{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "23bc2ee3-b625-4b4c-9c87-23dc715ad733",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "# Inverse design optimization of a mode converter\n",
    "\n",
    "In this notebook, we will use inverse design and Tidy3D to create an integrated photonics component to convert a fundamental waveguide mode to a higher order mode."
   ]
  },
  {
   "cell_type": "code",
   "id": "7257472c-5db1-4b93-8cdb-24b3cc32775d",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:28:03.617384Z",
     "start_time": "2026-03-16T10:28:01.563799Z"
    }
   },
   "source": [
    "from typing import List\n",
    "\n",
    "import autograd.numpy as anp\n",
    "import matplotlib.pylab as plt\n",
    "import numpy as np\n",
    "\n",
    "# import regular tidy3d\n",
    "import tidy3d as td\n",
    "import tidy3d.web as web\n",
    "from autograd import value_and_grad\n",
    "from tidy3d.plugins.mode import ModeSolver\n",
    "\n",
    "# set random seed to get same results\n",
    "np.random.seed(2)"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "id": "718337a6-e356-4810-8836-48ada41f31d2",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "We wish to recreate a device like the diagram below:\n",
    "\n",
    "<img src=\"img/AdjointInvDes.png\" width=800 alt=\"Schematic of the mode converter\">\n",
    "\n",
    "A mode source is injected into a waveguide on the left-hand side. The light propagates through a rectangular region with pixelated permittivity with the value of each pixel independently tunable between 1 (vacuum) and some maximum permittivity. Finally, we measure the transmission of the light into a waveguide on the right-hand side.\n",
    "\n",
    "The goal of the inverse design exercise is to find the best distribution of permittivities ($\\epsilon_{ij}$) in the coupling region to maximize the power conversion between the input mode and the output mode.\n",
    "\n",
    "We also apply our built-in smoothening and binarization filters to ensure that the final device has smooth features, and permittivity values that are all either 1, or the maximum permittivity of the waveguide material.\n",
    "\n",
    "### Parameters\n",
    "\n",
    "First we will define some parameters. "
   ]
  },
  {
   "cell_type": "code",
   "id": "b2c592b4-c210-46e3-94c2-d6a9bfb3ca73",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:28:03.627661Z",
     "start_time": "2026-03-16T10:28:03.623546Z"
    }
   },
   "source": [
    "# wavelength and frequency\n",
    "wavelength = 1.0\n",
    "freq0 = td.C_0 / wavelength\n",
    "k0 = 2 * np.pi * freq0 / td.C_0\n",
    "\n",
    "# resolution control\n",
    "min_steps_per_wvl = 16\n",
    "# in the design region, we set uniform grid resolution,\n",
    "# and define the design parameters on the same grid\n",
    "dl_design_region = 0.01\n",
    "\n",
    "# space between boxes and PML\n",
    "buffer = 1.0 * wavelength\n",
    "\n",
    "# optimize region size\n",
    "lz = td.inf\n",
    "lx = 5.0\n",
    "ly = 3.0\n",
    "\n",
    "# position of source and monitor (constant for all)\n",
    "source_x = -lx / 2 - buffer * 0.8\n",
    "meas_x = lx / 2 + buffer * 0.8\n",
    "\n",
    "# total size\n",
    "Lx = lx + 2 * buffer\n",
    "Ly = ly + 2 * buffer\n",
    "Lz = 0.0\n",
    "\n",
    "# permittivity and width of the input/output waveguide\n",
    "eps_wg = 2.75\n",
    "wg_width = 0.7\n",
    "\n",
    "# random starting parameters between 0 and 1\n",
    "nx = int(lx / dl_design_region)\n",
    "ny = int(ly / dl_design_region)\n",
    "params0 = np.random.random((nx, ny))\n",
    "\n",
    "# frequency width and run time\n",
    "freqw = freq0 / 10\n",
    "run_time = 50 / freqw"
   ],
   "outputs": [],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "id": "ac035f60-95f7-4f99-989d-67855acd5b15",
   "metadata": {},
   "source": [
    "### Static Components\n",
    "\n",
    "Next, we will set up the static parts of the geometry, the input source, and the output monitor using these parameters."
   ]
  },
  {
   "cell_type": "code",
   "id": "9aa55de4-f748-4939-8b26-9098bb573653",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:28:03.683032Z",
     "start_time": "2026-03-16T10:28:03.668829Z"
    }
   },
   "source": [
    "waveguide = td.Structure(\n",
    "    geometry=td.Box(size=(2 * Lx, wg_width, lz)), medium=td.Medium(permittivity=eps_wg)\n",
    ")\n",
    "\n",
    "mode_size = (0, wg_width * 3, lz)\n",
    "\n",
    "source_plane = td.Box(\n",
    "    center=[source_x, 0, 0],\n",
    "    size=mode_size,\n",
    ")\n",
    "\n",
    "measure_plane = td.Box(\n",
    "    center=[meas_x, 0, 0],\n",
    "    size=mode_size,\n",
    ")"
   ],
   "outputs": [],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "id": "afe16823-2271-4773-b0e3-a5ce3788ecae",
   "metadata": {},
   "source": [
    "### Input Structures\n",
    "\n",
    "Next, we write a function to return the pixelated array given our flattened tuple of permittivity values $\\epsilon_{ij}$ using the `tidy3d.plugins.autograd` plugin.\n",
    "\n",
    "We start with an array of parameters between 0 and 1, apply a conic filter and tanh projection to compute smooth, well-binarized features."
   ]
  },
  {
   "cell_type": "code",
   "id": "2d3e00d9-35f1-4e83-807c-66102b96ed5a",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:28:04.031734Z",
     "start_time": "2026-03-16T10:28:03.725410Z"
    }
   },
   "source": [
    "from tidy3d.plugins.autograd import make_filter_and_project, rescale\n",
    "\n",
    "# radius of the circular filter (um) and the threshold strength\n",
    "radius = 0.120\n",
    "beta = 50\n",
    "\n",
    "filter_project = make_filter_and_project(radius, lx / nx)\n",
    "\n",
    "\n",
    "def get_eps(params, beta):\n",
    "    \"\"\"Get the permittivity values (1, eps_wg) array as a function of the parameters (0, 1)\"\"\"\n",
    "    processed_params = filter_project(params, beta)\n",
    "    eps = rescale(processed_params, 1, eps_wg)\n",
    "    return eps\n",
    "\n",
    "\n",
    "def make_input_structures(params, beta) -> List[td.Structure]:\n",
    "    box = td.Box(center=(0, 0, 0), size=(lx, ly, lz))\n",
    "    eps_data = get_eps(params, beta=beta).reshape((nx, ny, 1))\n",
    "    custom_structure = td.Structure.from_permittivity_array(geometry=box, eps_data=eps_data)\n",
    "\n",
    "    return [custom_structure]"
   ],
   "outputs": [],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "id": "75983c02-ca0f-4dcb-9c51-04ce9b5ac7ed",
   "metadata": {},
   "source": [
    "### Making the Simulation\n",
    "Next, we write a function to return a basic `td.Simulation` as a function of our parameter values.\n",
    "\n",
    "We make sure to add the pixelated `td.Structure` list to `input_structures` but leave out the sources and monitors for now as we'll want to add those after the mode solver is run so we can inspect them."
   ]
  },
  {
   "cell_type": "code",
   "id": "3b09827b-a607-4631-977d-466f732e1d90",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:28:04.036509Z",
     "start_time": "2026-03-16T10:28:04.034646Z"
    }
   },
   "source": [
    "def make_sim_base(params: np.ndarray, beta: float) -> td.Simulation:\n",
    "    \"\"\"Create the simulation given the parameters and some beta value.\"\"\"\n",
    "\n",
    "    structures = make_input_structures(params, beta=beta)\n",
    "    design_region_mesh = td.MeshOverrideStructure(\n",
    "        geometry=td.Box(size=(lx, ly, lz)),\n",
    "        dl=[dl_design_region] * 3,\n",
    "        enforce=True,\n",
    "    )\n",
    "    grid_spec = td.GridSpec.auto(\n",
    "        wavelength=wavelength,\n",
    "        min_steps_per_wvl=16,\n",
    "        override_structures=[design_region_mesh],\n",
    "    )\n",
    "\n",
    "    return td.Simulation(\n",
    "        size=[Lx, Ly, Lz],\n",
    "        grid_spec=grid_spec,\n",
    "        structures=[waveguide] + structures,\n",
    "        sources=[],\n",
    "        monitors=[],\n",
    "        run_time=run_time,\n",
    "        boundary_spec=td.BoundarySpec.pml(x=True, y=True, z=False),\n",
    "    )"
   ],
   "outputs": [],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "id": "2e7cd9e9-a41a-4353-a0ee-cec464bc2f2d",
   "metadata": {},
   "source": [
    "### Visualize\n",
    "Let's visualize the simulation to see how it looks"
   ]
  },
  {
   "cell_type": "code",
   "id": "ae07fed6-c0e4-415a-8a55-58f1b02bd311",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:28:04.412285Z",
     "start_time": "2026-03-16T10:28:04.078040Z"
    }
   },
   "source": [
    "sim_start = make_sim_base(params0, beta=1.0)\n",
    "\n",
    "ax = sim_start.plot_eps(z=0, freq=freq0)\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "id": "5dc853c5-a191-4602-bf5b-7fa8761d51f1",
   "metadata": {},
   "source": [
    "### Select Input and Output Modes\n",
    "\n",
    "Next, let's visualize the first 4 mode profiles so we can select which mode indices we want to inject and transmit."
   ]
  },
  {
   "cell_type": "code",
   "id": "6fc8e702-bfec-4b7f-8dd1-2b5189f9087f",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:29:37.980484Z",
     "start_time": "2026-03-16T10:28:04.416104Z"
    }
   },
   "source": [
    "from tidy3d.plugins.mode.web import run as run_mode_solver\n",
    "\n",
    "num_modes = 4\n",
    "mode_spec = td.ModeSpec(num_modes=num_modes)\n",
    "\n",
    "mode_solver = ModeSolver(\n",
    "    simulation=sim_start,\n",
    "    plane=source_plane,\n",
    "    mode_spec=td.ModeSpec(num_modes=num_modes),\n",
    "    freqs=[freq0],\n",
    ")\n",
    "modes = run_mode_solver(mode_solver, reduce_simulation=True)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:28:05 CET\u001b[0m\u001b[2;36m \u001b[0mMode solver created with                                           \n",
       "\u001b[2;36m             \u001b[0m\u001b[33mtask_id\u001b[0m=\u001b[32m'fdve-17b73fbb-d92b-402d-ad88-8304dd4336ac'\u001b[0m,               \n",
       "\u001b[2;36m             \u001b[0m\u001b[33msolver_id\u001b[0m=\u001b[32m'mo-323f720b-a4b0-43c8-bde4-9d6f14686958'\u001b[0m.               \n"
      ],
      "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\">11:28:05 CET </span>Mode solver created with                                           \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #808000; text-decoration-color: #808000\">task_id</span>=<span style=\"color: #008000; text-decoration-color: #008000\">'fdve-17b73fbb-d92b-402d-ad88-8304dd4336ac'</span>,               \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #808000; text-decoration-color: #808000\">solver_id</span>=<span style=\"color: #008000; text-decoration-color: #008000\">'mo-323f720b-a4b0-43c8-bde4-9d6f14686958'</span>.               \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "83338562c4e54fcfaa9ece3366ce29e0"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "ab4f5410f2264d8f94746aa4fdb83f51"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:28:09 CET\u001b[0m\u001b[2;36m \u001b[0mMode solver status: queued                                         \n"
      ],
      "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\">11:28:09 CET </span>Mode solver status: queued                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:29:31 CET\u001b[0m\u001b[2;36m \u001b[0mMode solver status: running                                        \n"
      ],
      "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\">11:29:31 CET </span>Mode solver status: running                                        \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:29:36 CET\u001b[0m\u001b[2;36m \u001b[0mMode solver status: success                                        \n"
      ],
      "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\">11:29:36 CET </span>Mode solver status: success                                        \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "86efa3e1b69542febe9531a5519f5186"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "id": "378dba26-b679-4302-8160-c6df489c7a65",
   "metadata": {},
   "source": [
    "Let's visualize the modes next."
   ]
  },
  {
   "cell_type": "code",
   "id": "72502ab0-1055-4409-b11e-fae676f1d53e",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:29:38.765937Z",
     "start_time": "2026-03-16T10:29:37.989586Z"
    }
   },
   "source": [
    "fig, axs = plt.subplots(num_modes, 3, figsize=(12, 12), tight_layout=True)\n",
    "for mode_index in range(num_modes):\n",
    "    vmax = 1.1 * max(\n",
    "        abs(modes.field_components[n].sel(mode_index=mode_index)).max() for n in (\"Ex\", \"Ey\", \"Ez\")\n",
    "    )\n",
    "    for field_name, ax in zip((\"Ex\", \"Ey\", \"Ez\"), axs[mode_index]):\n",
    "        field = modes.field_components[field_name].sel(mode_index=mode_index)\n",
    "        field.real.plot(label=\"Real\", ax=ax)\n",
    "        field.imag.plot(ls=\"--\", label=\"Imag\", ax=ax)\n",
    "        ax.set_title(f\"index={mode_index}, {field_name}\")\n",
    "        ax.set_ylim(-vmax, vmax)\n",
    "\n",
    "axs[0, 0].legend()\n",
    "\n",
    "print(\"Effective index of computed modes: \", np.array(modes.n_eff))"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Effective index of computed modes:  [[1.5720801  1.53546291 1.30322985 1.18481493]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x1200 with 12 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "id": "d5a09ce7-4e64-4ccb-8a8f-54c23c5c7d4a",
   "metadata": {},
   "source": [
    "We want to inject the fundamental, Ez-polarized input into the 1st order Ez-polarized input.\n",
    "\n",
    "From the plots, we see that these modes correspond to the first and third rows, or `mode_index=0` and `mode_index=2`, respectively. \n",
    "\n",
    "So we make sure that the `mode_index_in` and `mode_index_out` variables are set appropriately and we set a `ModeSpec` with 3 modes to be able to capture the `mode_index_out` in our output data."
   ]
  },
  {
   "cell_type": "code",
   "id": "14f6113f-e7fa-4c8d-93e4-9764f396caaa",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-16T10:29:38.772069Z",
     "start_time": "2026-03-16T10:29:38.770272Z"
    }
   },
   "source": [
    "mode_index_in = 0\n",
    "mode_index_out = 2\n",
    "\n",
    "num_modes = max(mode_index_in, mode_index_out) + 1\n",
    "\n",
    "mode_spec = td.ModeSpec(num_modes=num_modes)"
   ],
   "outputs": [],
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "id": "5f7dc503-a3cf-486e-8779-727952a721df",
   "metadata": {},
   "source": [
    "Then it is straightforward to generate our source and monitor."
   ]
  },
  {
   "cell_type": "code",
   "id": "5bae2746-7ca7-420c-b727-309508621a5a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-16T10:29:38.825415Z",
     "start_time": "2026-03-16T10:29:38.815341Z"
    }
   },
   "source": [
    "# source seeding the simulation\n",
    "forward_source = td.ModeSource(\n",
    "    source_time=td.GaussianPulse(freq0=freq0, fwidth=freqw),\n",
    "    center=[source_x, 0, 0],\n",
    "    size=mode_size,\n",
    "    mode_index=mode_index_in,\n",
    "    mode_spec=mode_spec,\n",
    "    direction=\"+\",\n",
    ")\n",
    "\n",
    "# we'll refer to the measurement monitor by this name often\n",
    "measurement_monitor_name = \"measurement\"\n",
    "\n",
    "# monitor where we compute the objective function from\n",
    "measurement_monitor = td.ModeMonitor(\n",
    "    center=[meas_x, 0, 0],\n",
    "    size=mode_size,\n",
    "    freqs=[freq0],\n",
    "    mode_spec=mode_spec,\n",
    "    name=measurement_monitor_name,\n",
    ")"
   ],
   "outputs": [],
   "execution_count": 10
  },
  {
   "cell_type": "markdown",
   "id": "87968720-3cd4-434c-97c4-acdb54b18b37",
   "metadata": {},
   "source": [
    "Finally, we create a new function that calls our `make_sim_base()` function and adds the source and monitor to the result. This is the function we will use in our objective function to generate our `td.Simulation` given the input parameters."
   ]
  },
  {
   "cell_type": "code",
   "id": "5dfc5be5-99f6-4c9c-8d73-15e696933013",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-16T10:29:38.869118Z",
     "start_time": "2026-03-16T10:29:38.867531Z"
    }
   },
   "source": [
    "def make_sim(params, beta):\n",
    "    sim = make_sim_base(params, beta=beta)\n",
    "    return sim.updated_copy(sources=[forward_source], monitors=[measurement_monitor])"
   ],
   "outputs": [],
   "execution_count": 11
  },
  {
   "cell_type": "code",
   "id": "bf1a6dd5-d6da-4ba5-94ec-6bb401f3f872",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-16T10:29:39.078569Z",
     "start_time": "2026-03-16T10:29:38.911190Z"
    }
   },
   "source": [
    "sim_start = make_sim_base(params0, beta=1.0)\n",
    "\n",
    "ax = sim_start.plot_eps(z=0, freq=freq0)\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "id": "61522716-a26f-400b-a005-5d9493ef7264",
   "metadata": {},
   "source": [
    "### Post Processing\n",
    "\n",
    "Next, we will define a function to tell us how we want to postprocess the output `td.SimulationData` object to give the conversion power that we are interested in maximizing."
   ]
  },
  {
   "cell_type": "code",
   "id": "2081ff1b-46fe-4bb0-9027-8c4ca0a359bd",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:29:39.083123Z",
     "start_time": "2026-03-16T10:29:39.081648Z"
    }
   },
   "source": [
    "def measure_power(sim_data: td.SimulationData) -> float:\n",
    "    \"\"\"Return the power in the output_data amplitude at the mode index of interest.\"\"\"\n",
    "    output_amps = sim_data[\"measurement\"].amps\n",
    "    amp = output_amps.sel(direction=\"+\", f=freq0, mode_index=mode_index_out).values\n",
    "    return anp.sum(anp.abs(amp) ** 2)"
   ],
   "outputs": [],
   "execution_count": 13
  },
  {
   "cell_type": "markdown",
   "id": "a22f9915-559a-4f6a-a4d3-853f103aacab",
   "metadata": {},
   "source": [
    "Then, we add a penalty to produce structures that are invariant under erosion and dilation, which is a useful approach to implementing minimum length scale features."
   ]
  },
  {
   "cell_type": "code",
   "id": "b035a178-048c-4404-97c8-f694a94c087a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-16T10:29:39.126439Z",
     "start_time": "2026-03-16T10:29:39.124484Z"
    }
   },
   "source": [
    "from tidy3d.plugins.autograd import make_erosion_dilation_penalty\n",
    "\n",
    "penalty = make_erosion_dilation_penalty(radius, lx / nx)"
   ],
   "outputs": [],
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "id": "5863a5c3-3b5e-4927-9e18-749b660e7c3f",
   "metadata": {},
   "source": [
    "### Define Objective Function\n",
    "\n",
    "Finally, we need to define the objective function that we want to maximize as a function of our input parameters (permittivity of each pixel) that returns the conversion power. This is the function we will differentiate later."
   ]
  },
  {
   "cell_type": "code",
   "id": "71c5b2ed-a036-4578-ad44-89aa70f59e28",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:29:39.168950Z",
     "start_time": "2026-03-16T10:29:39.167411Z"
    }
   },
   "source": [
    "def J(params: np.ndarray, beta: float, step_num: int = None, verbose: bool = False) -> float:\n",
    "    sim = make_sim(params, beta=beta)\n",
    "    task_name = \"inv_des\"\n",
    "    if step_num:\n",
    "        task_name += f\"_step_{step_num}\"\n",
    "    sim_data = web.run(sim, task_name=task_name, verbose=verbose)\n",
    "    penalty_weight = np.minimum(1, beta / 25)\n",
    "    density = filter_project(params, beta)\n",
    "    return measure_power(sim_data) - penalty_weight * penalty(density)"
   ],
   "outputs": [],
   "execution_count": 15
  },
  {
   "cell_type": "markdown",
   "id": "075f3d66-c98f-4410-829a-b178464de0b8",
   "metadata": {},
   "source": [
    "## Inverse Design\n",
    "\n",
    "Now we are ready to perform the optimization.\n",
    "\n",
    "We use the `autograd.value_and_grad` function to get the gradient of `J` with respect to the permittivity of each `Box`, while also returning the converted power associated with the current iteration, so we can record this value for later.\n",
    "\n",
    "Let's try running this function once to make sure it works."
   ]
  },
  {
   "cell_type": "code",
   "id": "9ee539ec-11a2-4107-8270-9d58c7607562",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:29:39.211518Z",
     "start_time": "2026-03-16T10:29:39.210344Z"
    }
   },
   "source": [
    "dJ_fn = value_and_grad(J)"
   ],
   "outputs": [],
   "execution_count": 16
  },
  {
   "cell_type": "code",
   "id": "9c60dfdf-3518-44ce-b658-ea192950aa83",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T10:35:16.787143Z",
     "start_time": "2026-03-16T10:29:39.253011Z"
    }
   },
   "source": [
    "val, grad = dJ_fn(params0, beta=1, verbose=True)\n",
    "print(grad.shape)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:29:39 CET\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'inv_des'\u001b[0m with resource_id                            \n",
       "\u001b[2;36m             \u001b[0m\u001b[32m'fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e'\u001b[0m and task_type \u001b[32m'FDTD'\u001b[0m.  \n"
      ],
      "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\">11:29:39 CET </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'inv_des'</span> with resource_id                            \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                          \n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=894604;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[32m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=742157;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[32mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=894604;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[32m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=906848;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[32mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=894604;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[32m-e7c379ff-082\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=894604;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[32m5-4b34-8ac7-7cb8ce48be4e'\u001b[0m\u001b]8;;\u001b\\.                                         \n"
      ],
      "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-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-082</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">5-4b34-8ac7-7cb8ce48be4e'</span></a>.                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mTask folder: \u001b]8;id=700909;https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\u001b\\\u001b[32m'default'\u001b[0m\u001b]8;;\u001b\\.                                            \n"
      ],
      "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/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "ea9e966d27ba4e6cade7331032a33d29"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "bef4f82d294e4b9b8aadb1edca53df06"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:30:08 CET\u001b[0m\u001b[2;36m \u001b[0mEstimated FlexCredit cost: \u001b[1;36m0.025\u001b[0m. Minimum cost depends on task     \n",
       "\u001b[2;36m             \u001b[0mexecution details. Use \u001b[32m'web.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed  \n",
       "\u001b[2;36m             \u001b[0mFlexCredit cost after a simulation run.                            \n"
      ],
      "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\">11:30:08 CET </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.025</span>. Minimum cost depends on task     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>execution details. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the billed  \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>FlexCredit cost after a simulation run.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:30:10 CET\u001b[0m\u001b[2;36m \u001b[0mstatus = queued                                                    \n"
      ],
      "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\">11:30:10 CET </span>status = queued                                                    \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mTo cancel the simulation, use \u001b[32m'web.abort\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or              \n",
       "\u001b[2;36m             \u001b[0m\u001b[32m'web.delete\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or abort/delete the task in the web UI.      \n",
       "\u001b[2;36m             \u001b[0mTerminating the Python script will not stop the job running on the \n",
       "\u001b[2;36m             \u001b[0mcloud.                                                             \n"
      ],
      "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>To cancel the simulation, use <span style=\"color: #008000; text-decoration-color: #008000\">'web.abort(task_id)'</span> or              \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'web.delete(task_id)'</span> or abort/delete the task in the web UI.      \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Terminating the Python script will not stop the job running on the \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>cloud.                                                             \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "aaaf589d28974daaa3e41423ffa258e8"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:30:31 CET\u001b[0m\u001b[2;36m \u001b[0mstatus = preprocess                                                \n"
      ],
      "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\">11:30:31 CET </span>status = preprocess                                                \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:30:37 CET\u001b[0m\u001b[2;36m \u001b[0mstarting up solver                                                 \n"
      ],
      "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\">11:30:37 CET </span>starting up solver                                                 \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mrunning solver                                                     \n"
      ],
      "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>running solver                                                     \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "f4b1d9f930b84ee18043c0ae5ed2d79f"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:30:39 CET\u001b[0m\u001b[2;36m \u001b[0mearly shutoff detected at \u001b[1;36m7\u001b[0m%, exiting.                             \n"
      ],
      "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\">11:30:39 CET </span>early shutoff detected at <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">7</span>%, exiting.                             \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mstatus = success                                                   \n"
      ],
      "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>status = success                                                   \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mView simulation result at                                          \n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=285065;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=116488;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=285065;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=615069;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=285065;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[4;34m-e7c379ff-082\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=285065;https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\u001b\\\u001b[4;34m5-4b34-8ac7-7cb8ce48be4e'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                         \n"
      ],
      "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 simulation result at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-082</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-e7c379ff-0825-4b34-8ac7-7cb8ce48be4e\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">5-4b34-8ac7-7cb8ce48be4e'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "59cf2a9ae94d4b948ce704e47980928e"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:30:43 CET\u001b[0m\u001b[2;36m \u001b[0mLoading results from simulation_data.hdf5                          \n"
      ],
      "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\">11:30:43 CET </span>Loading results from simulation_data.hdf5                          \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:30:44 CET\u001b[0m\u001b[2;36m \u001b[0mStarted working on Batch containing \u001b[1;36m1\u001b[0m tasks.                       \n"
      ],
      "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\">11:30:44 CET </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</span> tasks.                       \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:32:59 CET\u001b[0m\u001b[2;36m \u001b[0mMaximum FlexCredit cost: \u001b[1;36m0.025\u001b[0m for the whole batch.                \n"
      ],
      "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\">11:32:59 CET </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.025</span> for the whole batch.                \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mUse \u001b[32m'Batch.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed FlexCredit cost after    \n",
       "\u001b[2;36m             \u001b[0mcompletion.                                                        \n"
      ],
      "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>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "6b5cc2fa470546a8a8f4917dae6cc0c1"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:35:12 CET\u001b[0m\u001b[2;36m \u001b[0mBatch complete.                                                    \n"
      ],
      "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\">11:35:12 CET </span>Batch complete.                                                    \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "c88841b65d29405c81fd2a1956e6d82c"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(500, 300)\n"
     ]
    }
   ],
   "execution_count": 17
  },
  {
   "cell_type": "code",
   "id": "fc7c5898-e2f5-45f0-9273-64efc725417e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-16T10:35:16.797173Z",
     "start_time": "2026-03-16T10:35:16.795412Z"
    }
   },
   "source": [
    "print(grad)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.31319548e-08  2.58622923e-08  2.50785165e-08 ... -5.59115896e-09\n",
      "  -5.68803065e-09 -2.86998836e-09]\n",
      " [ 2.64122741e-08  5.20509736e-08  5.05113897e-08 ... -1.12309080e-08\n",
      "  -1.14508379e-08 -5.77353153e-09]\n",
      " [ 2.70542496e-08  5.33724985e-08  5.17169899e-08 ... -1.15085313e-08\n",
      "  -1.18146503e-08 -5.96819456e-09]\n",
      " ...\n",
      " [ 3.52287314e-07  7.05309441e-07  7.13280892e-07 ... -6.01235223e-07\n",
      "  -5.90383617e-07 -2.93407763e-07]\n",
      " [ 3.50668991e-07  7.02072068e-07  7.10151956e-07 ... -5.94554123e-07\n",
      "  -5.83636475e-07 -2.90016188e-07]\n",
      " [ 1.75123039e-07  3.50621032e-07  3.54595729e-07 ... -2.96194622e-07\n",
      "  -2.90716762e-07 -1.44459760e-07]]\n"
     ]
    }
   ],
   "execution_count": 18
  },
  {
   "cell_type": "markdown",
   "id": "529fad9d-3692-464b-9a45-bea3e084c1b5",
   "metadata": {},
   "source": [
    "### Optimization\n",
    "\n",
    "We will use \"Adam\" optimization strategy to perform sequential updates of each of the permittivity values in the `td.CustomMedium`.\n",
    "\n",
    "For more information on what we use to implement this method, see [this article](https://optimization.cbe.cornell.edu/index.php?title=Adam).\n",
    "\n",
    "We will run 10 steps and measure both the permittivities and powers at each iteration.\n",
    "\n",
    "We run this process explicitly below with Tidy3D's built-in Adam optimizer.\n"
   ]
  },
  {
   "cell_type": "code",
   "id": "3eedf09a-9265-43ec-a557-3d0ec5b774bb",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T11:09:15.031812Z",
     "start_time": "2026-03-16T10:35:16.843503Z"
    }
   },
   "source": [
    "from tidy3d.plugins.autograd import adam, apply_updates\n",
    "\n",
    "# hyperparameters\n",
    "num_steps = 20\n",
    "learning_rate = 1.0\n",
    "\n",
    "# initialize adam optimizer with starting parameters\n",
    "params = np.array(params0)\n",
    "optimizer = adam(learning_rate=learning_rate)\n",
    "opt_state = optimizer.init(params)\n",
    "\n",
    "# store history\n",
    "Js = []\n",
    "params_history = [params]\n",
    "beta_history = []\n",
    "\n",
    "# gradually increase the binarization strength\n",
    "beta0 = 1\n",
    "beta_increment = 1\n",
    "\n",
    "for i in range(num_steps):\n",
    "    # compute gradient and current objective function value\n",
    "\n",
    "    density = filter_project(params, beta)\n",
    "    plt.subplots(figsize=(2, 2))\n",
    "    plt.imshow(np.flipud(1 - density.T), cmap=\"gray\")\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "\n",
    "    beta = beta0 + i * beta_increment\n",
    "    value, gradient = dJ_fn(params, step_num=i + 1, beta=beta)\n",
    "\n",
    "    # outputs\n",
    "    print(f\"step = {i + 1}\")\n",
    "    print(f\"\\tbeta = {beta:.4e}\")\n",
    "    print(f\"\\tJ = {value:.4e}\")\n",
    "    print(f\"\\tgrad_norm = {np.linalg.norm(gradient):.4e}\")\n",
    "\n",
    "    # compute and apply updates to the optimizer based on gradient (-1 sign to maximize obj_fn)\n",
    "    updates, opt_state = optimizer.update(-gradient, opt_state, params)\n",
    "    params[:] = apply_updates(params, updates)\n",
    "\n",
    "    # cap the parameters\n",
    "    anp.clip(params, 0.0, 1.0, out=params)\n",
    "\n",
    "    # save history\n",
    "    Js.append(value)\n",
    "    params_history.append(params.copy())\n",
    "    beta_history.append(beta)\n",
    "\n",
    "power = J(params_history[-1], beta=beta)\n",
    "Js.append(power)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 1\n",
      "\tbeta = 1.0000e+00\n",
      "\tJ = -3.9947e-02\n",
      "\tgrad_norm = 4.5956e-04\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 2\n",
      "\tbeta = 2.0000e+00\n",
      "\tJ = 3.2623e-02\n",
      "\tgrad_norm = 1.0681e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 3\n",
      "\tbeta = 3.0000e+00\n",
      "\tJ = -5.2977e-02\n",
      "\tgrad_norm = 6.3744e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 4\n",
      "\tbeta = 4.0000e+00\n",
      "\tJ = 5.1894e-02\n",
      "\tgrad_norm = 9.1340e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 5\n",
      "\tbeta = 5.0000e+00\n",
      "\tJ = 7.6458e-02\n",
      "\tgrad_norm = 1.6607e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 6\n",
      "\tbeta = 6.0000e+00\n",
      "\tJ = 2.1385e-01\n",
      "\tgrad_norm = 1.6287e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 7\n",
      "\tbeta = 7.0000e+00\n",
      "\tJ = 4.7841e-01\n",
      "\tgrad_norm = 1.5914e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 8\n",
      "\tbeta = 8.0000e+00\n",
      "\tJ = 5.8958e-01\n",
      "\tgrad_norm = 2.0013e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 9\n",
      "\tbeta = 9.0000e+00\n",
      "\tJ = 6.8790e-01\n",
      "\tgrad_norm = 1.5947e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 10\n",
      "\tbeta = 1.0000e+01\n",
      "\tJ = 7.4614e-01\n",
      "\tgrad_norm = 1.6623e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 11\n",
      "\tbeta = 1.1000e+01\n",
      "\tJ = 7.8526e-01\n",
      "\tgrad_norm = 2.0973e-02\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 12\n",
      "\tbeta = 1.2000e+01\n",
      "\tJ = 8.6161e-01\n",
      "\tgrad_norm = 7.7794e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 13\n",
      "\tbeta = 1.3000e+01\n",
      "\tJ = 8.6791e-01\n",
      "\tgrad_norm = 8.4331e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 14\n",
      "\tbeta = 1.4000e+01\n",
      "\tJ = 8.8755e-01\n",
      "\tgrad_norm = 4.7085e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 15\n",
      "\tbeta = 1.5000e+01\n",
      "\tJ = 8.9702e-01\n",
      "\tgrad_norm = 4.3314e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 16\n",
      "\tbeta = 1.6000e+01\n",
      "\tJ = 8.9651e-01\n",
      "\tgrad_norm = 9.0923e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 17\n",
      "\tbeta = 1.7000e+01\n",
      "\tJ = 8.8915e-01\n",
      "\tgrad_norm = 8.1182e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 18\n",
      "\tbeta = 1.8000e+01\n",
      "\tJ = 9.0444e-01\n",
      "\tgrad_norm = 3.3758e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 19\n",
      "\tbeta = 1.9000e+01\n",
      "\tJ = 9.0623e-01\n",
      "\tgrad_norm = 4.6192e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 20\n",
      "\tbeta = 2.0000e+01\n",
      "\tJ = 9.1375e-01\n",
      "\tgrad_norm = 2.5673e-03\n"
     ]
    }
   ],
   "execution_count": 19
  },
  {
   "cell_type": "code",
   "id": "30ce10a9-526c-434a-8606-f31c33949a41",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T11:09:15.098929Z",
     "start_time": "2026-03-16T11:09:15.091105Z"
    }
   },
   "source": [
    "params_final = params_history[-1]"
   ],
   "outputs": [],
   "execution_count": 20
  },
  {
   "cell_type": "markdown",
   "id": "6af5ad27-46a0-4f72-975d-ebe3040ee446",
   "metadata": {},
   "source": [
    "Let's run the optimize function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd0b335a-c8bd-49a9-a1c5-f08b6125f21b",
   "metadata": {},
   "source": [
    "and then record the final power value (including the last iteration's parameter updates)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0b44fda-bf57-42cf-8370-05bf20de96df",
   "metadata": {},
   "source": [
    "### Results\n",
    "\n",
    "First, we plot the objective function (power converted to 1st order mode) as a function of step and notice that it converges nicely!"
   ]
  },
  {
   "cell_type": "code",
   "id": "bc757643-2b71-4394-8fa6-f24c305848af",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T11:09:15.187143Z",
     "start_time": "2026-03-16T11:09:15.137186Z"
    }
   },
   "source": [
    "plt.plot(Js)\n",
    "plt.xlabel(\"iterations\")\n",
    "plt.ylabel(\"objective function\")\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 21
  },
  {
   "cell_type": "markdown",
   "id": "209d151d-4fe5-4b5e-8c3b-633c0b451c70",
   "metadata": {},
   "source": [
    "We then will visualize the final structure, so we convert it to a regular `Simulation` using the final permittivity values and plot it."
   ]
  },
  {
   "cell_type": "code",
   "id": "cfde96ed-f4b4-4106-b70e-0659058a82d6",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T11:09:15.272099Z",
     "start_time": "2026-03-16T11:09:15.194120Z"
    }
   },
   "source": [
    "sim_final = make_sim(params_final, beta=beta)"
   ],
   "outputs": [],
   "execution_count": 22
  },
  {
   "cell_type": "code",
   "id": "2c1ec6e0-cd42-4ef3-af95-5cbf7e0327a1",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T11:09:15.463246Z",
     "start_time": "2026-03-16T11:09:15.275590Z"
    }
   },
   "source": [
    "sim_final.plot_eps(z=0, freq=freq0)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 23
  },
  {
   "cell_type": "markdown",
   "id": "a6309d9a-01da-46da-96f1-236e86d7aa30",
   "metadata": {},
   "source": [
    "Finally, we want to inspect the fields, so we add a field monitor to the `Simulation` and perform one more run to record the field values for plotting."
   ]
  },
  {
   "cell_type": "code",
   "id": "3d9e6150-7b42-42c8-8418-2af4d02a1ec8",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T11:09:15.511639Z",
     "start_time": "2026-03-16T11:09:15.467416Z"
    }
   },
   "source": [
    "field_mnt = td.FieldMonitor(\n",
    "    size=(td.inf, td.inf, 0),\n",
    "    freqs=[freq0],\n",
    "    name=\"field_mnt\",\n",
    ")\n",
    "\n",
    "sim_final = sim_final.copy(update=dict(monitors=(field_mnt, measurement_monitor)))"
   ],
   "outputs": [],
   "execution_count": 24
  },
  {
   "cell_type": "code",
   "id": "eb9e98d5-70e7-4fea-abcf-047489bd6a22",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T11:09:57.279317Z",
     "start_time": "2026-03-16T11:09:15.515356Z"
    }
   },
   "source": [
    "sim_data_final = web.run(sim_final, task_name=\"inv_des_final\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m12:09:15 CET\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'inv_des_final'\u001b[0m with resource_id                      \n",
       "\u001b[2;36m             \u001b[0m\u001b[32m'fdve-eb7e48c0-ed69-4cee-b685-9139dc307114'\u001b[0m and task_type \u001b[32m'FDTD'\u001b[0m.  \n"
      ],
      "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\">12:09:15 CET </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'inv_des_final'</span> with resource_id                      \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-eb7e48c0-ed69-4cee-b685-9139dc307114'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                          \n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=516463;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[32m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=161111;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[32mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=516463;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[32m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=750125;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[32mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=516463;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[32m-eb7e48c0-ed6\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=516463;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[32m9-4cee-b685-9139dc307114'\u001b[0m\u001b]8;;\u001b\\.                                         \n"
      ],
      "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-eb7e48c0-ed69-4cee-b685-9139dc307114\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed6</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">9-4cee-b685-9139dc307114'</span></a>.                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mTask folder: \u001b]8;id=986340;https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\u001b\\\u001b[32m'default'\u001b[0m\u001b]8;;\u001b\\.                                            \n"
      ],
      "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/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "6bf6f9cac6ca4997a7dfa111c04f5a64"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m12:09:27 CET\u001b[0m\u001b[2;36m \u001b[0mEstimated FlexCredit cost: \u001b[1;36m0.025\u001b[0m. Minimum cost depends on task     \n",
       "\u001b[2;36m             \u001b[0mexecution details. Use \u001b[32m'web.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed  \n",
       "\u001b[2;36m             \u001b[0mFlexCredit cost after a simulation run.                            \n"
      ],
      "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\">12:09:27 CET </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.025</span>. Minimum cost depends on task     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>execution details. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the billed  \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>FlexCredit cost after a simulation run.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m12:09:29 CET\u001b[0m\u001b[2;36m \u001b[0mstatus = queued                                                    \n"
      ],
      "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\">12:09:29 CET </span>status = queued                                                    \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mTo cancel the simulation, use \u001b[32m'web.abort\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or              \n",
       "\u001b[2;36m             \u001b[0m\u001b[32m'web.delete\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or abort/delete the task in the web UI.      \n",
       "\u001b[2;36m             \u001b[0mTerminating the Python script will not stop the job running on the \n",
       "\u001b[2;36m             \u001b[0mcloud.                                                             \n"
      ],
      "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>To cancel the simulation, use <span style=\"color: #008000; text-decoration-color: #008000\">'web.abort(task_id)'</span> or              \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'web.delete(task_id)'</span> or abort/delete the task in the web UI.      \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Terminating the Python script will not stop the job running on the \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>cloud.                                                             \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "f936e0b187814199ba514eab711333c9"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m12:09:41 CET\u001b[0m\u001b[2;36m \u001b[0mstarting up solver                                                 \n"
      ],
      "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\">12:09:41 CET </span>starting up solver                                                 \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m12:09:42 CET\u001b[0m\u001b[2;36m \u001b[0mrunning solver                                                     \n"
      ],
      "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\">12:09:42 CET </span>running solver                                                     \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "0d17287b697a4a268276b6179d0a3526"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m12:09:43 CET\u001b[0m\u001b[2;36m \u001b[0mearly shutoff detected at \u001b[1;36m11\u001b[0m%, exiting.                            \n"
      ],
      "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\">12:09:43 CET </span>early shutoff detected at <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">11</span>%, exiting.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m12:09:44 CET\u001b[0m\u001b[2;36m \u001b[0mstatus = success                                                   \n"
      ],
      "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\">12:09:44 CET </span>status = success                                                   \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mView simulation result at                                          \n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=176812;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=712778;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=176812;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=551622;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=176812;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[4;34m-eb7e48c0-ed6\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=176812;https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\u001b\\\u001b[4;34m9-4cee-b685-9139dc307114'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                         \n"
      ],
      "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 simulation result at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed6</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-eb7e48c0-ed69-4cee-b685-9139dc307114\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">9-4cee-b685-9139dc307114'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "c3ad8c3afc3447c2a8168b0eb079f528"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m12:09:57 CET\u001b[0m\u001b[2;36m \u001b[0mLoading results from simulation_data.hdf5                          \n"
      ],
      "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\">12:09:57 CET </span>Loading results from simulation_data.hdf5                          \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 25
  },
  {
   "cell_type": "markdown",
   "id": "6840c1ae-bd2a-470f-9875-cb05759d2df5",
   "metadata": {},
   "source": [
    "We notice that the behavior is as expected and the device performs exactly how we intended!"
   ]
  },
  {
   "cell_type": "code",
   "id": "0a28c766-f877-4760-a0f5-ba7851d1759a",
   "metadata": {
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-16T11:09:58.454953Z",
     "start_time": "2026-03-16T11:09:57.283318Z"
    }
   },
   "source": [
    "f, (ax0, ax1, ax2) = plt.subplots(1, 3, figsize=(12, 3), tight_layout=True)\n",
    "sim_final.plot_eps(z=0.01, freq=freq0, ax=ax0)\n",
    "ax1 = sim_data_final.plot_field(\"field_mnt\", \"Ez\", z=0, ax=ax1)\n",
    "ax2 = sim_data_final.plot_field(\"field_mnt\", \"E\", \"abs^2\", z=0, ax=ax2)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x300 with 6 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 26
  },
  {
   "cell_type": "markdown",
   "id": "104d7469-8489-44d2-8a60-d5b813c6331b",
   "metadata": {},
   "source": [
    "The final device converts more than 90% of the input power to the 1st mode, up from < 1% when we started."
   ]
  },
  {
   "cell_type": "code",
   "id": "ebd825e4-6dfe-4836-940c-cf9bd491522a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-16T11:09:58.462859Z",
     "start_time": "2026-03-16T11:09:58.459062Z"
    }
   },
   "source": [
    "final_power = (\n",
    "    sim_data_final[\"measurement\"].amps.sel(direction=\"+\", f=freq0, mode_index=mode_index_out).abs\n",
    "    ** 2\n",
    ")\n",
    "print(f\"Final power conversion = {final_power * 100:.2f}%\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final power conversion = 97.10%\n"
     ]
    }
   ],
   "execution_count": 27
  },
  {
   "cell_type": "markdown",
   "id": "eb6d530a",
   "metadata": {},
   "source": [
    "## Export to GDS\n",
    "The `Simulation` object has the [.to_gds_file](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.Simulation.html#tidy3d.Simulation.to_gds_file) convenience function to export the final design to a `GDS` file. In addition to a file name, it is necessary to set a cross-sectional plane (`z = 0` in this case) on which to evaluate the geometry, a `frequency` to evaluate the permittivity, and a `permittivity_threshold` to define the shape boundaries in custom mediums. See the [GDS export](https://www.flexcompute.com/tidy3d/examples/notebooks/GDSExport/) notebook for a detailed example on using `.to_gds_file` and other GDS related functions."
   ]
  },
  {
   "cell_type": "code",
   "id": "69afad7b-33ff-4a06-81bb-1c3bdbc50b6b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-16T11:09:58.528588Z",
     "start_time": "2026-03-16T11:09:58.504002Z"
    }
   },
   "source": [
    "sim_final.to_gds_file(\n",
    "    fname=\"./misc/inv_des_mode_conv.gds\",\n",
    "    z=0,\n",
    "    frequency=freq0,\n",
    "    permittivity_threshold=2.6,\n",
    ")"
   ],
   "outputs": [],
   "execution_count": 28
  }
 ],
 "metadata": {
  "applications": [
   "Passive photonic integrated circuit components"
  ],
  "description": "This notebook demonstrates how to perform inverse design optimization of an optical mode converter in Tidy3D FDTD.",
  "feature_image": "./img/adjoint_3.png",
  "features": [
   "Adjoint inverse design",
   "2D simulation"
  ],
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "keywords": "inverse design, adjoint optimization, optical mode converter, Tidy3D, FDTD",
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.10"
  },
  "nbdime-conflicts": {
   "local_diff": [
    {
     "diff": [
      {
       "diff": [
        {
         "key": 0,
         "length": 1,
         "op": "removerange"
        }
       ],
       "key": "version",
       "op": "patch"
      }
     ],
     "key": "language_info",
     "op": "patch"
    }
   ],
   "remote_diff": [
    {
     "diff": [
      {
       "diff": [
        {
         "diff": [
          {
           "key": 5,
           "op": "addrange",
           "valuelist": "9"
          },
          {
           "key": 5,
           "length": 1,
           "op": "removerange"
          }
         ],
         "key": 0,
         "op": "patch"
        }
       ],
       "key": "version",
       "op": "patch"
      }
     ],
     "key": "language_info",
     "op": "patch"
    }
   ]
  },
  "title": "Inverse Design of a Mode Converter | Flexcompute",
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "02bd58b8f27b49079c8cfaae08e484ed": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "0cc59d91e6884de8878637d06f69298f": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "131b81dce4714ce69a7ed086788d1178": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_346b3ff743f84696a2a3eb47172865a6",
       "msg_id": "",
       "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: #800000; text-decoration-color: #800000; font-weight: bold\">↑</span> <span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">simulation.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\">43.0/43.0 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;31m↑\u001b[0m \u001b[1;34msimulation.hdf5.gz\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m43.0/43.0 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "1c3c5d9b9f8c4762af46440e2f9de9b0": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_0cc59d91e6884de8878637d06f69298f",
       "msg_id": "",
       "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\">🚶 </span> <span style=\"color: #008000; text-decoration-color: #008000; font-weight: bold\">Starting 'inv_des'...</span>\n</pre>\n",
          "text/plain": "\u001b[32m🚶 \u001b[0m \u001b[1;32mStarting 'inv_des'...\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "28d2d187d50744619ffd15c7ae3d46ab": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "2cf4637d47444cb89788003100a96e1c": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "2d8b8f7952de4429a454df590618cd63": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_97b116cecc8d4eba90ff6f1899098767",
       "msg_id": "",
       "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: #800000; text-decoration-color: #800000; font-weight: bold\">↑</span> <span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">jax_info.json</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\">174/174 bytes</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;31m↑\u001b[0m \u001b[1;34mjax_info.json\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m174/174 bytes\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "346b3ff743f84696a2a3eb47172865a6": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "3b97302e734846f68dc34be2e1e9f622": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_477714e92f7845838dcca8908b862048",
       "msg_id": "",
       "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\">🏃 </span> <span style=\"color: #008000; text-decoration-color: #008000; font-weight: bold\">Finishing 'inv_des_final'...</span>\n</pre>\n",
          "text/plain": "\u001b[32m🏃 \u001b[0m \u001b[1;32mFinishing 'inv_des_final'...\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "3f3ecee4ff984da1ab6af8cde74aa4d6": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_2cf4637d47444cb89788003100a96e1c",
       "msg_id": "",
       "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\">monitor_data.hdf5</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\">148.6/148.6 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;34mmonitor_data.hdf5\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m148.6/148.6 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "43ee1faf5c0f4bd7952b4c9f3901f58d": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_28d2d187d50744619ffd15c7ae3d46ab",
       "msg_id": "",
       "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\">🏃 </span> <span style=\"color: #008000; text-decoration-color: #008000; font-weight: bold\">Finishing 'inv_des_adj'...</span>\n</pre>\n",
          "text/plain": "\u001b[32m🏃 \u001b[0m \u001b[1;32mFinishing 'inv_des_adj'...\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "477714e92f7845838dcca8908b862048": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "4d65e6b885674bc8bff06e62f0b089f6": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_a1c5f0dfa271458dad9e5ded066f966f",
       "msg_id": "",
       "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\">🏃 </span> <span style=\"color: #008000; text-decoration-color: #008000; font-weight: bold\">Finishing 'inv_des'...</span>\n</pre>\n",
          "text/plain": "\u001b[32m🏃 \u001b[0m \u001b[1;32mFinishing 'inv_des'...\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "51efd5e7d641461d9392377e4dc80027": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "5bb49f9b044f49518c9c2c21dffed65b": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_02bd58b8f27b49079c8cfaae08e484ed",
       "msg_id": "",
       "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\">solver progress (field decay = 0.00e+00) <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": "solver progress (field decay = 0.00e+00) \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "616294d7d1c243feb07bfcc5ab642cc5": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "6f6853ea5883400bbff752f3c60139c9": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "6fe1bfb2d1a14e339a1b711d8b1d89a1": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "706c91a16eb347379d86f710b83d7e6b": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_8078dc74436c47b093bd481bb6624578",
       "msg_id": "",
       "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\">jax_sim_vjp.hdf5</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\">237.1/237.1 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;34mjax_sim_vjp.hdf5\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m237.1/237.1 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "7417aa6cc0bb4350b3f28e1826298b03": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "756ecdb25ec94e52907adfd2ecb443f3": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_f52a00c4ea904dccb1418ba1a118d6be",
       "msg_id": "",
       "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\">🚶 </span> <span style=\"color: #008000; text-decoration-color: #008000; font-weight: bold\">Starting 'inv_des_adj'...</span>\n</pre>\n",
          "text/plain": "\u001b[32m🚶 \u001b[0m \u001b[1;32mStarting 'inv_des_adj'...\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "8078dc74436c47b093bd481bb6624578": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "8a006d803a9341ba81fc1cddec63f4cf": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_d61f53cb0349458ab366bebcc42a6028",
       "msg_id": "",
       "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: #800000; text-decoration-color: #800000; font-weight: bold\">↑</span> <span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">simulation.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\">110.6/110.6 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;31m↑\u001b[0m \u001b[1;34msimulation.hdf5.gz\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m110.6/110.6 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "97916d3681e24426a9724844691f7038": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_7417aa6cc0bb4350b3f28e1826298b03",
       "msg_id": "",
       "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\">🚶 </span> <span style=\"color: #008000; text-decoration-color: #008000; font-weight: bold\">Starting 'inv_des_final'...</span>\n</pre>\n",
          "text/plain": "\u001b[32m🚶 \u001b[0m \u001b[1;32mStarting 'inv_des_final'...\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "97b116cecc8d4eba90ff6f1899098767": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "9ac6fa173f624d24a2fce05e6f1327d0": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "a1c5f0dfa271458dad9e5ded066f966f": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "a992634b68574d25a4c65061ebdad55f": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_6fe1bfb2d1a14e339a1b711d8b1d89a1",
       "msg_id": "",
       "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\">monitor_data.hdf5</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\">13.3/13.3 MB</span> • <span style=\"color: #800000; text-decoration-color: #800000\">22.4 MB/s</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;34mmonitor_data.hdf5\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m13.3/13.3 MB\u001b[0m • \u001b[31m22.4 MB/s\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "b17032aa2dca423080814069bd0548cb": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_9ac6fa173f624d24a2fce05e6f1327d0",
       "msg_id": "",
       "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: #800000; text-decoration-color: #800000; font-weight: bold\">↑</span> <span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">simulation.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\">100.1/100.1 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;31m↑\u001b[0m \u001b[1;34msimulation.hdf5.gz\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m100.1/100.1 kB\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "d61f53cb0349458ab366bebcc42a6028": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     },
     "e84d3af0debd414ba94b938d3a285d75": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_6f6853ea5883400bbff752f3c60139c9",
       "msg_id": "",
       "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\">solver progress (field decay = 0.00e+00) <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": "solver progress (field decay = 0.00e+00) \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "f2fb4fc3f8be4eb7acfb42679d70a73c": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_51efd5e7d641461d9392377e4dc80027",
       "msg_id": "",
       "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: #800000; text-decoration-color: #800000; font-weight: bold\">↑</span> <span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">jax_info.json</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\">174/174 bytes</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;31m↑\u001b[0m \u001b[1;34mjax_info.json\u001b[0m \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100.0%\u001b[0m • \u001b[32m174/174 bytes\u001b[0m • \u001b[31m?\u001b[0m • \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "f3e34e693eff477797f8c8517fbf1a82": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/output",
       "_model_module_version": "1.0.0",
       "_model_name": "OutputModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/output",
       "_view_module_version": "1.0.0",
       "_view_name": "OutputView",
       "layout": "IPY_MODEL_616294d7d1c243feb07bfcc5ab642cc5",
       "msg_id": "",
       "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\">solver progress (field decay = 0.00e+00) <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": "solver progress (field decay = 0.00e+00) \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[35m100%\u001b[0m \u001b[36m0:00:00\u001b[0m\n"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ],
       "tabbable": null,
       "tooltip": null
      }
     },
     "f52a00c4ea904dccb1418ba1a118d6be": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {
       "_model_module": "@jupyter-widgets/base",
       "_model_module_version": "2.0.0",
       "_model_name": "LayoutModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "2.0.0",
       "_view_name": "LayoutView",
       "align_content": null,
       "align_items": null,
       "align_self": null,
       "border_bottom": null,
       "border_left": null,
       "border_right": null,
       "border_top": null,
       "bottom": null,
       "display": null,
       "flex": null,
       "flex_flow": null,
       "grid_area": null,
       "grid_auto_columns": null,
       "grid_auto_flow": null,
       "grid_auto_rows": null,
       "grid_column": null,
       "grid_gap": null,
       "grid_row": null,
       "grid_template_areas": null,
       "grid_template_columns": null,
       "grid_template_rows": null,
       "height": null,
       "justify_content": null,
       "justify_items": null,
       "left": null,
       "margin": null,
       "max_height": null,
       "max_width": null,
       "min_height": null,
       "min_width": null,
       "object_fit": null,
       "object_position": null,
       "order": null,
       "overflow": null,
       "padding": null,
       "right": null,
       "top": null,
       "visibility": null,
       "width": null
      }
     }
    },
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}