{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Modes of a Ring Resonator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As described in Introduction, another common task for FDTD simulation is to find the resonant modes — frequencies and decay rates — of some cavity structure. You might want to read that again to recall the basic simulation strategy. We will show how this works for a ring resonator, which is simply a waveguide bent into a circle. This script can be also found in examples/ring.py; the notebook is examples/ring.ipynb. In fact, since this structure has cylindrical symmetry, we can simulate it much more efficiently by using cylindrical coordinates, but for illustration here we'll just use an ordinary 2d simulation.\n", "\n", "As before, we'll define some parameters to describe the geometry, so that we can easily change the structure:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Using MPI version 3.1, 1 processes\n" ] } ], "source": [ "import meep as mp\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import numpy as np\n", "from IPython.display import Video\n", "\n", "n = 3.4 # index of waveguide\n", "w = 1 # width of waveguide\n", "r = 1 # inner radius of ring\n", "pad = 4 # padding between waveguide and edge of PML\n", "dpml = 2 # thickness of PML\n", "sxy = 2*(r+w+pad+dpml) # cell size" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How do we make a circular waveguide? So far, we've only seen Block objects, but Meep also lets you specify cylinders, spheres, ellipsoids, and cones, as well as user-specified dielectric functions. In this case, we'll use two Cylinder objects, one inside the other:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "c1 = mp.Cylinder(radius=r+w, material=mp.Medium(index=n))\n", "c2 = mp.Cylinder(radius=r)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Later objects in the geometry object take precedence over or rather lie \"on top of\" earlier objects, so the second air ($\\epsilon$=1) cylinder cuts a circular hole out of the larger cylinder, leaving a ring of width w.\n", "\n", "We don't know the frequency of the mode(s) ahead of time, so we'll just hit the structure with a broad Gaussian pulse to excite all of the Ez-polarized modes in a chosen bandwidth:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "fcen = 0.15 # pulse center frequency\n", "df = 0.1 # pulse frequency width\n", "src = mp.Source(mp.GaussianSource(fcen, fwidth=df), mp.Ez, mp.Vector3(r+0.1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's formulate the simulation object and visualize the simulation domain." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-----------\n", "Initializing structure...\n", " cylinder, center = (0,0,0)\n", " radius 2, height 1e+20, axis (0, 0, 1)\n", " cylinder, center = (0,0,0)\n", " radius 1, height 1e+20, axis (0, 0, 1)\n" ] }, { "data": { "image/png": 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\n", 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