{ "cells": [ { "cell_type": "markdown", "id": "3e4d4e4c", "metadata": { "papermill": { "duration": 0.00139, "end_time": "2026-05-27T20:00:37.159118+00:00", "exception": false, "start_time": "2026-05-27T20:00:37.157728+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Hollow Rectangular Waveguide Modes\n", "\n", "This notebook solves a PEC rectangular waveguide with `WaveguideModeSolver`, compares against analytic TE/TM modes, and plots the first fields." ] }, { "cell_type": "code", "execution_count": 1, "id": "bfef1c6d", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T20:00:37.165276Z", "iopub.status.busy": "2026-05-27T20:00:37.165099Z", "iopub.status.idle": "2026-05-27T20:00:37.896231Z", "shell.execute_reply": "2026-05-27T20:00:37.895588Z" }, "papermill": { "duration": 0.733829, "end_time": "2026-05-27T20:00:37.897013+00:00", "exception": false, "start_time": "2026-05-27T20:00:37.163184+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "import palacetoolkit as ptk\n", "\n", "import gmsh\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from palacetoolkit.mode_solver import WaveguideModeSolver\n", "from palacetoolkit.utils import write_and_finalize_gmsh\n", "from palacetoolkit.viz import view_mesh\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "902f3519", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T20:00:37.903124Z", "iopub.status.busy": "2026-05-27T20:00:37.902866Z", "iopub.status.idle": "2026-05-27T20:00:37.908380Z", "shell.execute_reply": "2026-05-27T20:00:37.907930Z" }, "papermill": { "duration": 0.010789, "end_time": "2026-05-27T20:00:37.909040+00:00", "exception": false, "start_time": "2026-05-27T20:00:37.898251+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "def _set_transfinite_rect(surf_tag, nx, ny):\n", " bnd = gmsh.model.getBoundary([(2, surf_tag)], oriented=True)\n", " lines = [abs(t) for _, t in bnd]\n", " for line in lines:\n", " pts = gmsh.model.getBoundary([(1, line)], oriented=False)\n", " c0 = gmsh.model.getValue(0, pts[0][1], [])\n", " c1 = gmsh.model.getValue(0, pts[1][1], [])\n", " dx = abs(c1[0] - c0[0])\n", " dy = abs(c1[1] - c0[1])\n", " n = (nx + 1) if dx > dy else (ny + 1)\n", " gmsh.model.mesh.setTransfiniteCurve(line, n)\n", " gmsh.model.mesh.setTransfiniteSurface(surf_tag)\n", "\n", "\n", "def make_rectangular_mesh(a, b, nx, ny, structured=True, lc=None, filename=None):\n", " gmsh.initialize()\n", " gmsh.option.setNumber(\"General.Verbosity\", 0)\n", " gmsh.model.add(\"hollow_waveguide\")\n", "\n", " gmsh.model.occ.addRectangle(0, 0, 0, a, b, tag=1)\n", " gmsh.model.occ.synchronize()\n", "\n", " gmsh.model.addPhysicalGroup(2, [1], tag=1, name=\"domain\")\n", " bnd = gmsh.model.getBoundary([(2, 1)], oriented=False)\n", " bnd_tags = [abs(t) for _, t in bnd]\n", " gmsh.model.addPhysicalGroup(1, bnd_tags, tag=1, name=\"PEC\")\n", "\n", " if structured:\n", " _set_transfinite_rect(1, nx, ny)\n", " gmsh.model.mesh.setRecombine(2, 1)\n", " else:\n", " _lc = lc if lc is not None else max(a / nx, b / ny)\n", " gmsh.option.setNumber(\"Mesh.CharacteristicLengthMin\", 0.8 * _lc)\n", " gmsh.option.setNumber(\"Mesh.CharacteristicLengthMax\", 1.2 * _lc)\n", "\n", " gmsh.model.mesh.generate(2)\n", " return write_and_finalize_gmsh(filename, prefix=\"wg_rect_\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "ae6533ee", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T20:00:37.911957Z", "iopub.status.busy": "2026-05-27T20:00:37.911783Z", "iopub.status.idle": "2026-05-27T20:00:37.915400Z", "shell.execute_reply": "2026-05-27T20:00:37.914917Z" }, "papermill": { "duration": 0.005726, "end_time": "2026-05-27T20:00:37.915940+00:00", "exception": false, "start_time": "2026-05-27T20:00:37.910214+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "def analytic_kn(a, b, omega, m_max=5, n_max=5, mu=1.0, eps=1.0):\n", " modes = []\n", " k0_sq = omega**2 * mu * eps\n", "\n", " for m in range(0, m_max + 1):\n", " for n in range(0, n_max + 1):\n", " if m == 0 and n == 0:\n", " continue\n", " kc_sq = (m * np.pi / a) ** 2 + (n * np.pi / b) ** 2\n", " kn = np.sqrt((k0_sq - kc_sq) + 0j)\n", " modes.append((f\"TE{m}{n}\", np.sqrt(kc_sq), kn))\n", "\n", " for m in range(1, m_max + 1):\n", " for n in range(1, n_max + 1):\n", " kc_sq = (m * np.pi / a) ** 2 + (n * np.pi / b) ** 2\n", " kn = np.sqrt((k0_sq - kc_sq) + 0j)\n", " modes.append((f\"TM{m}{n}\", np.sqrt(kc_sq), kn))\n", "\n", " modes.sort(key=lambda x: -x[2].real)\n", " return modes" ] }, { "cell_type": "code", "execution_count": 4, "id": "3be79dcc", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T20:00:37.918523Z", "iopub.status.busy": "2026-05-27T20:00:37.918405Z", "iopub.status.idle": "2026-05-27T20:00:37.922021Z", "shell.execute_reply": "2026-05-27T20:00:37.921450Z" }, "papermill": { "duration": 0.005489, "end_time": "2026-05-27T20:00:37.922505+00:00", "exception": false, "start_time": "2026-05-27T20:00:37.917016+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Top 8 analytic modes:\n", " TE10 : kc= 1.5708, kn= +5.268611 +0.000000j\n", " TE01 : kc= 3.1416, kn= +4.511769 +0.000000j\n", " TE20 : kc= 3.1416, kn= +4.511769 +0.000000j\n", " TE11 : kc= 3.5124, kn= +4.229499 +0.000000j\n", " TM11 : kc= 3.5124, kn= +4.229499 +0.000000j\n", " TE21 : kc= 4.4429, kn= +3.238280 +0.000000j\n", " TM21 : kc= 4.4429, kn= +3.238280 +0.000000j\n", " TE30 : kc= 4.7124, kn= +2.831793 +0.000000j\n" ] } ], "source": [ "a, b = 2.0, 1.0\n", "mu, eps = 1.0, 1.0\n", "c0 = 1.0 / np.sqrt(mu * eps)\n", "\n", "fc_te10 = c0 * np.pi / a / (2 * np.pi)\n", "f_op = 3.5 * fc_te10\n", "omega = 2 * np.pi * f_op\n", "\n", "analytic = analytic_kn(a, b, omega, m_max=4, n_max=4, mu=mu, eps=eps)\n", "print(\"Top 8 analytic modes:\")\n", "for name, kc, kn in analytic[:8]:\n", " print(f\" {name:6s}: kc={kc:8.4f}, kn={kn.real:+10.6f}{kn.imag:+10.6f}j\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "3b2cd9cd", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T20:00:37.925186Z", "iopub.status.busy": "2026-05-27T20:00:37.925066Z", "iopub.status.idle": "2026-05-27T20:00:39.023255Z", "shell.execute_reply": "2026-05-27T20:00:39.022898Z" }, "papermill": { "duration": 1.101843, "end_time": "2026-05-27T20:00:39.025494+00:00", "exception": false, "start_time": "2026-05-27T20:00:37.923651+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loading mesh file: /tmp/wg_rect_mhlsva3w.msh\n", "Groups to render transparent: ['air_none', 'air_plastic_enclosure']\n", "\n", "Mesh loaded successfully with 2 cell blocks\n", "Found 1024 triangles total\n", "Physical group tags in mesh: {1: 'domain'}\n" ] }, { "data": { "text/html": [ "
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " FE spaces: ND dofs = 4192, H1 dofs = 2145, total = 6337\n", " Essential DOFs: ND = 192, H1 = 192, total = 384\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Solving eigenvalue problem (omega = 5.49779, sigma = -33.2482, size = 6337)...\n", " Found 8 modes:\n", " Mode 1: kn = +5.26861102e+00 -0.00000000e+00j <-- selected\n", " Mode 2: kn = +4.51176670e+00 -0.00000000e+00j\n", " Mode 3: kn = +4.51176670e+00 -0.00000000e+00j\n", " Mode 4: kn = +4.22949611e+00 -0.00000000e+00j\n", " Mode 5: kn = +4.22949611e+00 -0.00000000e+00j\n", " Mode 6: kn = +3.23827331e+00 -0.00000000e+00j\n", " Mode 7: kn = +3.23827331e+00 -0.00000000e+00j\n", " Mode 8: kn = +2.83175256e+00 -0.00000000e+00j\n", "\n", "Numerical modes:\n", " Mode 1: kn= +5.268611 -0.000000j\n", " Mode 2: kn= +4.511767 -0.000000j\n", " Mode 3: kn= +4.511767 -0.000000j\n", " Mode 4: kn= +4.229496 -0.000000j\n", " Mode 5: kn= +4.229496 -0.000000j\n", " Mode 6: kn= +3.238273 -0.000000j\n", " Mode 7: kn= +3.238273 -0.000000j\n", " Mode 8: kn= +2.831753 -0.000000j\n" ] } ], "source": [ "mesh_file = make_rectangular_mesh(\n", " a,\n", " b,\n", " nx=32,\n", " ny=16,\n", " structured=True,\n", ")\n", "view_mesh(mesh_file)\n", "solver = WaveguideModeSolver(mesh_file, order=2, mu_inv=1.0 / mu, eps=eps, pec_bdr=\"all\")\n", "results = solver.solve(omega, num_modes=8, mode_idx=1)\n", "\n", "print(\"\\nNumerical modes:\")\n", "for i, kn in enumerate(results[\"kn\"], start=1):\n", " print(f\" Mode {i}: kn={kn.real:+10.6f}{kn.imag:+10.6f}j\")" ] }, { "cell_type": "code", "execution_count": 6, "id": "eb43ec99", "metadata": { "execution": { "iopub.execute_input": "2026-05-27T20:00:39.086774Z", "iopub.status.busy": "2026-05-27T20:00:39.086423Z", "iopub.status.idle": "2026-05-27T20:00:41.285461Z", "shell.execute_reply": "2026-05-27T20:00:41.284801Z" }, "papermill": { "duration": 2.230172, "end_time": "2026-05-27T20:00:41.285866+00:00", "exception": false, "start_time": "2026-05-27T20:00:39.055694+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Solving eigenvalue problem (omega = 5.49779, sigma = -33.2482, size = 6337)...\n", " Found 8 modes:\n", " Mode 1: kn = +5.26861102e+00 -0.00000000e+00j <-- selected\n", " Mode 2: kn = +4.51176670e+00 -0.00000000e+00j\n", " Mode 3: kn = +4.51176670e+00 -0.00000000e+00j\n", " Mode 4: kn = +4.22949611e+00 -0.00000000e+00j\n", " Mode 5: kn = +4.22949611e+00 -0.00000000e+00j\n", " Mode 6: kn = +3.23827331e+00 -0.00000000e+00j\n", " Mode 7: kn = +3.23827331e+00 -0.00000000e+00j\n", " Mode 8: kn = +2.83175256e+00 -0.00000000e+00j\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Solving eigenvalue problem (omega = 5.49779, sigma = -33.2482, size = 6337)...\n", " Found 8 modes:\n", " Mode 1: kn = +5.26861102e+00 -0.00000000e+00j\n", " Mode 2: kn = +4.51176670e+00 -0.00000000e+00j <-- selected\n", " Mode 3: kn = +4.51176670e+00 -0.00000000e+00j\n", " Mode 4: kn = +4.22949611e+00 -0.00000000e+00j\n", " Mode 5: kn = +4.22949611e+00 -0.00000000e+00j\n", " Mode 6: kn = +3.23827331e+00 -0.00000000e+00j\n", " Mode 7: kn = +3.23827331e+00 -0.00000000e+00j\n", " Mode 8: kn = +2.83175256e+00 -0.00000000e+00j\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Solving eigenvalue problem (omega = 5.49779, sigma = -33.2482, size = 6337)...\n", " Found 8 modes:\n", " Mode 1: kn = +5.26861102e+00 -0.00000000e+00j\n", " Mode 2: kn = +4.51176670e+00 -0.00000000e+00j\n", " Mode 3: kn = +4.51176670e+00 -0.00000000e+00j <-- selected\n", " Mode 4: kn = +4.22949611e+00 -0.00000000e+00j\n", " Mode 5: kn = +4.22949611e+00 -0.00000000e+00j\n", " Mode 6: kn = +3.23827331e+00 -0.00000000e+00j\n", " Mode 7: kn = +3.23827331e+00 -0.00000000e+00j\n", " Mode 8: kn = +2.83175256e+00 -0.00000000e+00j\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(2, 3, figsize=(14, 8))\n", "fig.suptitle(\"Hollow Waveguide First Modes\", fontsize=14)\n", "\n", "for mode_i in range(3):\n", " r = solver.solve(omega, num_modes=8, mode_idx=mode_i + 1)\n", " X, Y, Ex, Ey, Ez = solver.get_field_on_grid(r[\"Et_vec\"], r[\"En_vec\"], nx=60, ny=30)\n", "\n", " Et_mag = np.sqrt(np.abs(Ex) ** 2 + np.abs(Ey) ** 2)\n", " En_mag = np.abs(Ez)\n", "\n", " ax = axes[0, mode_i]\n", " im = ax.pcolormesh(X, Y, Et_mag, cmap=\"hot\", shading=\"auto\")\n", " ax.set_title(f\"|Et| mode {mode_i+1}\")\n", " ax.set_aspect(\"equal\")\n", " fig.colorbar(im, ax=ax, fraction=0.046)\n", "\n", " ax = axes[1, mode_i]\n", " im = ax.pcolormesh(X, Y, En_mag, cmap=\"hot\", shading=\"auto\")\n", " ax.set_title(f\"|En| mode {mode_i+1}\")\n", " ax.set_aspect(\"equal\")\n", " fig.colorbar(im, ax=ax, fraction=0.046)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" }, "papermill": { "default_parameters": {}, "duration": 5.445503, "end_time": "2026-05-27T20:00:41.912857+00:00", "environment_variables": {}, "exception": null, "input_path": "docs/examples/hollow_waveguide_modes.ipynb", "output_path": "docs/examples/hollow_waveguide_modes.ipynb", "parameters": {}, "start_time": "2026-05-27T20:00:36.467354+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }