{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# A 90° Bend" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll start a new simulation where we look at the fields propagating through a waveguide bend, and we'll do a couple of other things differently as well. \n", "\n", "As usual, the first thing to do is to load the Meep library:" ] }, { "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", "from matplotlib import pyplot as plt\n", "import numpy as np\n", "from IPython.display import Video\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then let's set up the bent waveguide in a slightly larger cell:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "cell = mp.Vector3(16,16,0)\n", "geometry = [mp.Block(mp.Vector3(12,1,mp.inf),\n", " center=mp.Vector3(-2.5,-3.5),\n", " material=mp.Medium(epsilon=12)),\n", " mp.Block(mp.Vector3(1,12,mp.inf),\n", " center=mp.Vector3(3.5,2),\n", " material=mp.Medium(epsilon=12))]\n", "pml_layers = [mp.PML(1.0)]\n", "resolution = 10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we have two blocks, both off-center to produce the bent waveguide structure pictured below. As illustrated in the figure, the origin (0,0) of the coordinate system is at the center of the cell, with positive $y$ being downwards, and thus the block of size 12$\\times$1 is centered at (-2,-3.5). Also shown in green is the source plane at $x=−7$ which is shifted to $y=−3.5$ so that it is still inside the waveguide." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are a couple of items to note. First, a point source does not couple very efficiently to the waveguide mode, so we'll expand this into a line source, centered at (-7,-3.5), with the same width as the waveguide by adding a size property to the source. This is shown in green in the figure above. An eigenmode source can also be used which is described in Tutorial/Optical Forces. Second, instead of turning the source on suddenly at t=0 which excites many other frequencies because of the discontinuity, we will ramp it on slowly. Meep uses a hyperbolic tangent (tanh) turn-on function over a time proportional to the width of 20 time units which is a little over three periods. Finally, just for variety, we'll specify the vacuum wavelength instead of the frequency; again, we'll use a wavelength such that the waveguide is half a wavelength wide." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "sources = [mp.Source(mp.ContinuousSource(wavelength=2*(11**0.5), width=20),\n", " component=mp.Ez,\n", " center=mp.Vector3(-7,-3.5),\n", " size=mp.Vector3(0,1))]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we'll set up and visualize the simulation domain." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "sim = mp.Simulation(cell_size=cell,\n", " boundary_layers=pml_layers,\n", " geometry=geometry,\n", " sources=sources,\n", " resolution=resolution)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-----------\n", "Initializing structure...\n", " block, center = (-2.5,-3.5,0)\n", " size (12,1,1e+20)\n", " axes (1,0,0), (0,1,0), (0,0,1)\n", " block, center = (3.5,2,0)\n", " size (1,12,1e+20)\n", " axes (1,0,0), (0,1,0), (0,0,1)\n" ] }, { "data": { "image/png": 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\n", 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