Calculate Relative intensity noise using Rate equations

[mido41854]

Hello Everybody,

I'm trying to plot the frequency spectrum of RIN using Matlab.

I've the following code

function p=rateblock
tau_s = 3e-9;
N0 = 1e24;
A =1e-12;
P0 = 1/(A*tau_s);

TSPAN = 0:1e-2:10.23;;
Y0 =[0 0];

[T,Y] = ODE45(@rate_equation,TSPAN,Y0);
subplot(2,1,1)
plot(T*tau_s ,Y(:,1)*N0)
title('carriers density in high laser level')
subplot(2,1,2)
plot(T*tau_s ,Y(:,2)*P0)
title('photons density in activer region') %

dt=1e-2;
s_avg=sum(Y(:,2))/1024;%average photon numbers
ds=Y(:,2)-s_avg;%photon fluctuation with respect to average
TT=1e-6; %total time of integration
N=1024;%fft length
F=[0:N-1]';
RIN=((dt^2)/((s_avg)^2*TT)).*(abs(fft(ds))).^2;
RIN=10*log10(RIN);
plot(F,RIN)
title('RIN')

And for the Rate equation i used this function
function dy = rate_equation(t,y)
dy = zeros(2,1);

tau_s = 3e-9; % carriers lifetime
tau_p = 1e-12; % photons lifetime
A = 1e-12; % linear gain costant
N0 = 1e24; % trasparency carries density
V = 3.75e-14; % modal volume
gamma = 1e-5; % gain compression factor
q = 1.6e-19; % electron charge

I0 = N0*q*V/tau_s; % trasparency current
tau_norm = tau_s/tau_p;
eta = A*tau_p*N0; % efficiency

I = 2.5*I0; % pumping current

dy(1)= I/I0 -y(2)*(y(1) - 1) -y(1);
dy(2) = tau_norm*(y(2)*(eta*(y(1) - 1) -1) + gamma*eta*y(1))


Although I'm facing problems with caluclating the RIN and plot it with frequency ...

Can anybody help me with this issue?

 

[gtoguy97]

</code>You need to take the Fourier transform of your data in order to get the frequency spectrum.In MATLAB, you can use the fft() function to take the Fourier transform of your data. The syntax is: X = fft(x), where x is the data vector you want to transform. Once you have the Fourier transform, you can plot it with the frequency using the plot() command in MATLAB. The syntax is: plot(f,X), where f is the frequency vector and X is the Fourier transform.I hope this helps!