxsdq5c6fDtjExMdYRV23atHFJ3HBvcXFx+vzzzyVJjz76qLnBOFG/fv1UpEgRHTt2\nTEuXLjU7HAAAskSSCgAAuETbt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          }
        }
      ],
      "source": [
        "ce_3d = np.abs(sim_data[\"mode\"].amps.sel(direction=\"-\")) ** 2\n",
        "\n",
        "plt.plot(ldas, 10 * np.log10(ce_3d), c=\"red\")\n",
        "plt.ylim(-12, 0)\n",
        "plt.xlabel(\"Wavelength (μm)\")\n",
        "plt.ylabel(\"Coupling efficiency (dB)\")\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "id": "a68592fd"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Final Remarks\n",
        "\n",
        "In this notebook, we use the Gaussian beam as the source and use a mode\n",
        "monitor to measure the coupling efficiency. Due to reciprocity, one can\n",
        "use a mode source at the waveguide as excitation and then take the\n",
        "radiated field and do a mode overlap with a Gaussian profile to\n",
        "calculate the same value. In addition, in this setup, one can also\n",
        "perform near field to far field projection by using monitors like\n",
        "[FieldProjectionAngleMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FieldProjectionAngleMonitor.html)\n",
        "to investigate he radiation angle of the grating if that’s of interest.\n",
        "\n",
        "In the simulations we only focus on the coupling efficiency and hence\n",
        "only use a\n",
        "[ModeMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ModeMonitor.html)\n",
        "to measure the power of the fundamental mode in the waveguide. One can\n",
        "also add\n",
        "[FieldMonitors](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FieldMonitor.html)\n",
        "in the simulations to help visualize the field distribution if needed."
      ],
      "id": "f60107a5-2245-4b75-8870-cf9693614a2d"
    }
  ],
  "nbformat": 4,
  "nbformat_minor": 5,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    }
  }
}