{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c7191a28-9d25-46f3-8015-be2b45fdb068",
   "metadata": {},
   "source": [
    "# Monostatic radar cross section (RCS) of a PEC sphere\n",
    "\n",
    "Monostatic RCS measures the power of an electromagnetic wave reflected directly back to the radar source (transmitter and receiver are co-located). Mathematically, it is defined as:\n",
    "\n",
    "$$\n",
    "\\sigma = \\lim_{R \\to \\infty} 4\\pi R^2 \\frac{|\\mathbf{E}_{\\text{scattered}}|^2}{|\\mathbf{E}_{\\text{incident}}|^2} \n",
    "$$\n",
    "\n",
    "where:\n",
    "- $ R $  : Distance between the radar and target.\n",
    "- $ \\mathbf{E}_{\\text{scattered}} $ : Electric field of the scattered wave.\n",
    "- $ \\mathbf{E}_{\\text{incident}} $  : Electric field of the incident wave.\n",
    "\n",
    "In this notebook, we aim to benchmark the accuracy of Tidy3D by simulating the monostatic RCS of a PEC sphere and compare the results to the well-known analytical solution based on Mie theory. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4fa361f0-7eab-46cb-8c46-019577734505",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import tidy3d as td\n",
    "import tidy3d.web as web"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73461dd3-7de8-42f1-83a8-cbe3735d26c4",
   "metadata": {},
   "source": [
    "## Simulation Setup\n",
    "\n",
    "The monostatic RCS calculation for a PEC sphere is a classic problem in electromagnetics. The RCS is usually normalized by the physical cross section area of the sphere $\\pi r^2$, where $r$ is the radius. Our goal is to calculate the normalized RCS as a function of the unitless relative frequency $2 \\pi r/\\lambda_0$. \n",
    "\n",
    "In this particular case, we will calculate the RCS for a relative frequency range from 1 to 10. The result will be plotted in a log scale so the frequency points are generated in a log scale here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9d127fdb-9850-4a5b-b84f-bbdedba8bb9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "r = 1  # radius of the sphere\n",
    "rel_freqs = np.logspace(0, 1, 201)  # relative frequency in log scale\n",
    "ldas = 2 * np.pi * r / rel_freqs  # wavelength range\n",
    "freqs = td.C_0 / ldas  # frequency range\n",
    "\n",
    "freq0 = (freqs[-1] + freqs[0]) / 2  # central frequency for the source\n",
    "fwidth = (freqs[-1] - freqs[0]) / 2  # frequency width for the source"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "132bc4dc-98b7-4744-b1b4-bc9648cc0850",
   "metadata": {},
   "source": [
    "Create the PEC sphere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d9a705d8-f8d7-4303-8cc0-d479effedb76",
   "metadata": {},
   "outputs": [],
   "source": [
    "sphere = td.Structure(geometry=td.Sphere(radius=r), medium=td.PECMedium())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "156aad7b-ec20-4385-a29f-83c010d6bb4b",
   "metadata": {},
   "source": [
    "Next, we define a [TFSF](https://www.flexcompute.com/tidy3d/examples/notebooks/TFSF/) source as the excitation. For RCS calculation, the [TFSF](https://www.flexcompute.com/tidy3d/examples/notebooks/TFSF/) source is the most suitable since it injects a plane wave with unit power density, which makes the normalization of the RCS calculation automatic. The source needs to enclose the sphere. The incident angle and direction do not matter due to the symmetry of the sphere but we have it injected in the $z$ axis in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "18b49c47-978b-448a-b951-53af81162c06",
   "metadata": {},
   "outputs": [],
   "source": [
    "source_size = 3 * r\n",
    "\n",
    "source = td.TFSF(\n",
    "    size=[source_size] * 3,\n",
    "    source_time=td.GaussianPulse(freq0=freq0, fwidth=fwidth),\n",
    "    injection_axis=2,\n",
    "    direction=\"-\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17330b75-cd40-41eb-9f2b-1c9fbf8414c1",
   "metadata": {},
   "source": [
    "The RCS calculation is automatically done in a [FieldProjectionAngleMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FieldProjectionAngleMonitor.html). The monitor needs to enclose both the source and the sphere. Since we are only interested in the monostatic RCS, we only need to project to one particular angle, namely the opposite direction of the incident direction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5654f64c-a5f2-4dfe-a866-d0b6b15d3ca3",
   "metadata": {},
   "outputs": [],
   "source": [
    "monitor_size = 4 * r\n",
    "\n",
    "monitor = td.FieldProjectionAngleMonitor(\n",
    "    size=[monitor_size] * 3,\n",
    "    freqs=freqs,\n",
    "    name=\"far_field\",\n",
    "    phi=[0],\n",
    "    theta=[0],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb00c406-9835-44ec-b7a4-1af4f2270f3f",
   "metadata": {},
   "source": [
    "Put everything into a [Simulation](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.Simulation.html) instance. Here we use a uniform grid of size $r$/100 to sufficiently resolve the curved surface of the sphere. By default, we apply a subpixel averaging method known as the conformal mesh scheme to PEC boundaries.\n",
    "\n",
    "The automatic shutoff level by default is at `1e-5`. Here to further push the accuracy, we lower it to `1e-8`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8c2b38a5-d5fb-4d22-9610-d6c29597a3b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "run_time = 1e-13\n",
    "sim_size = 6 * r\n",
    "\n",
    "sim = td.Simulation(\n",
    "    size=[sim_size] * 3,\n",
    "    grid_spec=td.GridSpec.uniform(dl=r / 100),\n",
    "    structures=[sphere],\n",
    "    sources=[source],\n",
    "    monitors=[monitor],\n",
    "    run_time=run_time,\n",
    "    shutoff=1e-8,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85cdc7c3-bcd0-4336-81ca-1cf9ebb22ba0",
   "metadata": {},
   "source": [
    "Visualize the simulation to ensure the setup is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "efa5c6b5-5699-4230-91f7-3baf2f598d66",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim.plot(y=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a675e12-e0de-44f3-b177-81ca04aa1724",
   "metadata": {},
   "source": [
    "## Submit the Simulation to the Server\n",
    "\n",
    "Once we confirm that the simulation is set up properly, we can run it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "48f6a2ae-53d3-45a0-a0cd-af22d9f7334b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:41:26 CEST </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'pec_sphere_rcs'</span> with task_id                        \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>. \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m14:41:26 CEST\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'pec_sphere_rcs'\u001b[0m with task_id                        \n",
       "\u001b[2;36m              \u001b[0m\u001b[32m'fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a'\u001b[0m and task_type \u001b[32m'FDTD'\u001b[0m. \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><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-5b87798a-dd38-426e-9e3a-ec376bb6b19a\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">38-426e-9e3a-ec376bb6b19a'</span></a>.                                       \n",
       "</pre>\n"
      ],
      "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=140781;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[32m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=408431;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[32mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=140781;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[32m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=506818;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[32mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=140781;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[32m-5b87798a-dd\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=140781;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[32m38-426e-9e3a-ec376bb6b19a'\u001b[0m\u001b]8;;\u001b\\.                                       \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/9b36e144-ddb6-41f8-8dd8-30b62b26a870\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                           \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mTask folder: \u001b]8;id=491246;https://tidy3d.simulation.cloud/folders/9b36e144-ddb6-41f8-8dd8-30b62b26a870\u001b\\\u001b[32m'default'\u001b[0m\u001b]8;;\u001b\\.                                           \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "faeaf4d4acd9491fbe259974b5b060d9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:41:30 CEST </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.595</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"
      ],
      "text/plain": [
       "\u001b[2;36m14:41:30 CEST\u001b[0m\u001b[2;36m \u001b[0mMaximum FlexCredit cost: \u001b[1;36m0.595\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"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:41:32 CEST </span>status = queued                                                   \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m14:41:32 CEST\u001b[0m\u001b[2;36m \u001b[0mstatus = queued                                                   \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><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"
      ],
      "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"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6c2e8fc162bf42e88e2d4e6800d2d853",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:41:46 CEST </span>status = preprocess                                               \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m14:41:46 CEST\u001b[0m\u001b[2;36m \u001b[0mstatus = preprocess                                               \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:41:51 CEST </span>starting up solver                                                \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m14:41:51 CEST\u001b[0m\u001b[2;36m \u001b[0mstarting up solver                                                \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>running solver                                                    \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mrunning solver                                                    \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f91baf123f684212968b119b31ba409f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:42:36 CEST </span>early shutoff detected at <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">64</span>%, exiting.                           \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m14:42:36 CEST\u001b[0m\u001b[2;36m \u001b[0mearly shutoff detected at \u001b[1;36m64\u001b[0m%, exiting.                           \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>status = success                                                  \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mstatus = success                                                  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span>View simulation result at                                         \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">              </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">38-426e-9e3a-ec376bb6b19a'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                       \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m             \u001b[0m\u001b[2;36m \u001b[0mView simulation result at                                         \n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=457539;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=865135;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=457539;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=99344;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=457539;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[4;34m-5b87798a-dd\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m              \u001b[0m\u001b]8;id=457539;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b87798a-dd38-426e-9e3a-ec376bb6b19a\u001b\\\u001b[4;34m38-426e-9e3a-ec376bb6b19a'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                       \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "model_id": "a677093252d24a798c87eb3993400209",
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       "version_minor": 0
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      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">14:42:38 CEST </span>loading simulation from simulation_data.hdf5                      \n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[2;36m14:42:38 CEST\u001b[0m\u001b[2;36m \u001b[0mloading simulation from simulation_data.hdf5                      \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_data = web.run(simulation=sim, task_name=\"pec_sphere_rcs\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bad69c9-5d18-4f34-be20-6f87a40e7348",
   "metadata": {},
   "source": [
    "## Postprocessing and Visualization\n",
    "\n",
    "Once the simulation is complete, we can calculate the RCS directly from the monitor data and normalize it to the physical cross section of the sphere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "71339b47-11aa-4d12-9a07-cc7c39ec9314",
   "metadata": {},
   "outputs": [],
   "source": [
    "rcs_tidy3d = sim_data[\"far_field\"].radar_cross_section.real.squeeze(drop=True).values / (\n",
    "    np.pi * r**2\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e78b2b6c-6afc-4de4-984e-5c35e9e03c3d",
   "metadata": {},
   "source": [
    "The normalized monostatic RCS (σ/πr²) of a PEC sphere is calculated using the Mie series solution:\n",
    "\n",
    "$$\n",
    "\\frac{\\sigma}{\\pi r^2} = \\frac{4}{x^2} \\left| \\sum_{n=1}^\\infty (-1)^n (n + 0.5) \\left(a_n - b_n \\right) \\right|^2 ,\n",
    "$$\n",
    "\n",
    "where:\n",
    "\n",
    "- Relative frequency:  \n",
    "  $$ x = \\frac{2\\pi r}{\\lambda} \\quad \\text{(unitless)} $$\n",
    "- Mie coefficients: \n",
    "    $$ a_n = -\\frac{\\left[x j_n(x)\\right]'}{\\left[x h_n^{(1)}(x)\\right]'} $$  \n",
    "    $$ b_n = -\\frac{j_n(x)}{h_n^{(1)}(x)} $$\n",
    "\n",
    "- Spherical Bessel function: $$ j_n(x) $$\n",
    "- Spherical Hankel function (1st kind):  \n",
    "    $$ h_n^{(1)}(x) = j_n(x) + i y_n(x) $$\n",
    "\n",
    "We calculate the RCS according to the formula above and compare it to the simulated RCS from Tidy3D."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "25b2710c-0dc7-4647-9177-acbc232fa442",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import spherical_jn, spherical_yn\n",
    "\n",
    "\n",
    "def normalized_rcs(rel_freq):\n",
    "    \"\"\"\n",
    "    Calculate the monostatic RCS of a PEC sphere normalized by πr².\n",
    "\n",
    "    Parameters:\n",
    "    relative_frequency (float): The relative frequency (2πr/λ), unitless.\n",
    "\n",
    "    Returns:\n",
    "    float: Normalized RCS (σ / πr²), unitless.\n",
    "    \"\"\"\n",
    "\n",
    "    if rel_freq <= 0:\n",
    "        return 0.0\n",
    "\n",
    "    # determine the maximum number of terms in the series\n",
    "    N_max = int(np.floor(rel_freq + 4 * rel_freq ** (1 / 3) + 2))\n",
    "    total_sum = 0.0j\n",
    "\n",
    "    for n in range(1, N_max + 1):\n",
    "        # compute spherical Bessel (jn) and Neumann (yn) functions\n",
    "        jn = spherical_jn(n, rel_freq)  # j_n(x)\n",
    "        jn_deriv = spherical_jn(n, rel_freq, True)  # j_n'(x)\n",
    "\n",
    "        yn = spherical_yn(n, rel_freq)  # y_n(x)\n",
    "        yn_deriv = spherical_yn(n, rel_freq, True)  # y_n'(x)\n",
    "\n",
    "        # spherical Hankel function of the first kind (hn1)\n",
    "        hn1 = jn + 1j * yn  # h_n^(1)(x)\n",
    "        hn1_deriv = jn_deriv + 1j * yn_deriv  # [h_n^(1)]'(x)\n",
    "\n",
    "        # calculate (x * jn)' and (x * hn1)'\n",
    "        x_jn_deriv = jn + rel_freq * jn_deriv\n",
    "        x_hn1_deriv = hn1 + rel_freq * hn1_deriv\n",
    "\n",
    "        # Mie coefficients for PEC sphere\n",
    "        a_n = -x_jn_deriv / x_hn1_deriv\n",
    "        b_n = -jn / hn1\n",
    "\n",
    "        # series term\n",
    "        term = ((-1) ** n) * (n + 0.5) * (a_n - b_n)\n",
    "        total_sum += term\n",
    "\n",
    "    # compute the normalized RCS\n",
    "    if rel_freq == 0:\n",
    "        return 0.0\n",
    "    rcs_normalized = (4.0 / rel_freq**2) * (np.abs(total_sum) ** 2)\n",
    "    return rcs_normalized.real\n",
    "\n",
    "\n",
    "rcs_analytic = [normalized_rcs(rel_freq) for rel_freq in rel_freqs]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecc0513f-5a62-4c26-8d5e-1f3779c6e95c",
   "metadata": {},
   "source": [
    "Plot the simulated and calculated RCS together. The results overlap very well, indicating the good accuracy of the Tidy3D solver."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fa2934bb-5196-4800-8bf5-f7e39f5d1937",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rel_freqs, rcs_tidy3d, \"red\", linewidth=2, label=\"Tidy3D\")\n",
    "plt.scatter(rel_freqs, rcs_analytic, c=\"blue\", label=\"Analytic\")\n",
    "plt.xlabel(r\"Relative frequency (2$\\pi r$/$\\lambda_0$)\")\n",
    "plt.ylabel(r\"Monostatic RCS (2$\\pi r^2$)\")\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "description": "This notebook demonstrates how to simulate the monostatic RCS of a PEC sphere in Tidy3D and compare its accuracy to the analytical solution.",
  "feature_imag": "",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "keywords": "monostatic RCS, RF, microwave, 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": "3.11.12"
  },
  "title": "Monostatic Radar Cross Section (RCS) of a PEC Sphere in Tidy3D | Flexcompute"
 },
 "nbformat": 4,
 "nbformat_minor": 5
}