fmm_balance.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 the power balance (check the energy conservation law) in case
% of the collinear diffraction by 1D gratings
% the returned value should be close to zero for pure dielectric structures
% with no losses
%% input:
% no: number of Fourier harmonics
% V_inc: incident field amplitude matrix of size (no, 2)
% V_dif: diffracted field amplitude matrix of size (no, 2)
%  first index of V_inc, V_dif indicates diffraction harmonics
%   (0-th order index is ind_0 = ceil(no/2))
%  second index of V_inc, V_dif, V_eff indicates whether the diffraction orders
%   are in the substrate (V(:,1)) or in the superstrate (V(:,2))
% kx0: incident plane wave wavevector x-projection (Bloch wavevector)
% kg: wavelength-to-period ratio (grating vector)
% eps1, eps2: substrate and superstrate permittivities
% pol: polarization (either "TE" or "TM")
%% output:
% if the incident field has propagating harmonics the function returns the
%  normalized difference between the incident and diffractied field total
%  power, otherwise (if the incident field is purely evanescent) it returns
%  the total power carried by propagating diffraction orders
%% implementation
function [b] = fmm_balance(no, V_inc, V_dif, kx0, kg, eps1, eps2, pol)
	[kz1, kz2] = fmm_kxz(no, kx0, 0, kg, eps1, eps2);
	kz1 = transpose(kz1);
	kz2 = transpose(kz2);

	if (strcmp(pol,'TM'))
		kz1 = kz1/eps1;
		kz2 = kz2/eps2;
	end
	P_inc = sum( abs(V_inc(:,1).^2).*real(kz1) + abs(V_inc(:,2).^2).*real(kz2) );
	P_dif = sum( abs(V_dif(:,1).^2).*real(kz1) + abs(V_dif(:,2).^2).*real(kz2) );

	if (abs(P_inc) > 1e-15)
		b = abs(P_dif/P_inc-1);
	else
		b = 0.5*P_dif;
	end
end
%
% END
%