fmm_kxz.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
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with GratingFMM. If not, see <https://www.gnu.org/licenses/>.
%}
%% description:
% calculate grating vectors for 1D grating (periodicity in x direction)
% and plane wave propagation constants in homogeneous media below and 
% above the grating (substrate and superstrate)
%% input:
% no: number of Fourier harmonics
% kx0, ky0: wavevector projections of an incident plane wave
% kg: wavelength-to-period ratio
% eps1: permittivity of a medium below the grating (substrate)
% eps2: permittivity of a medium above the grating (superstrate)
%% output:
% kz1: row of propagation constants in the substrate
% kz2: row of propagation constants in the superstrate
% kx: row of grating vectors in x-direction
% kxy: row of grating vectors in xy plane
%% implementation:
function [kz1, kz2, kx, kxy] = fmm_kxz(no, kx0, ky0, kg, eps1, eps2)
	ind = linspace(1,no,no);
	kx = kx0 + kg*(ind - ceil(no/2));
	kxy = kx.^2 + ky0^2;

	kz1 = sqrt(eps1 - kxy);
	kz2 = sqrt(eps2 - kxy);

	if sum(abs(kz1) < 1e-12) > 0 || sum(abs(kz2) < 1e-12) > 0
		kz1 = sqrt(eps1 - kxy + 1e-10);
		kz2 = sqrt(eps2 - kxy + 1e-10);
	end

	ind = angle(kz1) < -1e-12;
	kz1(ind) = -kz1(ind);
	ind = angle(kz2) < -1e-12;
	kz2(ind) = -kz2(ind);

	kxy = sqrt(kxy);
end
%
% end of fmm_kxz
%