%***********************************************************************
%?????3-D?FDTD?code?with?PEC?boundaries
%***********************************************************************
%
%?????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.
%
%?????The?computational?domain?is?truncated?using?PEC?boundary?
%?????conditions:
%??????????ex（ijk）=0?on?the?j=1?j=jb?k=1?and?k=kb?planes
%??????????ey（ijk）=0?on?the?i=1?i=ib?k=1?and?k=kb?planes
%??????????ez（ijk）=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?“fdtd3D“?at?the?MATLAB?prompt.
%?????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?“movie“?command.
%
%***********************************************************************

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?