Dielectric slab waveguide modes

Hi,

I am new to waveguide and I want to plot the mode profiles of slab waveguide as shown in this figure http://wwwhome.math.utwente.nl/~hammer/Metric/Fig/tefEy00L.gif. Can some one please help me in this manner. I have made a code but it was not working. Code is given below. Thanks in advance.

n1c=1.77;

n2s=1.45;

n3cd=1.0;

d=2.0*10^-6;

lambda=1.00*10^-6;

c=3*10^8;

f=c/lambda;

omega=2*pi*f;

k0=omega/c;

neff=n2s:0.00001:n1c;

beta=k0.*neff;

r=sqrt((beta.^2)-(k0^2*n3cd^2));

q=sqrt(((k0^2)*n1c^2)-(beta.^2));

p=sqrt((beta.^2)-(k0^2*n2s^2));

    x=-5*10^-6:2.0*10^-6:4*d;

 Ey=zeros(length(x),length(r));

   for i=1:length(x)
    if (x(i)<0)
        Ey(i,:)=exp(r*x(i));   
%     Ef1=Ey;

    elseif (0<=x(i) )&& (x(i)<=2*d)
        Ey(i,:)=cos(q*x(i))+sin(q*x(i));   
%        Ef2=Ey;

    else 
        Ey(i,:)=(cos(2*d*q)+sin(2*d*q)).*exp(-p*(x(i)-(2*d)));
%        Ef3=Ey;
    end
   end
% Ef=[Ef1 Ef2 Ef3];
mesh (abs(Ey));

Answer 1

[Elad]

I think you first need to solve the equations and find the propogation constant \beta for the modes and than plot the fields with constant p, q and h.

[Rizwan]

I think beta will be calculated according to Neff which is varying in between n1c and n2s. If you have any idea then please help me.

[Elad]

The image you attached seems like a field profile of a single mode, (single beta) See if this helps: http://www.mathworks.com/matlabcentral/fileexchange/12734-waveguide-mode-solver