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input_Polariton_d.m
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input_Polariton_d.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%% Polariton structure %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
h=6.62606896e-34; %% Planck constant J.s
hbar=h/(2*pi);
e=1.602176487e-19; %% charge de l electron Coulomb
c=2.99792458e8; %% vitesse de la lumiere m/s
Epsi0=8.854187817620e-12; %% constant dielectric du vide F/m
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
nL=3;
nR=3;
lambda0=940e-9; %% Central wavelength
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%% Lorenztian build %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener,
% “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,”
% Appl. Phys. Lett. 98(20), 203103 (2011).
% J. Faist, "Optical properties of semiconductor"
% chap3: "Light-matter interaction"
% 3.5.2 A polarization field
N=10e22; %% electron density [m-3]
z0=2e-9; %% dipole of the transition [meter]
DeltaE=0.010; %% half broadening of the transition Energy [eV]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
w=2*pi*c./lambda; %% transformation of lambda in pulsation
w0=2*pi*c/lambda0; %% transformation of lambda in pulsation
G0=2*pi*DeltaE*e/h; %% broadening of the transition
Cst=(N*e^2*z0^2/(Epsi0*hbar));
Lorentz1 = w0 ./ ( w0^2-w.^2 - 1i*G0*w );
%Lorentz2 = 1/2 * ( w0-w+1i*G0/2 ) ./ ( (w0-w).^2 + (G0/2)^2 );
%Lorentz3 = 1/2 * (1./(w+w0+1i*G0/2) - 1./(w-w0+1i*G0/2) );
nc=3.55;
Ki=(nc^2-1) + Cst*Lorentz1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Epsi=1+Ki;
R=real(Epsi);
I=imag(Epsi);
nn = (1/sqrt(2))*sqrt(R+sqrt(R.^2+I.^2));
kk = (1/sqrt(2))*sqrt(-R+sqrt(R.^2+I.^2));
n3=nn+1i*kk;
l3=5 * lambda0/(2*abs(mean(n3)));
alpha=2*kk.*w/c; %% Absorbance [m-1]
Trans=exp(-alpha*l3);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot(2,2,1)
hold on;grid on;box on;
plot(lambda*1e9, nn ,'bo-')
xlabel('lambda (nm)')
ylabel('n')
subplot(2,2,2)
hold on;grid on;box on;
plot(lambda*1e9, kk ,'bo-')
xlabel('lambda (nm)')
ylabel('k')
subplot(2,2,3)
hold on;grid on;box on;
plot(lambda*1e9, Trans ,'bo-')
xlabel('lambda (nm)')
ylabel('Transmission')
ylim([0 1])
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
n1=zeros(1,length(lambda))+3.55; % GaAs
n2=zeros(1,length(lambda))+2.97; % AlAs
l1=lambda0/(4*abs(mean(n1))); % thickness at lambda/4
l2=lambda0/(4*abs(mean(n2))); % thickness at lambda/4
layer=[
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l3 n3
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
l2 n2
l1 n1
];