Dispersion plot of frequency vs Bloch wave function, K

The problem is to plot w(omega) vs K(capital k) using the highlighted equation when beta is equal to zero. I need help with this, thank you in advance.

clear

clc

echo off

n2=2.89; %refractive index in length a

n1=3.38; %refractive index in length b

c=1e8; %volecity of light m/s

a=0.5*1e-6; %length of a in m

b=0.5*1e-6; %length of b in m

TM=(n1/n2)^2;

Cap_lamda=a+b; %period

w=0.0001:0.01:3*pi;

beta=0.0001:0.01:6*pi;

for i=1:length(w)

for j=1:length(beta)

beta=0;

k1(i,j)=sqrt((w(i)*n1/Cap_lamda).^2-(beta(j)/Cap_lamda)^2);

k2(i,j)=sqrt((w(i)*n2/Cap_lamda).^2-(beta(j)/Cap_lamda)^2);

AplusD(i,j)=cos(k2(i,j)*b)*cos(k1(i,j)*a)*2-sin(k2(i,j)*b)*sin(k1(i,j)*a)*(TM^-1*k1(i,j)/k2(i,j)+TM*k2(i,j)/k1(i,j));

K(w,beta)=(1/(Cap_lamda)^2)*(acos(AplusD(i,j)/2));

exp(-1i*K*Cap_lamda)=(1/2)*(AplusD(i,j))+[1 -1]*(((1/2*(AplusD(i,j)))^2)-1)^0.5;

%%M(i,j)=1/2*(AplusD(i,j))+[1 -1]*(((1/2*(AplusB(i,j)))^2)-1)^0.5;

%%M=exp(-1i*K*Cap_lamda);

end;

end;

Answer 1

[Gokul Nath S J]

Hi Emma,

The code has an error on the following line. ω(omega) is an array while betaβ is zero.

K(w,beta)=(1/(Cap_lamda)^2)*(acos(AplusD(i,j)/2)); 

Unrecognized function or variable 'Cap_lamda'.

Matlab does not support zero based indexing. Since ω is an array, you must also make sure that you are assigning an array having the same dimension as that of K.

Thanks

Gokul Nath S J