How to multiply matrices randomly?

I need a matlab code for positional-random matrix multiplication (choose M1 or M2 randomly)

frequency = 100 to 200 THz (i.e 100e12 to 200e12 Hz)

M1=[ cos(phi_1), sin(phi_1); sin(phi_1), cos(phi_1) ] where phi_1=d1*n1*frequency, d1= 258 nm and n1=1.45

M2=[ cos(phi_2), sin(phi_2); sin(phi_2), cos(phi_2) ] where phi_2=d2*n2*frequency, d2= 163 nm and n2=2.3

M=M1M2M1M1M2M1M2M1M2M2........ (random multiplication) (total matrix) (200 micro meters length i.e approximately 500 layers)

I need a plot of transmission vs frequency

T=1/M(1,1) (transmission vs frequency)

And I need a plot of average transmission vs total length (200 micro meters)

Mean_T=avg(T) (average transmission vs total length)

Answer 1

[Hassaan]

% Parameters
d1 = 258e-9; % meters
n1 = 1.45;
d2 = 163e-9; % meters
n2 = 2.3;
totalLength = 200e-6; % meters
layerCount = 500; % Approximate layers for 200 micrometers
frequencyRange = 100e12:1e12:200e12; % 100 to 200 THz, step by 1 THz for smooth plot

% Preallocate transmission array
transmission = zeros(length(frequencyRange), 1);

% Loop over each frequency
for i = 1:length(frequencyRange)
    frequency = frequencyRange(i);
    
    % Initialize total matrix as identity
    M_total = eye(2);
    
    % Generate random sequence of M1 and M2 multiplications
    for j = 1:layerCount
        if rand > 0.5
            phi_1 = d1 * n1 * frequency;
            M = [cos(phi_1), sin(phi_1); sin(phi_1), -cos(phi_1)];
        else
            phi_2 = d2 * n2 * frequency;
            M = [cos(phi_2), sin(phi_2); sin(phi_2), -cos(phi_2)];
        end
        M_total = M_total * M;
    end
    
    % Calculate transmission
    T = 1 / M_total(1,1);
    transmission(i) = T;
end

% Plot Transmission vs Frequency
figure;
plot(frequencyRange * 1e-12, abs(transmission)); % Convert frequency to THz for plotting
xlabel('Frequency (THz)');
ylabel('Transmission');
title('Transmission vs Frequency');

% Plot Average Transmission vs Total Length
% Since total length is constant in this scenario, we show how to calculate the average
mean_T = mean(abs(transmission));
figure;
plot(totalLength * 1e6, mean_T, 'ro'); % Convert meters to micrometers for plotting
xlabel('Total Length (micrometers)');
ylabel('Average Transmission');
title('Average Transmission vs Total Length');
ylim([0, max(abs(transmission)) + 0.1]); % Adjust ylim to make the single point more visible

% Note: The calculation of average transmission vs total length doesn't vary with length in this script,
% as we've kept the length constant at 200 micrometers. This plot will just illustrate the average transmission for the given length.

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[GULZAR]

It's working well.

[GULZAR]

I need the plot of average transmission versus sample length (i.e 1 micro meter to 200 micro meters range)