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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Band structure calculation of hexagonal lattices\n",
+ "\n",
+ "In this notebook, we demonstrate the approach for simulating band diagrams of periodic structures defined in hexagonal lattices. We will reproduce the TM band diagram calculation presented in the paper by `Tsung-li Liu, Kasey J. Russell, Shanying Cui, and Evelyn L. Hu, \"Two-dimensional hybrid photonic/plasmonic crystal cavities\", Optics Express, (2014).` [DOI:10.1364/OE.22.008219](https://doi.org/10.1364/oe.22.008219).\n",
+ "\n",
+ "For calculating band diagrams of periodic structures in a **square** lattice, please refer to our [band diagrams for a photonic crystal slab](https://www.flexcompute.com/tidy3d/examples/notebooks/Bandstructure/) example notebook.\n",
+ "\n",
+ "\n",
+ "\n",
+ "Due to the rectangular nature of the FDTD simulation domain, a primitive hexagonal unit cell **cannot** be represented directly; therefore, it is necessary to use a rectangular supercell of size $(a \\times \\sqrt{3}a$), constructed from two primitive real-space lattice vectors. However, this supercell enlarges the real-space period and reduces the Brillouin zone, which introduces artificial band folding.\n",
+ "\n",
+ "To suppress these folded modes, we apply **matching dipoles**. For each dipole placed in the supercell, a second dipole is added at the position shifted by the primitive lattice vector $\\vec{r}$ of the true hexagonal cell. The second dipole is driven with a Bloch phase factor \n",
+ "\n",
+ "$$e^{-i 2\\pi\\,\\vec{b}\\cdot\\vec{r}}$$\n",
+ "\n",
+ "where $\\vec{b}$ is the Bloch wavevector. This enforces the correct Bloch periodicity of the primitive cell, ensuring that only the physical (unfolded) Bloch modes are excited, and allowing the band diagram to be computed using the standard high-symmetry points of the hexagonal Brillouin zone.\n",
+ "\n",
+ "This notebook is structured as follows:\n",
+ "\n",
+ "[1)](#1) Definition of the K-points for the hexagonal lattice \n",
+ "[2)](#2) Supercell definition and base simulation setup \n",
+ "[3)](#3) Function for creating matching dipoles for a given Bloch vector \n",
+ "[4)](#4) Band diagram calculation\n",
+ "\n",
+ "
"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from typing import Callable\n",
+ "\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "import tidy3d as td\n",
+ "from tidy3d import web\n",
+ "\n",
+ "# Defining a random seed for reproducibility\n",
+ "np.random.seed(12)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## K-points Definition \n",
+ "\n",
+ "For a hexagonal lattice, we can define the two real-space lattice vectors as \n",
+ "$a_1 = (a,\\,0)$ and \n",
+ "$a_2 = a(\\cos(\\pi/3),\\,\\sin(\\pi/3))$.\n",
+ "\n",
+ "To transform these vectors into reciprocal space, we use the standard definition, where $a_3$ is simply (0,0,1).\n",
+ "\n",
+ "$b_i = 2\\pi\\, \\frac{a_j \\times a_k}{a_1 \\cdot (a_2 \\times a_3)}$\n",
+ "\n",
+ "\n",
+ "Hence, the vectors in the reciprocal space are:\n",
+ "\n",
+ "$ b_1 = \\frac{2\\pi}{a}(1,-\\frac{1}{\\sqrt{3}}) $ \n",
+ "$ b_2 = \\frac{2\\pi}{a}(0,\\frac{2}{\\sqrt{3}}) $\n",
+ "\n",
+ "For band calculations, we only need to sweep points in the irreducible Brillouin zone (IBZ), which in reduced reciprocal coordinates corresponds to the triangular region defined by the points\n",
+ "\n",
+ "- $\\Gamma = (0,\\,0)$ \n",
+ "- $M = \\left(0,\\,\\tfrac{1}{\\sqrt{3}}\\right)$ \n",
+ "- $K = \\left(\\tfrac{1}{3},\\,\\tfrac{1}{\\sqrt{3}}\\right)$.\n",
+ "\n",
+ "The code below illustrates the real and reciprocal spaces."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "# -------------------------------------------------\n",
+ "# Lattice definitions\n",
+ "# -------------------------------------------------\n",
+ "a = 1.0 # lattice constant\n",
+ "\n",
+ "# Real-space lattice vectors\n",
+ "a1 = np.array([a, 0.0])\n",
+ "a2 = a * np.array([np.cos(np.pi / 3), np.sin(np.pi / 3)])\n",
+ "\n",
+ "# Reciprocal-space lattice vectors\n",
+ "b1 = (2 * np.pi / a) * np.array([1.0, -1.0 / np.sqrt(3)])\n",
+ "b2 = (2 * np.pi / a) * np.array([0.0, 2.0 / np.sqrt(3)])\n",
+ "\n",
+ "# -------------------------------------------------\n",
+ "# Generate lattice points\n",
+ "# -------------------------------------------------\n",
+ "N = 5 # number of points in each direction (odd, so we get symmetry around 0)\n",
+ "\n",
+ "# Real space points\n",
+ "pts_real = []\n",
+ "for i in range(-(N // 2), N // 2 + 1):\n",
+ " for j in range(-(N // 2), N // 2 + 1):\n",
+ " pts_real.append(i * a1 + j * a2)\n",
+ "pts_real = np.array(pts_real)\n",
+ "\n",
+ "# Reciprocal space points\n",
+ "pts_rec = []\n",
+ "for i in range(-(N // 2), N // 2 + 1):\n",
+ " for j in range(-(N // 2), N // 2 + 1):\n",
+ " pts_rec.append(i * b1 + j * b2)\n",
+ "pts_rec = np.array(pts_rec)\n",
+ "\n",
+ "\n",
+ "# -------------------------------------------------\n",
+ "# IBZ path in reciprocal space\n",
+ "# (given in reduced coordinates; convert to Cartesian k)\n",
+ "# -------------------------------------------------\n",
+ "Gamma = 2 * np.pi / a * np.array([0.0, 0.0])\n",
+ "M = 2 * np.pi / a * np.array([0.0, 1.0 / np.sqrt(3)])\n",
+ "K = 2 * np.pi / a * np.array([1.0 / 3.0, 1.0 / np.sqrt(3)])\n",
+ "\n",
+ "ibz_path = np.vstack([Gamma, M, K, Gamma])\n",
+ "\n",
+ "# -------------------------------------------------\n",
+ "# Plot\n",
+ "# -------------------------------------------------\n",
+ "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 6))\n",
+ "\n",
+ "\n",
+ "# --- Real space ---\n",
+ "ax1.scatter(pts_real[:, 0], pts_real[:, 1], marker=\"o\", s=200, color=\"black\")\n",
+ "ax1.quiver(0, 0, a1[0], a1[1], angles=\"xy\", scale_units=\"xy\", scale=1)\n",
+ "ax1.quiver(0, 0, a2[0], a2[1], angles=\"xy\", scale_units=\"xy\", scale=1)\n",
+ "ax1.set_title(\"Real-space lattice and vectors\")\n",
+ "ax1.set_xlabel(\"x\")\n",
+ "ax1.set_ylabel(\"y\")\n",
+ "ax1.set_aspect(\"equal\")\n",
+ "ax1.grid(True)\n",
+ "\n",
+ "# Supercell corners in real space\n",
+ "W = a / 2\n",
+ "H = (a * np.sqrt(3)) / 2\n",
+ "\n",
+ "# Rectangle corners (closed loop)\n",
+ "rect = np.array([[-W, -H], [W, -H], [W, H], [-W, H], [-W, -H]])\n",
+ "\n",
+ "# Draw rectangle\n",
+ "ax1.plot(rect[:, 0], rect[:, 1], \"--\")\n",
+ "\n",
+ "# Fill it\n",
+ "ax1.fill(rect[:, 0], rect[:, 1], alpha=0.15)\n",
+ "\n",
+ "\n",
+ "# --- Reciprocal space ---\n",
+ "ax2.scatter(pts_rec[:, 0], pts_rec[:, 1], marker=\"o\", s=200, color=\"black\")\n",
+ "ax2.quiver(0, 0, b1[0], b1[1], angles=\"xy\", scale_units=\"xy\", scale=1)\n",
+ "ax2.quiver(0, 0, b2[0], b2[1], angles=\"xy\", scale_units=\"xy\", scale=1)\n",
+ "\n",
+ "# IBZ path Γ–M–K–Γ\n",
+ "ax2.plot(ibz_path[:, 0], ibz_path[:, 1], marker=\"o\")\n",
+ "\n",
+ "# Label the special points\n",
+ "ax2.text(Gamma[0], Gamma[1], r\"$\\Gamma$\", ha=\"right\", va=\"bottom\")\n",
+ "ax2.text(M[0], M[1], r\"$M$\", ha=\"right\", va=\"bottom\")\n",
+ "ax2.text(K[0], K[1], r\"$K$\", ha=\"left\", va=\"bottom\")\n",
+ "\n",
+ "ax2.set_title(\"Reciprocal-space lattice, vectors and IBZ path\")\n",
+ "ax2.set_xlabel(r\"$k_x$\")\n",
+ "ax2.set_ylabel(r\"$k_y$\")\n",
+ "ax2.set_aspect(\"equal\")\n",
+ "ax2.grid(True)\n",
+ "\n",
+ "ax1.set_xlim(-1.1, 1.1)\n",
+ "ax1.set_ylim(-1.1, 1.1)\n",
+ "\n",
+ "ax2.set_xlim(-3.1 * np.pi / a, 3.1 * np.pi / a)\n",
+ "ax2.set_ylim(-3.1 * np.pi / a, 3.1 * np.pi / a)\n",
+ "\n",
+ "plt.tight_layout()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Simulation Setup "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, we will define the global parameters to be used in the simulation.\n",
+ "Since we can express everything in terms of the lattice constant, we will set it to 1 and then scale the frequency accordingly during post-processing."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Source polarization\n",
+ "polarization = \"Ez\"\n",
+ "\n",
+ "theta = np.pi / 6\n",
+ "sizeZ = 6\n",
+ "\n",
+ "# Option to add or not add matching dipoles\n",
+ "matchingDipoles = True\n",
+ "\n",
+ "# K-points of the Brillouin zone of the hexagonal lattice\n",
+ "kPoints = [(0, 0), (0, 1 / (np.sqrt(3))), (1 / 3, 1 / np.sqrt(3)), (0, 0)]\n",
+ "\n",
+ "# Source frequency and width\n",
+ "freq0 = 200e12\n",
+ "fwidth = 150e12\n",
+ "\n",
+ "runTime = 2e-12\n",
+ "\n",
+ "rodMaterial = td.Medium(permittivity=2.5**2)\n",
+ "\n",
+ "# Lattice constant defined as 1. Then we just scale the results\n",
+ "latticeConstant = 1\n",
+ "\n",
+ "radius = 0.28 * latticeConstant\n",
+ "height = 1 * latticeConstant\n",
+ "\n",
+ "\n",
+ "# Lattice vectors\n",
+ "y = latticeConstant * np.cos(theta)\n",
+ "x = latticeConstant * np.sin(theta)\n",
+ "a1 = np.array([x, y, 0])\n",
+ "a2 = np.array([-x, y, 0])\n",
+ "\n",
+ "\n",
+ "# Creating the supercell\n",
+ "centerRod = td.Cylinder(center=(0, 0, 0), radius=radius, length=height)\n",
+ "\n",
+ "geometry = centerRod\n",
+ "geometry += centerRod.updated_copy(center=tuple(-a1))\n",
+ "geometry += centerRod.updated_copy(center=tuple(a2))\n",
+ "geometry += centerRod.updated_copy(center=tuple(-a2))\n",
+ "geometry += centerRod.updated_copy(center=tuple(a1))\n",
+ "\n",
+ "\n",
+ "structure = td.Structure(geometry=geometry, medium=rodMaterial)\n",
+ "\n",
+ "size = (2 * x, 2 * y, sizeZ)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To ensure periodicity, we will use a [MeshOverrideStructure](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.MeshOverrideStructure.html) to create a custom grid with a fixed number of grid points in x and y."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "grid = td.MeshOverrideStructure(\n",
+ " geometry=td.Box(center=(0, 0, 0), size=(td.inf, td.inf, td.inf)),\n",
+ " dl=(size[0] / 40, size[1] / 60, 0.1),\n",
+ ")\n",
+ "\n",
+ "grid_spec = td.GridSpec.auto(\n",
+ " override_structures=[grid],\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, we will define the sources and monitors.\n",
+ "\n",
+ "We will place 5 sources randomly distributed in the lower-left unit cell region, and 5 [FieldTimeMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FieldTimeMonitor.html) objects randomly distributed in the supercell."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "
09:56:18 -03 WARNING: The monitor 'interval' field was left as its default \n",
+ "value, which will set it to 1 internally. A value of 1 means that \n",
+ "the data will be sampled at every time step, which may potentially \n",
+ "produce more data than desired, depending on the use case. To \n",
+ "reduce data storage, one may downsample the data by setting \n",
+ "'interval > 1' or by choosing alternative 'start' and 'stop' values\n",
+ "for the time sampling. If you intended to use the highest \n",
+ "resolution time sampling, you may suppress this warning by \n",
+ "explicitly setting 'interval=1' in the monitor. \n",
+ "
\n"
+ ],
+ "text/plain": [
+ "\u001b[2;36m09:56:18 -03\u001b[0m\u001b[2;36m \u001b[0m\u001b[31mWARNING: The monitor \u001b[0m\u001b[32m'interval'\u001b[0m\u001b[31m field was left as its default \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mvalue, which will set it to \u001b[0m\u001b[1;36m1\u001b[0m\u001b[31m internally. A value of \u001b[0m\u001b[1;36m1\u001b[0m\u001b[31m means that \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mthe data will be sampled at every time step, which may potentially \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mproduce more data than desired, depending on the use case. To \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mreduce data storage, one may downsample the data by setting \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[32m'interval > 1'\u001b[0m\u001b[31m or by choosing alternative \u001b[0m\u001b[32m'start'\u001b[0m\u001b[31m and \u001b[0m\u001b[32m'stop'\u001b[0m\u001b[31m values\u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mfor the time sampling. If you intended to use the highest \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mresolution time sampling, you may suppress this warning by \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mexplicitly setting \u001b[0m\u001b[32m'\u001b[0m\u001b[32minterval\u001b[0m\u001b[32m=\u001b[0m\u001b[32m1\u001b[0m\u001b[32m'\u001b[0m\u001b[31m in the monitor. \u001b[0m\n"
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+ },
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+ "output_type": "display_data"
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+ {
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WARNING: The monitor 'interval' field was left as its default \n",
+ "value, which will set it to 1 internally. A value of 1 means that \n",
+ "the data will be sampled at every time step, which may potentially \n",
+ "produce more data than desired, depending on the use case. To \n",
+ "reduce data storage, one may downsample the data by setting \n",
+ "'interval > 1' or by choosing alternative 'start' and 'stop' values\n",
+ "for the time sampling. If you intended to use the highest \n",
+ "resolution time sampling, you may suppress this warning by \n",
+ "explicitly setting 'interval=1' in the monitor. \n",
+ "
\n"
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+ "\u001b[2;36m \u001b[0m\u001b[31mvalue, which will set it to \u001b[0m\u001b[1;36m1\u001b[0m\u001b[31m internally. A value of \u001b[0m\u001b[1;36m1\u001b[0m\u001b[31m means that \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mthe data will be sampled at every time step, which may potentially \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mproduce more data than desired, depending on the use case. To \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mreduce data storage, one may downsample the data by setting \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[32m'interval > 1'\u001b[0m\u001b[31m or by choosing alternative \u001b[0m\u001b[32m'start'\u001b[0m\u001b[31m and \u001b[0m\u001b[32m'stop'\u001b[0m\u001b[31m values\u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mfor the time sampling. If you intended to use the highest \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mresolution time sampling, you may suppress this warning by \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mexplicitly setting \u001b[0m\u001b[32m'\u001b[0m\u001b[32minterval\u001b[0m\u001b[32m=\u001b[0m\u001b[32m1\u001b[0m\u001b[32m'\u001b[0m\u001b[31m in the monitor. \u001b[0m\n"
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WARNING: The monitor 'interval' field was left as its default \n",
+ "value, which will set it to 1 internally. A value of 1 means that \n",
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+ "produce more data than desired, depending on the use case. To \n",
+ "reduce data storage, one may downsample the data by setting \n",
+ "'interval > 1' or by choosing alternative 'start' and 'stop' values\n",
+ "for the time sampling. If you intended to use the highest \n",
+ "resolution time sampling, you may suppress this warning by \n",
+ "explicitly setting 'interval=1' in the monitor. \n",
+ "
\n"
+ ],
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+ "\u001b[2;36m \u001b[0m\u001b[31mvalue, which will set it to \u001b[0m\u001b[1;36m1\u001b[0m\u001b[31m internally. A value of \u001b[0m\u001b[1;36m1\u001b[0m\u001b[31m means that \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mthe data will be sampled at every time step, which may potentially \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mproduce more data than desired, depending on the use case. To \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mreduce data storage, one may downsample the data by setting \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[32m'interval > 1'\u001b[0m\u001b[31m or by choosing alternative \u001b[0m\u001b[32m'start'\u001b[0m\u001b[31m and \u001b[0m\u001b[32m'stop'\u001b[0m\u001b[31m values\u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mfor the time sampling. If you intended to use the highest \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mresolution time sampling, you may suppress this warning by \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mexplicitly setting \u001b[0m\u001b[32m'\u001b[0m\u001b[32minterval\u001b[0m\u001b[32m=\u001b[0m\u001b[32m1\u001b[0m\u001b[32m'\u001b[0m\u001b[31m in the monitor. \u001b[0m\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
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+ "
WARNING: The monitor 'interval' field was left as its default \n",
+ "value, which will set it to 1 internally. A value of 1 means that \n",
+ "the data will be sampled at every time step, which may potentially \n",
+ "produce more data than desired, depending on the use case. To \n",
+ "reduce data storage, one may downsample the data by setting \n",
+ "'interval > 1' or by choosing alternative 'start' and 'stop' values\n",
+ "for the time sampling. If you intended to use the highest \n",
+ "resolution time sampling, you may suppress this warning by \n",
+ "explicitly setting 'interval=1' in the monitor. \n",
+ "
\n"
+ ],
+ "text/plain": [
+ "\u001b[2;36m \u001b[0m\u001b[2;36m \u001b[0m\u001b[31mWARNING: The monitor \u001b[0m\u001b[32m'interval'\u001b[0m\u001b[31m field was left as its default \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mvalue, which will set it to \u001b[0m\u001b[1;36m1\u001b[0m\u001b[31m internally. A value of \u001b[0m\u001b[1;36m1\u001b[0m\u001b[31m means that \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mthe data will be sampled at every time step, which may potentially \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mproduce more data than desired, depending on the use case. To \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mreduce data storage, one may downsample the data by setting \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[32m'interval > 1'\u001b[0m\u001b[31m or by choosing alternative \u001b[0m\u001b[32m'start'\u001b[0m\u001b[31m and \u001b[0m\u001b[32m'stop'\u001b[0m\u001b[31m values\u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mfor the time sampling. If you intended to use the highest \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mresolution time sampling, you may suppress this warning by \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mexplicitly setting \u001b[0m\u001b[32m'\u001b[0m\u001b[32minterval\u001b[0m\u001b[32m=\u001b[0m\u001b[32m1\u001b[0m\u001b[32m'\u001b[0m\u001b[31m in the monitor. \u001b[0m\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ "
WARNING: The monitor 'interval' field was left as its default \n",
+ "value, which will set it to 1 internally. A value of 1 means that \n",
+ "the data will be sampled at every time step, which may potentially \n",
+ "produce more data than desired, depending on the use case. To \n",
+ "reduce data storage, one may downsample the data by setting \n",
+ "'interval > 1' or by choosing alternative 'start' and 'stop' values\n",
+ "for the time sampling. If you intended to use the highest \n",
+ "resolution time sampling, you may suppress this warning by \n",
+ "explicitly setting 'interval=1' in the monitor. \n",
+ "
\n"
+ ],
+ "text/plain": [
+ "\u001b[2;36m \u001b[0m\u001b[2;36m \u001b[0m\u001b[31mWARNING: The monitor \u001b[0m\u001b[32m'interval'\u001b[0m\u001b[31m field was left as its default \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mvalue, which will set it to \u001b[0m\u001b[1;36m1\u001b[0m\u001b[31m internally. A value of \u001b[0m\u001b[1;36m1\u001b[0m\u001b[31m means that \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mthe data will be sampled at every time step, which may potentially \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mproduce more data than desired, depending on the use case. To \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mreduce data storage, one may downsample the data by setting \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[32m'interval > 1'\u001b[0m\u001b[31m or by choosing alternative \u001b[0m\u001b[32m'start'\u001b[0m\u001b[31m and \u001b[0m\u001b[32m'stop'\u001b[0m\u001b[31m values\u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mfor the time sampling. If you intended to use the highest \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mresolution time sampling, you may suppress this warning by \u001b[0m\n",
+ "\u001b[2;36m \u001b[0m\u001b[31mexplicitly setting \u001b[0m\u001b[32m'\u001b[0m\u001b[32minterval\u001b[0m\u001b[32m=\u001b[0m\u001b[32m1\u001b[0m\u001b[32m'\u001b[0m\u001b[31m in the monitor. \u001b[0m\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Sources\n",
+ "Nsources = 5\n",
+ "\n",
+ "sourceTime = [\n",
+ " td.GaussianPulse(freq0=freq0, fwidth=fwidth, phase=i)\n",
+ " for i in 2 * np.pi * np.random.random(2 * Nsources)\n",
+ "]\n",
+ "\n",
+ "\n",
+ "# Random positions for the sources\n",
+ "posySource = np.random.uniform(-0.8, -0.2, Nsources)\n",
+ "posxSource = np.random.uniform(-0.2, -0.1, Nsources)\n",
+ "\n",
+ "\n",
+ "# Monitors\n",
+ "Nmonitors = 5\n",
+ "\n",
+ "posyMon = np.random.uniform(-0.8, 0.8, Nmonitors)\n",
+ "posxMon = np.random.uniform(-0.2, 0.2, Nmonitors)\n",
+ "\n",
+ "monitors = [\n",
+ " td.FieldTimeMonitor(center=(posxMon[i], posyMon[i], 0), name=f\"mon{i}\", size=(0, 0, 0), start=0)\n",
+ " for i in range(Nmonitors)\n",
+ "]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Defining the [Simulation](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.Simulation.html) and Matching Dipoles \n",
+ "\n",
+ "Finally, we define a function to generate the [Simulation](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.Simulation.html) object as a function of the parameters below."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Function to return a simulation for each Bloch vector\n",
+ "def getSim(pol, bloch_x, bloch_y, matchingDipoles=True):\n",
+ " symmetry = [0, 0, -1] if pol == \"Ez\" else [0, 0, 1]\n",
+ "\n",
+ " boundary_spec = td.BoundarySpec(\n",
+ " x=td.Boundary.bloch(bloch_x * size[0]),\n",
+ " y=td.Boundary.bloch(bloch_y * size[1]),\n",
+ " z=td.Boundary.pml(),\n",
+ " )\n",
+ "\n",
+ " bVector = np.array([bloch_x, bloch_y, 0])\n",
+ "\n",
+ " # Creating the sources\n",
+ " sources = [\n",
+ " td.PointDipole(\n",
+ " center=(posxSource[i], posySource[i], 0), polarization=pol, source_time=sourceTime[i]\n",
+ " )\n",
+ " for i in range(len(posxSource))\n",
+ " ]\n",
+ "\n",
+ " # Creating the matching dipoles\n",
+ " matching_dipoles = []\n",
+ " if matchingDipoles:\n",
+ " for i, sc in enumerate(sources):\n",
+ " # Coordinates of the matching dipole\n",
+ " px = sc.center[0] + 0.5\n",
+ " py = sc.center[1] + np.sqrt(3) / 2\n",
+ "\n",
+ " # Adjust the phase\n",
+ " phase = sc.source_time.phase\n",
+ " r_vec = np.array((px, py, 0)) - np.array(sc.center)\n",
+ " deltaPhase = 2 * np.pi * bVector.dot(r_vec)\n",
+ "\n",
+ " source_time = sc.source_time.updated_copy(phase=phase + deltaPhase)\n",
+ "\n",
+ " sp = sc.updated_copy(center=(px, py, 0), source_time=source_time)\n",
+ " matching_dipoles.append(sp)\n",
+ "\n",
+ " sim = td.Simulation(\n",
+ " size=size,\n",
+ " structures=[structure],\n",
+ " sources=sources + matching_dipoles,\n",
+ " monitors=monitors,\n",
+ " run_time=runTime,\n",
+ " boundary_spec=boundary_spec,\n",
+ " grid_spec=grid_spec,\n",
+ " symmetry=symmetry,\n",
+ " medium=td.Medium(),\n",
+ " shutoff=False,\n",
+ " )\n",
+ " return sim"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we can create a simulation object and inspect the permittivity to confirm that the periodicity is preserved."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sim = getSim(polarization, 0, 0)\n",
+ "\n",
+ "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5))\n",
+ "\n",
+ "# Left: epsilon\n",
+ "eps = sim.epsilon(td.Box(center=(0, 0, 0), size=(99, 99, 0)))\n",
+ "ax1.imshow(abs(eps).squeeze().T)\n",
+ "ax1.set_title(\"epsilon\")\n",
+ "\n",
+ "# Right: structure\n",
+ "sim.plot(z=0, ax=ax2)\n",
+ "ax2.set_title(\"structure (z=0)\")\n",
+ "\n",
+ "plt.tight_layout()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we can interpolate points around the K-points and run a [Batch](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.web.api.container.Batch.html) simulation to execute the simulations in parallel."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Creating K points\n",
+ "pointsPerZone = 10\n",
+ "\n",
+ "createPoints = lambda init, end: [\n",
+ " init + (end - init) * i / pointsPerZone for i in range(pointsPerZone)\n",
+ "]\n",
+ "\n",
+ "KX = []\n",
+ "KY = []\n",
+ "\n",
+ "kx1, ky1 = kPoints[0]\n",
+ "for k in kPoints[1:]:\n",
+ " kx2, ky2 = k\n",
+ " KX += createPoints(kx1, kx2)\n",
+ " KY += createPoints(ky1, ky2)\n",
+ " kx1, ky1 = kx2, ky2\n",
+ "\n",
+ "# Visualizing the K-points\n",
+ "\n",
+ "fig, ax = plt.subplots()\n",
+ "ax.plot(KX, KY, \"-o\")\n",
+ "\n",
+ "\n",
+ "sims = {}\n",
+ "for i in range(len(KX)):\n",
+ " for pol in [polarization]:\n",
+ " sims[f\"s{i}{pol}\"] = getSim(pol, KX[i], KY[i])\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
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+ "Output()"
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+ "
09:56:30 -03 Started working on Batch containing 30 tasks. \n",
+ "
![](\"./img/HexagonalSupercell.png\")