FMM/fmm_calc_T.m

%{
Copyright © 2020 Alexey A. Shcherbakov. All rights reserved.

This file is part of GratingFMM.

GratingFMM is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 2 of the License, or
(at your option) any later version.

GratingFMM is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
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GNU General Public License for more details.

You should have received a copy of the GNU General Public License
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%}
%% description:
% T-matrix of an interface between a photonic crystal and a homogeneous medium
% the case of the collinear diffraction on 1D gratings
%% input:
% no: number of Fourier harmonics
% EV: matrix of the electric field eigenvectors for the photonic crystal
% HV: matrix of the magnetic field eigenvectors for the photonic crystal
% kz: row of plane wave propagation constants in the homogeneous medium
% eps: permittivity the homogeneous medium
% pol: polarization
%% output:
% T: T-matrix of size 4*no by 4*no
%% implementation:
function [T] = fmm_calc_T(no, EV, HV, kz, eps, pol)
    T = zeros(2*no,2*no);
		ib1 = [1:no];
		ib2 = [no+1:2*no];
    if strcmp(pol,'TE')
			ikz = transpose(0.5./kz);
			T(ib1,ib1) = HV.*ikz;
			T(ib2,ib1) = 0.5*EV - T(ib1,ib1);
			T(ib1,ib1) = T(ib1,ib1) + 0.5*EV;
			T(ib1,ib2) = T(ib2,ib1);
			T(ib2,ib2) = T(ib1,ib1);
    elseif strcmp(pol,'TM')
			eikz = transpose((0.5*eps)./kz);
			T(ib1,ib1) = EV.*eikz;
			T(ib2,ib1) = 0.5*HV - T(ib1,ib1);
			T(ib1,ib1) = T(ib1,ib1) + 0.5*HV;
			T(ib1,ib2) = -T(ib2,ib1);
			T(ib2,ib2) = -T(ib1,ib1);
    end
end