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

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Seyit Kagan el 20 de Dic. de 2022
Respondida: Muskan el 4 de Sept. de 2023
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);
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### Respuestas (1)

Muskan el 4 de Sept. de 2023
Hi Seyit,
I understand that you want to find modes occurring in a symmetrical dielectric plane waveguide.
You can use the built-in functions “besseljto 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
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