%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This Matlab script propagates a pulse down a parallel
% plate metallic waveguide
%
% It requires the Matlab script called MakeQTMovie
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

c=3e8;  % speed of light
m=1;    % mode number
d=1;    % waveguide thickness in m
%the close d is to the cutoff (d=pi c/w) the larger the difference in speeds
w=1e9;  % angular frequency

B=sqrt((w/c)^2-(m*pi/d)^2);             %the propagation constant
Bp=w/(c^2*sqrt((w/c)^2-(m*pi/d)^2));    % the derivative of the propagation constant

vp=(B/w)^(-1)   %the pahse velocity
vg=(Bp)^(-1)    % the group velocity

W=3e-15;        %the width of the pulse
z=linspace(0,100,501);  % the total length of the waveguide

tt=linspace(2e-7,2.3e-7,51);    % the time steps

MakeQTMovie start 'pulse.mov'
clf
for lp_t=1:length(tt)
    t=tt(lp_t);
    A=exp(-(t-Bp*z).^2/W);
    P=cos(w*t-B*z);
    I=A.*P;
    
%plot the 
%   (1) total pulse
%   (2) the pulse envelope
%   (3) the carrier
    subplot(3,1,1) 
    plot(z,I)
    subplot(3,1,2)
    plot(z,A)
    subplot(3,1,3)
    plot(z,P)
    MakeQTMovie addframe  
end
MakeQTMovie finish