{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e46397ed-22f3-4cac-be17-484c6396f5ba",
   "metadata": {},
   "source": [
    "# 2D effective index approximation of 3D simulations\n",
    "\n",
    "Large-scale 3D FDTD simulations are often required for accurate results but are associated with significant time and costs. Therefore, the development of methods to approximate 3D simulations using 2D models presents notable advantages. For instance, during the initial phase of design exploration, employing 2D simulations can effectively narrow down the range of parameters, with 3D simulations subsequently refining and finalizing the design.\n",
    "\n",
    "This notebook introduces an efficient index approximation method that enables the approximation of 3D FDTD simulations through 2D simulations, substantially reducing computational resources and simulation times, potentially by orders of magnitude, while still retaining a reasonable level of accuracy. This method is particularly suitable for modeling integrated photonic devices that support waveguide modes. We first outline the process for calculating the effective permittivity for the 2D simulation using the variational method.\n",
    "\n",
    "Following this, we compare the results of 1D approximation of a 2D device, and a 2D approximation of a 3D device to validate the approximation method's effectiveness. The findings indicate that, when applied appropriately, the approximated simulation maintains an acceptable fidelity to the corresponding full simulation response.\n",
    "\n",
    "<a href=\"https://doi.org/10.1007/s11082-009-9349-3\"><img src=\"img/effective_index_approximation.png\" width=\"500\" alt=\"Schematic of 2D-ifying\" ></a>\n",
    "\n",
    "First we start by importing the necessary libraries for our simulations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "835923fe-ae93-4798-a838-0a0cf493280f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import gdstk\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import tidy3d as td\n",
    "import tidy3d.web as web\n",
    "from tidy3d.plugins.dispersion import AdvancedFastFitterParam, FastDispersionFitter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "061a0426-269f-4408-a548-25ac000e1860",
   "metadata": {},
   "source": [
    "## Variational Effective Permittivity\n",
    "\n",
    "In order to match the material of our 2D structures with those of the corresponding 3D structures, we will calculate the <b>variational effective permittivity</b>, taken from `Manfred Hammer and Olena V. Ivanova, \"Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment,\" Opt Quant Electron 41, 267–283 (2009)`[DOI:10.1007/s11082-009-9349-3](https://doi.org/10.1007/s11082-009-9349-3):<br>\n",
    "$$\n",
    "\\epsilon_{eff}(x,y)=n_{eff}(x_r,y_r)^2+\\frac{\\int_z[\\epsilon(x,y,z)-\\epsilon(x_r,y_r,z,\\omega)]|M_r(z,\\omega)|^2dz}{\\int_z|M_r(z,\\omega)|^2dz},\n",
    "$$<br>\n",
    "where $x_r,y_r$ are the coordinates of the reference point, $n_{eff}(x_r,y_r)$ is the effective index of the slab waveguide, given the permittivity profile in the z direction, at the reference point, $\\epsilon$ is the permittivity profile, and $M_{ref}(z,\\omega)$ is the mode profile in $z$ at the reference point. This formula is based on the assumption that the different vertical slab modes remain relatively uncoupled.<br><br>\n",
    "\n",
    "The reference profile in $z$ at point $(x_r,y_r)$ is what we choose to compare other $z$ profiles against. In our examples, we choose this point to include the location of our waveguide.<br><br>\n",
    "\n",
    "Note: This is only the effective permittivity for the TE mode. A separate TM mode formula exists, and the interested user should refer to the TM formula given in the paper. Also, in the paper, the extrusion dimension is x. In our examples, the extrusion dimension is z."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7aa0e0a9-57c4-41af-ae80-5583cc96e508",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.interpolate\n",
    "from tidy3d.plugins.mode.web import run as run_mode_solver\n",
    "\n",
    "\n",
    "def var_eps_eff(point, ref_point, sim, wavelength=1.55, inf=1000, min_n=1, remote=False):\n",
    "    \"\"\"\n",
    "    To calculate the vertical slab mode at 'ref_point', we will create a 2D slice of the given simulation at\n",
    "    'ref_point' that extends in the yz plane infinitely, ensuring that it captures the entire permittivity\n",
    "    profile. Then, to find the 1D mode profile, we use the Tidy3D ModeSolver on a plane at 'ref_point' that\n",
    "    extends infinitely in the xz plane. This results in the ModeSolver operating on the intersecting line\n",
    "    at 'ref_point' that covers its entire z profile. We then use this to solve for n_eff and M in the above\n",
    "    formula.\n",
    "\n",
    "    The min_n parameter is set to ensure that the calculated refractive index is at least 1. This\n",
    "    calculation can well end up with a value less than 1, as mentioned in the paper. To ensure that the\n",
    "    returned refractive index is physical, we set min_n to 1 by default.\n",
    "\n",
    "    There is also the option to use the remote mode solver if the user desires greater accuracy.\n",
    "    \"\"\"\n",
    "    freq = td.C_0 / wavelength\n",
    "\n",
    "    sim_2d_center = (\n",
    "        ref_point[0],\n",
    "        ref_point[1],\n",
    "        0,\n",
    "    )  # given a 3D sim, we update the center to create our 2D slice\n",
    "    sim_2d_size = (\n",
    "        0,\n",
    "        inf,\n",
    "        inf,\n",
    "    )  # we ensure the 2D span of the simulation in the yz plane captures everything\n",
    "\n",
    "    # now we create the 2D simulation, keeping the structures and updating the boundary conditions\n",
    "    sim_2d = sim.updated_copy(\n",
    "        center=sim_2d_center,\n",
    "        size=sim_2d_size,\n",
    "        sources=[],\n",
    "        monitors=[],\n",
    "        symmetry=(0, 0, 0),\n",
    "        boundary_spec=sim.boundary_spec.updated_copy(x=td.Boundary.periodic()),\n",
    "    )\n",
    "\n",
    "    # Now we solve for the mode at 'ref_point':\n",
    "    # We create the plane in xz that we'll use to examine the mode in z\n",
    "    mode_solver_plane = td.Box(center=sim_2d.center, size=(td.inf, 0, td.inf))\n",
    "    # Now we define the mode solver using this plane. We need only solve for one mode here, hence the ModeSpec\n",
    "    mode_solver = td.plugins.mode.ModeSolver(\n",
    "        simulation=sim_2d, plane=mode_solver_plane, mode_spec=td.ModeSpec(num_modes=1), freqs=[freq]\n",
    "    )\n",
    "\n",
    "    # Note that here the mode solving is done locally. For users desiring more accuracy, the remote mode\n",
    "    # solver should be used.\n",
    "    if remote:\n",
    "        mode_data_ref = run_mode_solver(mode_solver)\n",
    "    else:\n",
    "        mode_data_ref = mode_solver.solve()\n",
    "\n",
    "    # get n_eff from the solver\n",
    "    n_eff = mode_data_ref.n_eff.item()\n",
    "    if point == ref_point:\n",
    "        return n_eff**2  # if point is the reference point, the integral is 0\n",
    "\n",
    "    # get z permittivity profile at 'ref_point'\n",
    "    x, y = ref_point\n",
    "    eps_ref = sim.epsilon(\n",
    "        box=td.Box(center=(x, y, list(sim.center)[2]), size=(0, 0, td.inf)), freq=freq\n",
    "    )\n",
    "\n",
    "    # get z permittivity profile at 'point'\n",
    "    x, y = point\n",
    "    eps = sim.epsilon(\n",
    "        box=td.Box(center=(x, y, list(sim.center)[2]), size=(0, 0, td.inf)), freq=freq\n",
    "    )\n",
    "\n",
    "    eps_dif = np.squeeze(eps.values) - np.squeeze(eps_ref.values)\n",
    "\n",
    "    # get M at the same z coordinates as those of (eps - eps_ref) so we can integrate their product\n",
    "    z_coords = eps_ref.z.values\n",
    "    mode_profile = mode_data_ref.Ex\n",
    "    Mz2 = scipy.interpolate.interp1d(\n",
    "        x=mode_profile.z.values, y=np.abs(np.squeeze(mode_profile.values)) ** 2\n",
    "    )\n",
    "    m_values = Mz2(z_coords)\n",
    "\n",
    "    # calculate integrals\n",
    "    num, denom = (\n",
    "        np.trapezoid(y=eps_dif * m_values, x=z_coords),\n",
    "        np.trapezoid(y=m_values, x=z_coords),\n",
    "    )\n",
    "\n",
    "    if n_eff**2 + num / denom < min_n:\n",
    "        return min_n\n",
    "    return n_eff**2 + num / denom"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d07a1d0d-c12d-4d77-ad49-57bf8dece598",
   "metadata": {},
   "source": [
    "Here we create a function that uses the above function to create the approximated materials used in the 2D simulation. It takes as input the 3D simulation, the mode reference point, the point describing the stack that the user would like to approximate, and the simulation spectrum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "62a8bae0-9e07-40c7-a811-0f883f4a92ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "def approximate_material(\n",
    "    sim_3D, approx_point, ref_point, spectrum, min_n=1, plot=False, min_num_poles=1\n",
    "):\n",
    "    eps = []\n",
    "    for wl in spectrum:  # at every [step]th wavelength, calculate the effective permittivity\n",
    "        eps.append(var_eps_eff(approx_point, ref_point, sim_3D, wavelength=wl, min_n=min_n))\n",
    "\n",
    "    # fit the materials with the FastDispersionFitter using the calculated effective permittivities\n",
    "    fitter = FastDispersionFitter(wvl_um=spectrum, n_data=np.sqrt(np.real(eps)))\n",
    "\n",
    "    # create the mediums using the material fit\n",
    "    medium, rms_error = fitter.fit(min_num_poles=min_num_poles)\n",
    "\n",
    "    if plot:\n",
    "        # plot the material fit\n",
    "        fig, ax = plt.subplots(1, 1, figsize=(3, 3))\n",
    "        fitter.plot(medium, ax=ax)\n",
    "        ax.set_title(\"Medium\")\n",
    "        plt.show()\n",
    "\n",
    "    return medium"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2361f1c4-6e45-4264-a41b-12c860d9d780",
   "metadata": {},
   "source": [
    "Here we create a function that, given a 3D simulation, creates a 2D copy with updated materials given by the user. This, like the previous function, is provided so Tidy3D users can easily 2D-ify their 3D simulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6b336f14-d163-4958-b3a6-c2fe1fbbdda3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_2D_sim(sim_3D, new_mediums):\n",
    "    # Redo the structures that were in our 3D simulation with our calculated material approximations\n",
    "    new_structures = []\n",
    "    for structure in sim_3D.structures:\n",
    "        new_structures.append(structure.updated_copy(medium=new_mediums[0]))\n",
    "\n",
    "    # Update the size to 3D\n",
    "    new_size = list(sim_3D.size)\n",
    "    new_size[2] = 0\n",
    "\n",
    "    # Update the symmetry to 2D\n",
    "    new_symmetry = list(sim_3D.symmetry)\n",
    "    if new_symmetry != [0, 0, 0]:\n",
    "        print(\n",
    "            \"Note: removed symmetry, as it is incompatible with the variational approximation method.\"\n",
    "        )\n",
    "    new_symmetry = (0, 0, 0)\n",
    "\n",
    "    # Create the 2D version of our 3D original\n",
    "    sim_2D = sim_3D.updated_copy(\n",
    "        size=new_size,\n",
    "        structures=new_structures,\n",
    "        boundary_spec=sim_3D.boundary_spec.updated_copy(z=td.Boundary.periodic()),\n",
    "        medium=new_mediums[1],\n",
    "        symmetry=new_symmetry,\n",
    "    )\n",
    "\n",
    "    return sim_2D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "997ad092-b76e-449b-87bc-1f04c337c519",
   "metadata": {},
   "source": [
    "Since the method that calculates the variational effective permittivity creates a 2D simulation from the given 3D simulation, generally there can be some objects (and symmetries) not included in the 2D simulation, which will throw some warnings. Furthermore, since we're using the local mode solver, Tidy3D will also print a warning that the remote mode solver should be used for greater accuracy. Since we're okay with this, it will be cleaner to suppress the warnings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "edb4545a-7412-410d-9fb8-6bb48b100760",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Suppress warnings for some of the structures not being included in the 2D simulation\n",
    "td.config.logging.level = \"ERROR\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f78574d-bbac-41f9-8a02-5bf8659b41f1",
   "metadata": {},
   "source": [
    "The above four code cells are all that is needed to use this approximation for a 3D simulation given by the user."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "3960e475-df77-4b54-b79a-cad5522323b8",
   "metadata": {},
   "source": [
    "## Example 1: 2D Planar Waveguide Bragg Grating\n",
    "To see this in action, we will apply this to a 2-dimensional waveguide Bragg grating described in the source paper.<br>\n",
    "\n",
    "First we quickly build the 2D simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f2013ffa-27cb-48be-8c24-b35f6b9c277a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define wavelength/frequency ranges\n",
    "ldas = np.linspace(0.4, 0.9, 101)\n",
    "lda0 = ldas[50]\n",
    "freqs = td.C_0 / ldas\n",
    "freq0 = td.C_0 / lda0\n",
    "\n",
    "# Refractive indices\n",
    "n_c = 1\n",
    "n_f = 2\n",
    "n_s = 1.45\n",
    "\n",
    "# Materials used\n",
    "air = td.Medium(permittivity=n_c**2)\n",
    "top_medium = td.Medium(permittivity=n_f**2)\n",
    "bottom_medium = td.Medium(permittivity=n_s**2)\n",
    "\n",
    "# Define geometries and their structures\n",
    "hole_length = 0.11\n",
    "hole_depth = 0.6\n",
    "hole_spacing = 0.21\n",
    "top_thickness = 0.2\n",
    "\n",
    "inf = 10\n",
    "\n",
    "holes_list = []\n",
    "for h in range(6):\n",
    "    holes_list.append(\n",
    "        td.Box(\n",
    "            center=(hole_depth + h * hole_spacing, 0, 0), size=(hole_length, inf, 2 * hole_depth)\n",
    "        )\n",
    "    )\n",
    "holes_geos = td.GeometryGroup(geometries=holes_list)\n",
    "holes = td.Structure(geometry=holes_geos, medium=air)\n",
    "\n",
    "top_geo = td.Box.from_bounds(rmin=(-inf, -inf, -top_thickness), rmax=(inf, inf, 0))\n",
    "bottom_geo = td.Box.from_bounds(rmin=(-inf, -inf, -inf), rmax=(inf, inf, 0))\n",
    "\n",
    "top = td.Structure(geometry=top_geo, medium=top_medium)\n",
    "bottom = td.Structure(geometry=bottom_geo, medium=bottom_medium)\n",
    "\n",
    "# The injection used in the paper is a plane wave source\n",
    "source = td.PlaneWave(\n",
    "    center=(hole_depth * 0.1, 0, -top_thickness / 2),\n",
    "    size=(0, inf, top_thickness),\n",
    "    source_time=td.GaussianPulse(freq0=freq0, fwidth=freqs[0] - freqs[-1]),\n",
    "    direction=\"+\",\n",
    ")\n",
    "\n",
    "# Add monitors\n",
    "reflection = td.FluxMonitor(\n",
    "    center=(hole_depth * 0.05, 0, 0), size=(0, inf, inf), name=\"R\", freqs=freqs, normal_dir=\"-\"\n",
    ")\n",
    "transmission = td.FluxMonitor(\n",
    "    center=(hole_depth + 7 * hole_spacing, 0, 0), size=(0, inf, inf), name=\"T\", freqs=freqs\n",
    ")\n",
    "\n",
    "# Define the simulation of adequate size\n",
    "sim_size_x = hole_depth * 1.1 + 7 * hole_spacing\n",
    "sim_2d = td.Simulation(\n",
    "    center=(sim_size_x / 2, 0, -hole_depth / 3),\n",
    "    size=(sim_size_x, 0, 4 * hole_depth),\n",
    "    medium=air,\n",
    "    structures=[bottom, top, holes],\n",
    "    sources=[source],\n",
    "    monitors=[reflection, transmission],\n",
    "    boundary_spec=td.BoundarySpec(\n",
    "        x=td.Boundary.pml(), y=td.Boundary.periodic(), z=td.Boundary.pml()\n",
    "    ),\n",
    "    grid_spec=td.GridSpec.auto(wavelength=lda0, min_steps_per_wvl=30),\n",
    "    run_time=150 / freq0,\n",
    ")\n",
    "\n",
    "# Visualize the simulation to check\n",
    "sim_2d.plot_eps(y=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b4f374c-d13a-41d0-a585-cda121bfc785",
   "metadata": {},
   "source": [
    "Next we calculate the variational effective indices at different steps in our input wavelengths. We will then fit a dispersive material to this data using Tidy3D's FastDispersionFitter.<br><br>\n",
    "To speed things up, we will reduce the number of times we need to solve for the mode, so we will downsample the wavelength points. Here we calculate the effective permittivity at every fifteenth wavelength."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7971bed4-577f-4144-add6-2642c440de2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">Best weighted RMS error so far: 0.00246 <span style=\"color: #729c1f; text-decoration-color: #729c1f\">━━━━━━━━━━━━━━━━━━━━━━━━━━━</span> <span style=\"color: #800080; text-decoration-color: #800080\">100%</span> <span style=\"color: #008080; text-decoration-color: #008080\">0:00:00</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "Best weighted RMS error so far: 0.00246 \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Downsample wavelengths to speed up the calculation\n",
    "spectrum = ldas[::15]\n",
    "waveguide_mat = approximate_material(sim_2d, (0.25, 0), (0.25, 0), spectrum, plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5a059418-86f2-448c-bb4e-1cde25bb759f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">Best weighted RMS error: 0 <span style=\"color: #729c1f; text-decoration-color: #729c1f\">━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━</span> <span style=\"color: #800080; text-decoration-color: #800080\">100%</span> <span style=\"color: #008080; text-decoration-color: #008080\">0:00:00</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "Best weighted RMS error: 0 \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hole_mat = approximate_material(sim_2d, (1, 0), (0.25, 0), spectrum)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "357cc006-a7f4-44a7-a878-5d48ef8a5786",
   "metadata": {},
   "source": [
    "We now create the 1D simulation with the calculated mediums:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a9478257-8f54-46b6-aef4-3d576be956eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Redo the structures that were in our 2D simulation with our calculated material approximations\n",
    "holes_list_1D = []\n",
    "for h in range(6):\n",
    "    holes_list_1D.append(\n",
    "        td.Box(center=(hole_depth + h * hole_spacing, 0, 0), size=(hole_length, inf, inf))\n",
    "    )\n",
    "holes_geos_1D = td.GeometryGroup(geometries=holes_list_1D)\n",
    "holes_1D = td.Structure(geometry=holes_geos_1D, medium=hole_mat)\n",
    "\n",
    "# Update the size to 1D\n",
    "new_size = list(sim_2d.size)\n",
    "new_size[2] = 0\n",
    "\n",
    "# Update the plane wave source for 1D\n",
    "source_1d = td.PlaneWave(\n",
    "    center=sim_2d.sources[0].center,\n",
    "    size=sim_2d.sources[0].size,\n",
    "    source_time=sim_2d.sources[0].source_time,\n",
    "    direction=sim_2d.sources[0].direction,\n",
    ")\n",
    "\n",
    "# Create the 1D version of our 2D original\n",
    "sim_1d = sim_2d.updated_copy(\n",
    "    size=new_size,\n",
    "    structures=[holes_1D],\n",
    "    sources=[source_1d],\n",
    "    boundary_spec=sim_2d.boundary_spec.updated_copy(z=td.Boundary.periodic()),\n",
    "    medium=waveguide_mat,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11e85207-1488-48f3-8d2e-fc6049e17865",
   "metadata": {},
   "source": [
    "Finally, we run both simulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fb80a1cd-8013-438f-9581-3617db296df0",
   "metadata": {},
   "outputs": [
    {
     "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: #008000; text-decoration-color: #008000; font-weight: bold\">↓</span> <span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">simulation_data.hdf5.gz</span> <span style=\"color: #729c1f; text-decoration-color: #729c1f\">━━━━━━━━━━━━━━━━━━━━</span> <span style=\"color: #800080; text-decoration-color: #800080\">100.0%</span> • <span style=\"color: #008000; text-decoration-color: #008000\">5.9/5.9 kB</span> • <span style=\"color: #800000; text-decoration-color: #800000\">?</span> • <span style=\"color: #008080; text-decoration-color: #008080\">0:00:00</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1;32m↓\u001b[0m \u001b[1;34msimulation_data.hdf5.gz\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m5.9/5.9 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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\">14:34:48 EDT </span>loading simulation from simulation_data.hdf5                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m14:34:48 EDT\u001b[0m\u001b[2;36m \u001b[0mloading simulation from simulation_data.hdf5                       \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_2d_data = web.run(sim_2d, task_name=\"var eps\")\n",
    "sim_1d_data = web.run(sim_1d, task_name=\"var eps\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d6294c1-5023-4c91-a3ef-b0de0b2297fd",
   "metadata": {},
   "source": [
    "### Example 1 Result Comparison\n",
    "\n",
    "Now that both the 2D and 1D simulations have run, we will compare their results to see how representative the 1D simulation is. The results of the 1D approximation retain a reasonable qualitative fidelity to the 2D version."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0f120c35-9ae2-4a94-8c6c-96c56b1ffc17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(12, 5))\n",
    "\n",
    "ax[0].plot(\n",
    "    td.C_0 / sim_1d_data[\"R\"].flux.f,\n",
    "    sim_1d_data[\"R\"].flux.data,\n",
    "    label=\"1D\",\n",
    "    color=\"red\",\n",
    "    linestyle=\"--\",\n",
    ")\n",
    "ax[0].plot(td.C_0 / sim_2d_data[\"R\"].flux.f, sim_2d_data[\"R\"].flux.data, label=\"2D\", color=\"red\")\n",
    "ax[0].set_title(\"2D vs 1D Reflection\")\n",
    "ax[0].set_xlabel(\"Wavelength (µm)\")\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].plot(\n",
    "    td.C_0 / sim_1d_data[\"R\"].flux.f,\n",
    "    sim_1d_data[\"T\"].flux.data,\n",
    "    label=\"1D\",\n",
    "    color=\"blue\",\n",
    "    linestyle=\"--\",\n",
    ")\n",
    "ax[1].plot(td.C_0 / sim_2d_data[\"R\"].flux.f, sim_2d_data[\"T\"].flux.data, label=\"2D\", color=\"blue\")\n",
    "ax[1].set_title(\"2D vs 1D Transmission\")\n",
    "ax[1].set_xlabel(\"Wavelength (µm)\")\n",
    "ax[1].legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35762762-3dcb-4f44-9ee6-eee60fff9ec2",
   "metadata": {},
   "source": [
    "## Example 2: Ring Resonator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "826c2941-9f86-4a72-acf8-11b70ef7bbe7",
   "metadata": {},
   "source": [
    "We will now apply this same method to transform a 3D simulation into its 2D approximation. We will use a ring resonator and check the transmission of the through ports of both setups.<br><br>\n",
    "First we quickly build the 3D simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7eb43d86-4e2b-43b4-93ab-ce0ce0be6cc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define wavelength/frequency ranges\n",
    "lambda_beg = 1.5\n",
    "lambda_end = 1.6\n",
    "freq_beg = td.C_0 / lambda_end\n",
    "freq_end = td.C_0 / lambda_beg\n",
    "freq0 = (freq_beg + freq_end) / 2\n",
    "fwidth = (freq_end - freq0) / 1.5\n",
    "lambdas_ring = np.linspace(lambda_beg, lambda_end, 301)\n",
    "freqs_ring = td.C_0 / lambdas_ring[::-1]\n",
    "\n",
    "# Refractive indices\n",
    "Si_n = 3.4777\n",
    "SiO2_n = 1.444\n",
    "\n",
    "# Materials used\n",
    "Si = td.Medium(permittivity=Si_n**2)\n",
    "SiO2 = td.Medium(permittivity=SiO2_n**2)\n",
    "\n",
    "# Define geometries and their structures\n",
    "h_clad = 2.8\n",
    "h_box = 2\n",
    "h_wafer = 0.5\n",
    "\n",
    "w_wg = 0.5\n",
    "h_wg = 0.22\n",
    "couple_gap = 0.1\n",
    "ring_radius = 5\n",
    "\n",
    "z_wafer = -h_box - h_wafer / 2\n",
    "\n",
    "y_wg = ring_radius + w_wg / 2 + couple_gap + w_wg / 2\n",
    "\n",
    "waveguide_top = td.Structure(\n",
    "    geometry=td.Box(\n",
    "        center=[0, y_wg, 0],\n",
    "        size=[td.inf, w_wg, h_wg],\n",
    "    ),\n",
    "    medium=Si,\n",
    ")\n",
    "\n",
    "waveguide_bottom = td.Structure(\n",
    "    geometry=td.Box(\n",
    "        center=[0, -y_wg, 0],\n",
    "        size=[td.inf, w_wg, h_wg],\n",
    "    ),\n",
    "    medium=Si,\n",
    ")\n",
    "\n",
    "wg_ring_geo = td.Cylinder(\n",
    "    center=[0, 0, 0], axis=2, radius=ring_radius + w_wg / 2.0, length=h_wg\n",
    ") - td.Cylinder(center=[0, 0, 0], axis=2, radius=ring_radius - w_wg / 2.0, length=w_wg * 1.5)\n",
    "\n",
    "wg_ring = td.Structure(geometry=wg_ring_geo, medium=Si)\n",
    "\n",
    "x_buffer = 2\n",
    "y_buffer = 1\n",
    "z_buffer = 1\n",
    "\n",
    "z_sim = (h_clad - h_box - h_wafer) / 2\n",
    "h_sim = 3\n",
    "l_sim = 2 * ring_radius + 2 * x_buffer\n",
    "w_sim = 2 * ring_radius + 4 * y_buffer\n",
    "\n",
    "# Create Mode Source\n",
    "wg_insert_x = ring_radius + 0.9 * x_buffer\n",
    "mode_plane = td.Box(\n",
    "    center=[-wg_insert_x, y_wg, 0],\n",
    "    size=[0, 2, 2],\n",
    ")\n",
    "mode_source = td.ModeSource(\n",
    "    size=mode_plane.size,\n",
    "    center=mode_plane.center,\n",
    "    source_time=td.GaussianPulse(freq0=freq0, fwidth=fwidth),\n",
    "    mode_index=0,\n",
    "    direction=\"+\",\n",
    "    num_freqs=7,\n",
    ")\n",
    "\n",
    "# Create monitor\n",
    "through_mode_mnt = td.ModeMonitor(\n",
    "    size=mode_plane.size,\n",
    "    center=[wg_insert_x, y_wg, 0],\n",
    "    freqs=freqs_ring,\n",
    "    mode_spec=td.ModeSpec(num_modes=2),\n",
    "    name=\"mode through\",\n",
    ")\n",
    "\n",
    "# Create simulation\n",
    "min_steps_per_wvl = 15\n",
    "run_time = 8e-11\n",
    "\n",
    "sim_ring_3D = td.Simulation(\n",
    "    size=[l_sim, w_sim, h_sim],\n",
    "    center=(0, 0, 0),\n",
    "    structures=[waveguide_top, waveguide_bottom, wg_ring],\n",
    "    grid_spec=td.GridSpec.auto(min_steps_per_wvl=min_steps_per_wvl, wavelength=td.C_0 / freq0),\n",
    "    sources=[mode_source],\n",
    "    monitors=[through_mode_mnt],\n",
    "    run_time=run_time,\n",
    "    medium=SiO2,\n",
    "    symmetry=(0, 0, 1),  # add symmetry to reduce cost\n",
    ")\n",
    "\n",
    "# Visualize the simulation to check\n",
    "sim_ring_3D.plot(z=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20af0a05-dd59-49a6-8ae3-272ffdd3d61d",
   "metadata": {},
   "source": [
    "Same as before, we'll calculate the variational effective indices at different input wavelengths, this time downsampled to every 10th wavelength."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "77c3ee34-8395-48db-8808-1f5b36cdf091",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">Best weighted RMS error so far: 1.64e-05 <span style=\"color: #729c1f; text-decoration-color: #729c1f\">━━━━━━━━━━━━━━━━━━━━━━━━━━</span> <span style=\"color: #800080; text-decoration-color: #800080\">100%</span> <span style=\"color: #008080; text-decoration-color: #008080\">0:00:00</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "Best weighted RMS error so far: 1.64e-05 \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reference_point = (0, -y_wg)\n",
    "waveguide_point = (0, -y_wg)\n",
    "other_point = (0, 0)\n",
    "\n",
    "# Downsample wavelengths to speed up the calculation\n",
    "spectrum = lambdas_ring[::10]\n",
    "ring_waveguide_medium = approximate_material(\n",
    "    sim_ring_3D, waveguide_point, reference_point, spectrum, plot=True, min_num_poles=4\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4ade732a-6ce6-4847-a5ba-c5923834d667",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">Best weighted RMS error: 0 <span style=\"color: #729c1f; text-decoration-color: #729c1f\">━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━</span> <span style=\"color: #800080; text-decoration-color: #800080\">100%</span> <span style=\"color: #008080; text-decoration-color: #008080\">0:00:00</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "Best weighted RMS error: 0 \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ring_background_medium = approximate_material(sim_ring_3D, other_point, reference_point, spectrum)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbda4057-4feb-4350-8de7-ac3d9668ba7f",
   "metadata": {},
   "source": [
    "As before, we create a 2D copy of the simulation and replace the mediums with those that we just calculated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4a0245f6-7372-4315-a919-1bfd49ea192f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: removed symmetry, as it is incompatible with the variational approximation method.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_ring_2D = create_2D_sim(sim_ring_3D, [ring_waveguide_medium, ring_background_medium])\n",
    "\n",
    "sim_ring_2D.plot_eps(z=0, freq=freq0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "71d391f2-3935-44a3-9a8d-1cf4abb4e219",
   "metadata": {},
   "outputs": [
    {
     "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: #008000; text-decoration-color: #008000; font-weight: bold\">↓</span> <span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">simulation_data.hdf5.gz</span> <span style=\"color: #729c1f; text-decoration-color: #729c1f\">━━━━━━━━━━━━━━━━━━</span> <span style=\"color: #800080; text-decoration-color: #800080\">100.0%</span> • <span style=\"color: #008000; text-decoration-color: #008000\">33.2/33.2 kB</span> • <span style=\"color: #800000; text-decoration-color: #800000\">?</span> • <span style=\"color: #008080; text-decoration-color: #008080\">0:00:00</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1;32m↓\u001b[0m \u001b[1;34msimulation_data.hdf5.gz\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m33.2/33.2 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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\">14:35:14 EDT </span>loading simulation from simulation_data.hdf5                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m14:35:14 EDT\u001b[0m\u001b[2;36m \u001b[0mloading simulation from simulation_data.hdf5                       \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_data_2D = web.run(sim_ring_2D, task_name=\"2.5D FDTD ring resonator 2D\")\n",
    "sim_data_3D = web.run(sim_ring_3D, task_name=\"2.5D FDTD ring resonator 3D\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dc98bc3-bbcf-4a4b-8d86-7fab1b9bd0a4",
   "metadata": {},
   "source": [
    "### Example 2 Result Comparison\n",
    "\n",
    "We will compare the results of our 2D and 3D simulations to see how representative our approximation is. As one can see, the resonant behavior of this setup is well-approximated, especially near the central frequency. The depth of the peaks is lower in the 2D simulation because the 3D simulation takes into account vertical coupling. Toward the ends of the spectrum, there is more error in the free spectral range and resonance frequencies, although this is still well within 1% of the resonant wavelength, as we show for the first resonance. However, the next example will show that this method will not always be a good approximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3e23ed0d-1a5f-4a7a-bfd2-ec7a5e3b975e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Difference in first resonant wavelength: 0.0033333333333331883\n"
     ]
    }
   ],
   "source": [
    "sim_data_2D[\"mode through\"].amps.sel(mode_index=0, direction=\"+\").abs.plot(x=\"f\")\n",
    "sim_data_3D[\"mode through\"].amps.sel(mode_index=0, direction=\"+\").abs.plot(x=\"f\")\n",
    "plt.legend([\"2D\", \"3D\"])\n",
    "plt.show()\n",
    "\n",
    "res_lda_2d = (\n",
    "    td.C_0 / sim_data_2D[\"mode through\"].amps.sel(mode_index=0, direction=\"+\").abs.f.data[46]\n",
    ")\n",
    "res_lda_3d = (\n",
    "    td.C_0 / sim_data_3D[\"mode through\"].amps.sel(mode_index=0, direction=\"+\").abs.f.data[56]\n",
    ")\n",
    "res_wavelength_dif = np.abs(res_lda_2d - res_lda_3d)\n",
    "print(f\"Difference in first resonant wavelength: {res_wavelength_dif}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59164d1d-6a30-4c1e-8570-69fb76fccc42",
   "metadata": {},
   "source": [
    "## Strip-to-slot Counter-example\n",
    "\n",
    "This approximation method is not always applicable, and care must be taken to ensure that a given material's approximation is not too far off from the physical constraints of the original material. If not, this can lead to poor approximations. (One can check this by printing out the $n_{eff}^2 + \\frac{num}{denom}$ value calculated in the variational method function above.)\n",
    "<br><br>\n",
    "We will now show an example where this approximation does not work as well. We will use the first design of our [strip to slot converter example](https://www.flexcompute.com/tidy3d/examples/notebooks/StripToSlotConverters/). First we copy the simulation parameters from the notebook, removing the field monitor, as it will be unnecessary for this illustration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2b46a885-4127-4b88-b32a-2c8714fe3b93",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define wavelength/frequency ranges\n",
    "lda0 = 1.55\n",
    "ldas = np.linspace(1.5, 1.6, 101)\n",
    "freq0 = td.C_0 / lda0\n",
    "freqs = td.C_0 / ldas\n",
    "fwidth = 0.5 * (np.max(freqs) - np.min(freqs))\n",
    "\n",
    "# Create materials\n",
    "n_si = 3.47\n",
    "si = td.Medium(permittivity=n_si**2)\n",
    "n_sio2 = 1.44\n",
    "sio2 = td.Medium(permittivity=n_sio2**2)\n",
    "\n",
    "# Define geometry\n",
    "L_mmi = 1.38\n",
    "W_mmi = 1.24\n",
    "L = 6\n",
    "buffer = 5\n",
    "h_si = 0.25\n",
    "w_strip = 0.4\n",
    "w_slot = 0.62\n",
    "g = 0.1\n",
    "\n",
    "vertices = [\n",
    "    (-buffer, w_strip / 2),\n",
    "    (0, w_strip / 2),\n",
    "    (0, W_mmi / 2),\n",
    "    (L_mmi, W_mmi / 2),\n",
    "    (L, w_slot / 2),\n",
    "    (L + buffer, w_slot / 2),\n",
    "    (L + buffer, g / 2),\n",
    "    (L_mmi, g / 2),\n",
    "    (L_mmi, -g / 2),\n",
    "    (L + buffer, -g / 2),\n",
    "    (L + buffer, -w_slot / 2),\n",
    "    (L, -w_slot / 2),\n",
    "    (L_mmi, -W_mmi / 2),\n",
    "    (0, -W_mmi / 2),\n",
    "    (0, -w_strip / 2),\n",
    "    (-buffer, -w_strip / 2),\n",
    "]\n",
    "\n",
    "converter = td.Structure(\n",
    "    geometry=td.PolySlab(vertices=vertices, axis=2, slab_bounds=(-h_si / 2, h_si / 2)), medium=si\n",
    ")\n",
    "\n",
    "# Define mode source\n",
    "mode_spec = td.ModeSpec(num_modes=1, target_neff=n_si)\n",
    "mode_source = td.ModeSource(\n",
    "    center=(-lda0, 0, 0),\n",
    "    size=(0, 4 * w_strip, 6 * h_si),\n",
    "    source_time=td.GaussianPulse(freq0=freq0, fwidth=fwidth),\n",
    "    direction=\"+\",\n",
    "    mode_spec=mode_spec,\n",
    "    mode_index=0,\n",
    "    num_freqs=7,\n",
    ")\n",
    "\n",
    "# Define mode monitor\n",
    "mode_monitor = td.ModeMonitor(\n",
    "    center=(L + lda0, 0, 0),\n",
    "    size=(0, 4 * w_strip, 6 * h_si),\n",
    "    freqs=freqs,\n",
    "    mode_spec=mode_spec,\n",
    "    name=\"mode\",\n",
    ")\n",
    "\n",
    "# Define misc. simulation parameters\n",
    "Lx = L + 3 * lda0\n",
    "Ly = W_mmi + lda0\n",
    "Lz = 10 * h_si\n",
    "sim_size = (Lx, Ly, Lz)\n",
    "\n",
    "run_time = 1e-12\n",
    "\n",
    "# construct simulation\n",
    "sim_splitter_3D = td.Simulation(\n",
    "    center=(L / 2, 0, 0),\n",
    "    size=sim_size,\n",
    "    grid_spec=td.GridSpec.auto(min_steps_per_wvl=30, wavelength=lda0),\n",
    "    structures=[converter],\n",
    "    sources=[mode_source],\n",
    "    monitors=[mode_monitor],\n",
    "    run_time=run_time,\n",
    "    boundary_spec=td.BoundarySpec.all_sides(boundary=td.PML()),\n",
    "    medium=sio2,\n",
    "    symmetry=(0, -1, 1),\n",
    ")\n",
    "\n",
    "# plot the simulation\n",
    "sim_splitter_3D.plot_eps(z=0, freq=freq0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68b9ba6d-af75-47bd-9bf7-9341f3693b97",
   "metadata": {},
   "source": [
    "Now we convert the 3D simulation to a 2D simulation, as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "dd794575-4213-4a95-9586-b1e1625eb316",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">Best weighted RMS error: 0 <span style=\"color: #729c1f; text-decoration-color: #729c1f\">━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━</span> <span style=\"color: #800080; text-decoration-color: #800080\">100%</span> <span style=\"color: #008080; text-decoration-color: #008080\">0:00:00</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "Best weighted RMS error: 0 \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: removed symmetry, as it is incompatible with the variational approximation method.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Approximate materials by downsampling again\n",
    "spectrum = ldas[::15]\n",
    "ref_point = (0, 0)\n",
    "core_point = (0, 0)\n",
    "other_point = (2, 0)\n",
    "\n",
    "waveguide_splitter_mat = approximate_material(sim_splitter_3D, core_point, ref_point, spectrum)\n",
    "background_splitter_mat = approximate_material(sim_splitter_3D, other_point, ref_point, spectrum)\n",
    "\n",
    "sim_splitter_2D = create_2D_sim(sim_splitter_3D, [waveguide_splitter_mat, background_splitter_mat])\n",
    "sim_splitter_2D.plot_eps(z=0, freq=freq0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f56574ce-a75a-4d93-bab8-8715c24ddbc7",
   "metadata": {},
   "outputs": [
    {
     "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: #008000; text-decoration-color: #008000; font-weight: bold\">↓</span> <span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">simulation_data.hdf5.gz</span> <span style=\"color: #729c1f; text-decoration-color: #729c1f\">━━━━━━━━━━━━━━━━━━━━</span> <span style=\"color: #800080; text-decoration-color: #800080\">100.0%</span> • <span style=\"color: #008000; text-decoration-color: #008000\">9.9/9.9 kB</span> • <span style=\"color: #800000; text-decoration-color: #800000\">?</span> • <span style=\"color: #008080; text-decoration-color: #008080\">0:00:00</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1;32m↓\u001b[0m \u001b[1;34msimulation_data.hdf5.gz\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m9.9/9.9 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "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\">14:36:33 EDT </span>loading simulation from simulation_data.hdf5                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m14:36:33 EDT\u001b[0m\u001b[2;36m \u001b[0mloading simulation from simulation_data.hdf5                       \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_splitter_data_2D = web.run(sim_splitter_2D, task_name=\"2.5D FDTD splitter 2D\")\n",
    "sim_splitter_data_3D = web.run(sim_splitter_3D, task_name=\"2.5D FDTD splitter 3D\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f23b0d3d-5899-479f-9c8a-a391850dff8d",
   "metadata": {},
   "source": [
    "### Counter-example Results\n",
    "\n",
    "Plotting the mode transmissions from the 2D and 3D simulations, we can see that the 2D transmission is significantly lower than that of the 3D simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "323a692c-77d9-4c87-be98-4a69c5501c3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T_2D = np.abs(sim_splitter_data_2D[\"mode\"].amps.sel(mode_index=0, direction=\"+\")) ** 2\n",
    "T_3D = np.abs(sim_splitter_data_3D[\"mode\"].amps.sel(mode_index=0, direction=\"+\")) ** 2\n",
    "\n",
    "# plot the coupling efficiency\n",
    "plt.plot(ldas, T_2D, label=\"2D\")\n",
    "plt.plot(ldas, T_3D, label=\"3D\")\n",
    "plt.xlim(1.5, 1.6)\n",
    "plt.ylim(0, 1)\n",
    "plt.title(\"Strip-to-slot Coupling Efficiency\")\n",
    "plt.xlabel(r\"Wavelength ($\\mu m$)\")\n",
    "plt.ylabel(\"Transmission\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa05c4dd-3f8f-4ee5-93b4-6d0bac511c8d",
   "metadata": {},
   "source": [
    "This shows that, depending on the mode profile in z, we can get differences in permittivity from the variational method that do not accurately capture the physics of the original simulation, as mentioned in Hammer & Ivanova. Therefore care must be taken when deciding on this approximation method, and, when possible, a final validation with a 3D simulation should be run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b19d3188-0686-4aa3-8681-a0b0cce69edb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "applications": [
   "Passive photonic integrated circuit components"
  ],
  "description": "When doing design exploration, one can greatly reduce the amount of time and computational power needed by running 2D approximations of 3D simulations. This notebook shows how to use the variational method to calculate the effective permittivity of materials used in certain 3D simulations, and makes 2D approximations of those simulations.",
  "feature_image": "./img/effective_index_approximation.png",
  "features": [
   "GDS component",
   "Material fitting",
   "2D simulation"
  ],
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "keywords": "variational, effective, index, approximation, 2D, two-dimensional, vertical, mode, permittivity",
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.20"
  },
  "title": "How to approximate 3D simulations with effective permittivity in Tidy3D FDTD"
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
