Propogating a Wave with a change in media

Hello!

I am trying to create an animation of a normally incident gaussian pulse, and its reflection and transmission when it changes media. So far all I have done is created the pulse itself as an initial condition. I am struggling to find an answer for how to code the reflection and transmission of the pulse as it interacts with a change in media.

This is the code that I have so far:

%Wave Animation

%Original Wave: yinc=A cos(k1x−ωt)

%Reflected Wave yref=B cos(k1x+ωt)

%Transmitted Wave: ytrans=C cos(k2x−ωt)

clear all

close all

clc

%System Parameters

Eps0 = 8.854E-12;

Eps1 = 1E-10;

E0=1;

x0=0;

Sigma=0.5; %Needs value

%Frame

InitialX = linspace(-2,2, 100);

TravelX=linspace(2, 10, 200);

FullX=[InitialX, TravelX];

% X=linspace(0, 5, 500);

T=linspace(0, 10, 1000);

nInit=Eps0;

for x_Initial=1:length(InitialX)

EyI(x_Initial)=E0*exp(-(InitialX(x_Initial)-x0)^2/Sigma^2);

BzI(x_Initial)=nInit*EyI(x_Initial);

end

EyFiller=zeros(1,200);

EyInitial=[EyI,EyFiller];

%Change media

if InitialX > 1

n=(Eps0);

else

n=sqrt(Eps1);

end

% ETest=[InitialX; EyI]

% plot(InitialX, EyI)

plot(FullX, EyInitial)

xlim([0,10])