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+%{
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+Copyright © 2020 Alexey A. Shcherbakov. All rights reserved.
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+
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+This file is part of GratingFMM.
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+
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+GratingFMM is free software: you can redistribute it and/or modify
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+it under the terms of the GNU General Public License as published by
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+the Free Software Foundation, either version 2 of the License, or
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+(at your option) any later version.
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+
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+GratingFMM is distributed in the hope that it will be useful,
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+but WITHOUT ANY WARRANTY; without even the implied warranty of
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+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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+GNU General Public License for more details.
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+
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+You should have received a copy of the GNU General Public License
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+along with GratingFMM. If not, see <https://www.gnu.org/licenses/>.
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+%}
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+%% demonstration script for the non-collinear 1D grating Fourier Modal Method calculations
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+clc;
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+format long;
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+%% initialization
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+wl = 1; % wavelength in micrometers
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+wv = 2*pi/wl; % wavevector
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+ % grating parameters
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+gp = 1.5; % grating period
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+gh = 0.5; % grating depth
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+ % dimensionless parameters
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+kg = wl/gp;
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+kh = wv*gh;
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+ % permittivities
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+eps_sub = 1.5^2; % substrate permittivity
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+eps_gr = 3.17^2; % grating permittivity
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+eps_sup = 1; % superstrate permittivity
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+ % method parameters
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+no = 15; % number of Fourier modes
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+ind0 = ceil(no/2); % index of the zero harmonic (0th order diffraction)
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+ % incidence
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+theta = 10; % angle of incidence (angle between the direction of incidence
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+ % and the vertical axis being perpendicular to the grating plane)
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+phi = 0; % turn angle in the grating plane,
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+ % phi = 0 corresponds to the case of collinear diffraction
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+ % incidence wavevector projections:
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+kx0 = sin(theta*pi/180)*cos(phi*pi/180);
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+ky0 = sin(theta*pi/180)*sin(phi*pi/180);
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+V_inc = zeros(2*no,2); % matrix of incident field amplitudes
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+ % first index indicates different Fourier harmonics, first (no) correspond
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+ % to the TE polarization; second (no) correspond to the TM polarization
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+ % second index indicates wether the amplitudes are in the substrate (1) in the superstrate (2)
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+V_inc(1*no+ind0,2) = 1; % "TM" polarized plane wave (0-th harmonic) incoming from the superstrate
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+
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+%% scattering matrix calculation
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+ % calculate Fourier image matrix of the dielectric permittivity function
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+ % for a lamellar grating with filling factor 0.4
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+FM = calc_emn_lam(no,0.4,eps_gr,eps_sup);
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+ % scattering matrix of the grating
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+SM = fmmnc(no,kx0,ky0,kg,kh,eps_sub,eps_sup,FM);
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+
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+%% diffraction of a plane wave example
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+V_sca = zeros(2*no,2); % allocate a vector of diffracted field amplitudes
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+ % apply the calculated scattering matrix to the incident vector:
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+V_sca(:,1) = SM(:,:,1,1)*V_inc(:,1) + SM(:,:,1,2)*V_inc(:,2); % diffraction to the substrate
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+V_sca(:,2) = SM(:,:,2,1)*V_inc(:,1) + SM(:,:,2,2)*V_inc(:,2); % diffraction to the superstrate
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+ % check the power conservation
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+b = fmmnc_balance(no,V_inc,V_sca,kx0,ky0,kg,eps_sub,eps_sup);
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+disp(b); % precicision of the power conservation
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+ % calculate the vector of diffraction efficiencies:
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+V_eff = fmmnc_efficiency(no,V_inc,V_sca,kx0,ky0,kg,eps_sub,eps_sup);
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+disp(V_eff(0*no+ind0,1)); % zero order power transmission to TE
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+disp(V_eff(0*no+ind0,2)); % zero order power reflection to TE
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+disp(V_eff(1*no+ind0,1)); % zero order power transmission to TM
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+disp(V_eff(1*no+ind0,2)); % zero order power reflection to TM
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+
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