The Transfer Matrix Method

transfer-method.mat

% This code is to perform the transfer matrix method
% T{1},T{2},T{3}, have been already calculated. they are
% obviously 2 by-2 matrices. Now we want to obtain vector D{i} for each transfer matrix coefficients above.


T{1} = [0.9982 - 0.0616i, -0.0119 + 0.0121i;
        -0.0119 - 0.0121i, 0.9982 + 0.0616i];

T{2} = [0.9831 - 0.1845i, -0.0157 - 0.0149i;
        -0.0157 + 0.0149i, 0.9831 + 0.1845i];

T{3} = [0.9527 - 0.3040i, -0.0074 + 0.0080i;
        -0.0074 - 0.0080i, 0.9527 + 0.3040i];

%Multiply T matrices 
M{1} = T{1};
M{2} = T{1} * T{2};
M{3} = T{1} * T{2} * T{3};

D = cell(1, 4); % Initialize cell array to store D{i}

for i = 1:3
    d1(i) = 1;
    d2(i) = M{i}(2, 1) / M{i}(1, 1); % r;
    d1(i+1) = 1 / M{i}(1, 1); % t;
    d2(i+1) = 0;
    D{i+1} = [d1(i+1); d2(i+1)];
end

D{4} = zeros(2, 1); % Initialize D{4} as zero vector

for i = 3:-1:1
    D{i} = M{i} * D{i+1};
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Check if D{1} is equal to TMC{1} * D{2}
is_equal1 = isequal(D{1}, M{1} * D{2});
disp(is_equal1);
% Check if D{2} is equal to TMC{2} * D{3}
is_equal2 = isequal(D{2}, M{2} * D{3});
disp(is_equal2);
% Check if D{3} is equal to TMC{3} * D{4}
is_equal3 = isequal(D{3}, M{3} * D{4});
disp(is_equal3);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%