% Program author: Susan C. Hagness
% Department of Electrical and Computer Engineering % University of Wisconsin-Madison % 1415 Engineering Drive % Madison, WI 53706-1691 % 608-265-5739
% hagness@engr.wisc.edu %
% Date of this version: February 2000 %
% This MATLAB M-file implements the finite-difference time-domain % solution of Maxwell's curl equations over a three-dimensional % Cartesian space lattice comprised of uniform cubic grid cells. %
% To illustrate the algorithm, an air-filled rectangular cavity % resonator is modeled. The length, width, and height of the % cavity are 10.0 cm (x-direction), 4.8 cm (y-direction), and % 2.0 cm (z-direction), respectively. % conditions:
% ex(i,j,k)=0 on the j=1, j=jb, k=1, and k=kb planes % ey(i,j,k)=0 on the i=1, i=ib, k=1, and k=kb planes % ez(i,j,k)=0 on the i=1, i=ib, j=1, and j=jb planes
% These PEC boundaries form the outer lossless walls of the cavity. %
% The cavity is excited by an additive current source oriented % along the z-direction. The source waveform is a differentiated % Gaussian pulse given by
% J(t)=-J0*(t-t0)*exp(-(t-t0)^2/tau^2),
% where tau=50 ps. The FWHM spectral bandwidth of this zero-dc- % content pulse is approximately 7 GHz. The grid resolution % (dx = 2 mm) was chosen to provide at least 10 samples per % wavelength up through 15 GHz. %
% To execute this M-file, type \% This M-file displays the FDTD-computed Ez fields at every other % time step, and records those frames in a movie matrix, M, which % is played at the end of the simulation using the \%
%*********************************************************************** clear
%*********************************************************************** % Fundamental constants
%***********************************************************************
cc=2.99792458e8; %speed of light in free space muz=4.0*pi*1.0e-7; %permeability of free space epsz=1.0/(cc*cc*muz); %permittivity of free space
%*********************************************************************** % Grid parameters
%***********************************************************************
ie=50; %number of grid cells in x-direction je=24; %number of grid cells in y-direction ke=10; %number of grid cells in z-direction ib=ie+1; jb=je+1; kb=ke+1;
is=26; %location of z-directed current source js=13; %location of z-directed current source kobs=5;
dx=0.002; %space increment of cubic lattice dt=dx/(2.0*cc); %time step
nmax=500; %total number of time steps
%*********************************************************************** % Differentiated Gaussian pulse excitation
%***********************************************************************
rtau=50.0e-12; tau=rtau/dt; ndelay=3*tau; srcconst=-dt*3.0e+11;
%*********************************************************************** % Material parameters
%*********************************************************************** eps=1.0; sig=0.0;
%*********************************************************************** % Updating coefficients
%***********************************************************************
ca=(1.0-(dt*sig)/(2.0*epsz*eps))/(1.0+(dt*sig)/(2.0*epsz*eps)); cb=(dt/epsz/eps/dx)/(1.0+(dt*sig)/(2.0*epsz*eps)); da=1.0; db=dt/muz/dx;
%*********************************************************************** % Field arrays
%***********************************************************************
ex=zeros(ie,jb,kb); ey=zeros(ib,je,kb); ez=zeros(ib,jb,ke); hx=zeros(ib,je,ke); hy=zeros(ie,jb,ke); hz=zeros(ie,je,kb);
%*********************************************************************** % Movie initialization
%***********************************************************************
tview(:,:)=ez(:,:,kobs); sview(:,:)=ez(:,js,:);
subplot('position',[0.15 0.45 0.7 0.45]),pcolor(tview'); shading flat; caxis([-1.0 1.0]); colorbar; axis image;
title(['Ez(i,j,k=5), time step = 0']); xlabel('i coordinate'); ylabel('j coordinate');
subplot('position',[0.15 0.10 0.7 0.25]),pcolor(sview'); shading flat; caxis([-1.0 1.0]); colorbar; axis image;
title(['Ez(i,j=13,k), time step = 0']); xlabel('i coordinate');