%% 1D photonic band off axis prop. isofrequency curves clear close all maxw=2.5e15; minw=1e11; Nw=20; w=linspace(minw,maxw,Nw); for j=1:Nw; kj=1; lam0=2*pi*3e14./w(j); % vacuum wavelength in micron %% unit cell (AB)%%%%%%%% nA=1.5; % refractive index of material A dA=0.25; % thickness of layer A in micron k0A=2*pi*nA./lam0; % modulus of the wavevector in layer A ( micron^(-1)) nB=3; % refractive index of material B dB=0.2; % thickness of layer B in micron k0B=2*pi*nB./lam0; % modulus of the wavevector in layer B ( micron^(-1)) a=dA+dB; % unit cell thickness kymin=-k0B; % wavevector component kymax=k0B; % max kymed=k0A; Nk=400*j; kyv=[ linspace((kymin),(-kymed),Nk) linspace((-kymed),(kymed),Nk) linspace((kymed),(kymax),Nk)]; Nkk=length(kyv); for k=1:Nkk ky=kyv(k); kxA=sqrt(k0A^2-ky^2); % x component of the wavevector in layer A ( micron^(-1)) kxB=sqrt(k0B^2-ky^2); % x component of the wavevector in layer B (micron^(-1)) %% Transfer matrix of the unit cell %%%% M=zeros(2,2); PB= [ exp(-i.*kxB.*dB) 0; 0 exp(i.*kxB.*dB)]; IBA=0.5*[ 1+(kxB/kxA) 1-(kxB/kxA); 1-(kxB/kxA) 1+(kxB/kxA)]; PA= [ exp(-i.*kxA.*dA) 0; 0 exp(i.*kxA.*dA)]; IAB=0.5*[ 1+(kxA/kxB) 1-(kxA/kxB); 1-(kxA/kxB) 1+(kxA/kxB)]; M=IAB*PA*IBA*PB; %% eigen values %% Ka=acos(0.5*(M(1,1)+M(2,2)))./a; %K=0; %KY=0; %if abs(imag(Ka))<2; if abs(real(Ka))>0; if abs(real(Ka))1 % y=interp1(KY,K,kyv); %% plot results hold off AA=num2str(w(j),'% 5.2e'); TEX=['w=' AA] plot(K*a./pi,KY.*a./pi,'.','MarkerSize',3) hold on plot(K*a./pi + 2,KY.*a./pi,'r.','MarkerSize',3) plot(K*a./pi -2,KY.*a./pi,'r.','MarkerSize',3) axis([-2 2, -2 2]); legend(TEX) grid on xlabel('Kx (units of \pi/a)') ylabel('Ky (units of \pi/a)') pause end clear K KY kj end;