{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Waves in the Steady State\n", "#### Solving the Helmholtz Equation\n", "For a wave which varies sinusoidally in time, the wave equation with a source term reduces to\n", "$$\\nabla^2 E + \\frac{k^2}{n^2} E = S,$$\n", "where $E$ and $S$ are vector fields representing the amplitude of the wave and the source, respectively. In the context of electromagnetic waves in the steady state, $E$ is the electric field, $k$ is the wavenumber and $n$ is the refractive index. This equation can be solved numerically on a grid by casting it into a matrix form. This is possible because the Helmholtz equation is linear.\n", "\n", "In 2D, this equation can be written as\n", "$$\\frac{E_{i+1,j}+E_{i-1,j}-2E_{ij}}{\\Delta x^2} + \\frac{E_{i,j+1}+E_{i,j-1}-2E_{ij}}{\\Delta y^2} + \\frac{k^2}{n_{ij}^2} E_{ij} = S_{ij},$$\n", "where $\\Delta x$ and $\\Delta y$ are the lengths and widths of the grid elements. In matrix form:\n", "$$M_{ijkl} E_{kl} = S_{ij},$$\n", "$$M_{ijkl} = \\frac{\\delta_{i+1,k}\\delta_{jl} +\\delta_{i-1,k}\\,\\delta_{jl} - 2\\delta_{ik}\\delta_{jl}}{\\Delta x^2} + \\frac{\\delta_{ik}\\delta_{j+1,l} + \\delta_{ik}\\delta_{j-1,l} - 2\\delta_{ik}\\delta_{jl}}{\\Delta y^2} + \\frac{k^2}{n_{ij}^2} \\delta_{ik}\\delta_{jl}$$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#NAME: Waves in the Steady State\n", "#DESCRIPTION: Solving the Helmholtz equation to find the electric field strength in the steady state.\n", "\n", "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.linalg as la\n", "\n", "#kronecker delta function\n", "def kd(i,j):\n", " d = 0.0\n", " if i == j:\n", " d = 1.0\n", " return d\n", "\n", "#the array is NxN\n", "N = 101\n", "#grid element length & width/m\n", "D = 0.2\n", "#wavelength of radiation/m\n", "wavelength = 3.2\n", "#wavenumber\n", "wavenumber = 2*np.pi/wavelength\n", "\n", "#refractive index array\n", "n = np.ones((N,N), dtype = np.complex128)\n", "for i in range(N):\n", " for j in range(N):\n", " if np.sqrt((D*(i-N/2))**2 + (D*(j-N/2))**2) > 8.0:\n", " n[i,j] = 2.2 - 0.1j" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Indexing\n", "The above equation can be recast as \n", "$$\\widetilde{M}_{pq} \\widetilde{E}_{q} = \\widetilde{S}_{p},$$\n", "so that it can be solved simply by finding the inverse of the sparse matrix $\\widetilde{M}$. The indexing scheme used to convert the $N \\times N \\times N \\times N$ matrix $M$ to the $N^2 \\times N^2$ matrix $\\widetilde{M}$ is\n", "$$\\widetilde{M}_{Ni+j, Nk+l} = M_{ijkl},$$\n", "$$\\widetilde{E}_{Nk+l} = E_{kl},$$\n", "but this is by no means unique! Careful investigation of $\\widetilde{M}$ shows that it is a band matrix with $N$ upper and $N$ lower diagonals. The `scipy` library provides a function `scipy.linalg.solve_banded()` which can then be used to solve for the electric field. This function requires all of the non-zero elements of $\\widetilde{M}$ to be stored in a $(2N+1) \\times N^2$ matrix $B$ indexed as\n", "$$B_{N+p-q,q} = \\widetilde{M}_{pq}.$$" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "B = np.zeros((2*N+1,N*N), dtype = np.complex128)\n", "for p in range(N*N):\n", " for q in range(p-N, p+N+1):\n", " if N*N > q and 0 <= q:\n", " i,j,k,l = int((p-(p%N))/N), int(p%N), int((q-(q%N))/N), int(q%N) #indices of the NxNxNxN array\n", " term1 = (1.0/D**2)*(kd(i+1,k)*kd(j,l)+kd(i-1,k)*kd(j,l)-2*kd(i,k)*kd(j,l))\n", " term2 = (1.0/D**2)*(kd(i,k)*kd(j+1,l)+kd(i,k)*kd(j-1,l)-2*kd(i,k)*kd(j,l))\n", " term3 = kd(i,k)*kd(j,l)*(wavenumber/n[i,j])**2\n", " B[N+p-q,q] = term1 + term2 + term3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculating $B$ takes awhile, but it's only a property of the 'room'. Once $B$ is known, the electric field for a range of sources can be found quickly!" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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fdmgNetTy04WZAKg1Pg9x3ZRBf6ynqzrBp57Wturzta34M+wqHEYCh8ABXzr0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\n9M5jCia1L1IX5DXYauHYq0UryWITj86gGT4Nhrymz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#create flattened source matrix \n", "Sf = np.zeros((N*N), dtype = np.complex128)\n", "for i in range(N):\n", " for j in range(N):\n", " Sf[N*i+j] = kd(int(N/4),i)*kd(int(N/2),j)\n", " \n", "#find flattened E matrix\n", "Ef = la.solve_banded((N,N),B,Sf)\n", "\n", "#unflatten E matrix\n", "E = np.zeros((N,N), dtype = np.complex128)\n", "S = np.zeros((N,N), dtype = np.complex128)\n", "for i in range(N):\n", " for j in range(N):\n", " E[i,j] = Ef[N*i+j]\n", " S[i,j] = Sf[N*i+j]\n", "\n", "#create x and y values for plot\n", "x = np.linspace(0.0, D*N, N)\n", "y = np.linspace(0.0, D*N, N)\n", "\n", "#generate plot\n", "plt.figure(figsize = (10,8))\n", "plt.pcolor(x,y,np.absolute(E), cmap = \"inferno\")#, extent = (x.min(), x.max(), y.min(), y.max()), interpolation = 'none')\n", "plt.colorbar()\n", "#add black contours for refractive index\n", "plt.contour(x,y, np.absolute(n), colors = 'k')\n", "#add white contours for the source\n", "plt.contour(x,y,np.absolute(S), colors = 'w')\n", "plt.xlabel(\"x/m\")\n", "plt.ylabel(\"y/m\")\n", "plt.title(\"Steady State Electric Field Strength\")\n", "plt.show()" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }