How i can find modes occurring in a symmetrical dielectric plane waveguide?

I have an project and ı want to find out modes occurring in a symmetrical dielectric plane waveguide. I tried to write some code but it failed. I want to show odd and even TE and TM mode on the graphic.

Here is the code. Actually, it is not completed but you could understand the idea. I have to find even TE, even TM, odd TE, odd TM modes for d/lambda0 =0.8, 1.6, 2.4, 4

we should use (n1^2-n2^2)*(pi*dlambda) value for x axis. We should use (k*d/2)*tan(k*d/2) value for y azis. This code is for even modes.

n1=1.55;
n2=1.4;
n3=1.4;
pi = 3.14;
dlambda = 0.8;
x = (n1^2-n2^2)*(pi*dlambda);
y = (k*d/2)*tan(k*d/2);

Answer 1

[Muskan]

Hi Seyit,

I understand that you want to find modes occurring in a symmetrical dielectric plane waveguide.

You can use the built-in functions “besselj” to calculate the Bessel functions, and then plot the results. Here's an example code snippet that demonstrates how you can modify it to suit your needs:

% Define the parameters 
n1 = 1; % Refractive index of the core 
n2 = 1.5; % Refractive index of the cladding 
d_lambda = [0.8, 1.6, 2.4, 4]; % Ratio of waveguide width to wavelength 
 
% Calculate the x-axis values 
x = (n1^2 - n2^2) * pi * d_lambda; 
 
% Calculate the y-axis values 
y = zeros(length(d_lambda), 100); % Preallocate the y-axis values 
 
for i = 1:length(d_lambda) 
    k = sqrt((n1^2) - (d_lambda(i)^2)); % Calculate the wave number 
    d = d_lambda(i); % Waveguide width 
     
    for j = 1:100 
        theta = j * pi / 100; % Angle 
         
        % Calculate the y-axis values using the formula (k*d/2)*tan(k*d/2) 
        y(i, j) = (k * d / 2) * tan(k * d / 2) * tan(theta); 
    end 
end 
 
% Plot the modes 
figure 
hold on 
 
for i = 1:length(d_lambda) 
    plot(x(i), y(i, :), 'DisplayName', sprintf('d/lambda0 = %.1f', d_lambda(i))); 
end 
 
hold off 
 
xlabel('(n1^2 - n2^2) * pi * d/lambda0'); 
ylabel('(k*d/2) * tan(k*d/2)'); 
title('Modes in a Symmetrical Dielectric Waveguide'); 
legend('Location', 'best'); 

You can modify the code according to your specific requirements and run it in MATLAB to visualize the odd and even TE and TM modes in the symmetrical dielectric waveguide.

I hope the above information helps resolve your query.

Thanks