What command/s can I use to multiply matrices M_G and M_A via Transfer Matrix Method N times given N pairs?

lambda_0 = 0.980;                                                          % Cavity length of DBR mirror in micron
d_G = 0.06975562993;                                                       % Thickness of GaAs layer in micron
d_A = 0.08148984639;                                                       % Thickness of AlAs layer in micron
lambda = 0.9:0.01:1.1;                                                     % Wavelength range in micron
n_G = @(lambda) sqrt(10.906+(0.97501./(lambda.^2-(0.52886)^2))-...         % Index of refraction of GaAs as a function of wavelength
    0.002467.*lambda.^2)
n_A = @(lambda) sqrt(7.986+(0.97501./(lambda.^2-(0.19886)^2))-...          % Index of refraction of AlAs as a function of wavelength
    0.0059457.*lambda.^2)
M_G = @(lambda) [cos((2*pi*d_G.*n_G(lambda))./lambda)...                   % Characteristic Matrix of GaAs
    (-i./n_G(lambda)).*sin((2*pi*d_G.*n_G(lambda))./lambda);...
    -i.*n_G(lambda).*sin((2*pi*d_G.*n_G(lambda))./lambda)...
    cos((2*pi*d_G.*n_G(lambda))./lambda)];
M_A = @(lambda) [cos((2*pi*d_A.*n_A(lambda))./lambda)...                   % Characteristic Matrix of AlAs
    (-i./n_A(lambda)).*sin((2*pi*d_A.*n_A(lambda))./lambda);...
    -i.*n_A(lambda).*sin((2*pi*d_A.*n_A(lambda))./lambda)...
    cos((2*pi*d_A.*n_A(lambda))./lambda)];

[Jan]

N pairs of what?

M_G and M_A are not matrices, but function handles. It is rather confusing, that "lambda" is an external variable and the variable of the anonymous function also.

Are you sure that the code is correct? This looks strange:

[cos((2*pi*d_A.*n_A(lambda))./lambda)...  % I'd expect an operator coming here
(-i./n_A(lambda)).*sin((2*pi*d_A.*n_A(lambda))./lambda);...
-i.*n_A(lambda).*sin((2*pi*d_A.*n_A(lambda))./lambda)...  % and here also
cos((2*pi*d_A.*n_A(lambda))./lambda)];

[Craig Egan Allistair Tan]

N pairs of dielectric material, with matrices M_A and M_G being the characteristic matrix of each dielectric. How can I properly represent M_A and M_G in matrix forms? All of the matrix elements of both matrices have a dependence of lambda.

[cos((2*pi*d_A.*n_A(lambda))./lambda),... % Should I put a comma here?

(-i./n_A(lambda)).*sin((2*pi*d_A.*n_A(lambda))./lambda);...

-i.*n_A(lambda).*sin((2*pi*d_A.*n_A(lambda))./lambda),... % They're supposed to be matrix elements of a 2x2 matrix

cos((2*pi*d_A.*n_A(lambda))./lambda)];

[Jan]

I do not get it. While M_G and M_A can functions replying a 2x2 matrices, this cannot work, if you provide the argument lambda = 0.9:0.01:1.1 to them.

Seeing the failing code only is not enough to clarify, what you want to achieve.

[Craig Egan Allistair Tan]

The lambda variable is the dependent variable. Do matrices work with elements being in terms of a dependent variable?

[Jan]

Matrices are rectangular shapes containing numeric elements.

It is still not clear, what you want to achieve.

[Craig Egan Allistair Tan]

I plan to define M_A and M_G as 2x2 matrices that represent the characteristic matrix of AlAs and GaAs, respectively, multiply them N times for each AlAs/GaAs pair, applying the Transfer Matrix Method, and then from the resulting 2x2 matrix, obtain the reflectivity of the overall DBR structure.

[Jan]

@Craig Egan Allistair Tan: Okay. I do neither know, what AIAs, GaAs means, nor what "N" is, nor where do you want to apply which kind of Transfer Matrix, nor what reflectivity or DBR structure is.

All I know, is that you have defined 2 anonymous functions, which reply a [2 x 2] matrix, if you use a scalar as input and that your lambda is a vector instead.

I cannot help you, because the problem is not getiing clear to me.