tmmforgrating.m

用传输矩阵法计算光栅场

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % calculates field distributions of forward and
% % backward propagating waves inside the grating
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% clear all
% L = 30; % grating length in microns
% z = [0:0.01:L]; % propagation distance
% lambda = 1.55; % input wavelength in microns
% lambdaB = 1.55; % Bragg wavelength in microns
% neff = 1.45; % mode effective index
% kappa = 0.03; % coupling coefficient in 1/microns
% dbeta=(1./lambda-1/lambdaB)*2*pi*neff; % delta beta
% S = sqrt(kappa^2-dbeta.^2);
% K = (1/lambdaB)*2*pi*neff;
% % find backward (aa) and forward (b) field amplitudes inside grating
% a = ((1*kappa.*exp(-j.*dbeta.*z))./(1*dbeta.*sinh(S.*L)-j.*S.*cosh(S*L))).*sinh(S.*(z-L));
% b = ((1*exp(-j.*dbeta.*z))./(1*dbeta.*sinh(S.*L)-j.*S.*cosh(S*L))).*(dbeta.*sinh(S.*(z-L))+j*S.*cosh(S.*(z-L)));
% figure, plot(z,abs(b).^2,z,abs(a).^2)
% xlabel('z (\mum)')
% ylabel('A')

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % TRANSFER MATRIX FORMALISM FOR GRATINGS %
% % calculates grating trasmissivity and %
% % finds bloch modes using transfer matrix %
% % formalism %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% clear all
% % define constants %
% lambda = linspace(0.8,10,5000)*1e-6; % wavelength range
% c = 3e8; % light velocity in m/s
% N = 100; % number of elementary cells
% n1 = 1; % index of first layer
% n2 = 3; % index of second layer
% d1 = 0.7e-6; % length of first layer
% d2 = 0.35e-6; % length of second layer
% L = d1+d2; % elementary cell period length
% r12 = (n1-n2)/(n1+n2); % 1-2 interface reflectivity
% r21 = -r12; % 2-1 interface reflectivity
% t = sqrt(1-r12^2); % interface trasmissivity
% % calculate interface transfer matrices %
% M12 = (1/t)*[1 r12; r12 1];
% M21 = (1/t)*[1 r21; r21 1];
% % calculate spectrum & band diagram %
% for mm = 1:length(lambda)
% k1 = 2*pi*n1./lambda(mm); % wave-vectors
% k2 = 2*pi*n2./lambda(mm);
% % calculate propagation matrices %
% Md1 = [exp(j*k1*d1) 0;0 exp(-j*k1*d1)];
% Md2 = [exp(j*k2*d2) 0;0 exp(-j*k2*d2)];
% ML1 = M21*Md1*M12*Md2; % grating period matrix (starting from layer 1)
% ML2 = M12*Md2*M21*Md1; % grating period matrix (starting from layer 2)
% % Bloch dispersion relation %
% K(mm) = (1/L)*acos(0.5*(ML1(1,1)+ML1(2,2)));
% % calculate frequency %
% w(mm) = 2*pi*c./lambda(mm);
% % total transmission matrix through N elementary cells (grating periods)
% Mtot = ML1^N;
% tt(mm) = 1/Mtot(1,1); % calcualte trasmissivity
% end
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % FIGURES %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% K = [K 0]; w = [w 0];
% figure, plot(lambda*1e6,log10(abs(tt).^2)), axis tight
% xlabel('\lambda (\mum)')
% ylabel('T (dB)')
% figure, plot(K*1e-6,w*1e-15), hold on, plot(-K*1e-6,w*1e-15)
% axis tight
% box on
% xlabel('k (\mum^{-1})')
% ylabel('\omega (THz)')