load('s_parameters.mat'); % your file should contain freq, S11, S21

d = 1e-3; % thickness of the metamaterial in meters

S11 = S11(:); S21 = S21(:); freq = freq(:);

omega = 2 * pi * freq;

c = 3e8; % speed of light

% Calculate the reflection (R) and transmission (T)

R = S11;

T = S21;

% Compute intermediate parameter V1 and V2

V1 = (R.^2 - T.^2 + 1)./(2*R);

V2 = sqrt(V1.^2 - 1);

% Determine the correct branch of the logarithm

X1 = V1 + V2;

X2 = V1 - V2;

% Choose branch with |X| < 1 to ensure physical solution

X = X1;

X(abs(X1) > 1) = X2(abs(X1) > 1);

% Calculate propagation constant (n_eff) and impedance (z_eff)

e_negikd = T ./ (1 - R .* X); % e^(-i*n*k*d)

n_eff = -1i ./ (omega * d) .* log(e_negikd); % effective refractive index

% Calculate impedance

z_eff = sqrt( ((1 + R).^2 - T.^2) ./ ((1 - R).^2 - T.^2) );

% Effective permittivity and permeability

epsilon_eff = n_eff ./ z_eff;

mu_eff = n_eff .* z_eff;