How to Solve Laser Rate Equations Using Matlab?

[mya246]

Hi, is there anyone familiar with rate equation solving using Matlab? I need help on this

 

[DrClaude]

Hi mya, welcome to PF!

You need to be more specific. What equation are you trying to solve? What exactly is the problem you are having?

 

[mya246]

I need to plot the light-current characteristic of laser (Pout vs I) by solving using ode45.

dy(1)= ((ni*I)/(q*V))-(N/tau)-(v_g*a*((N-N_tr)/(1+epsilon*N_p))*N_p);
dy(2)= (T*v_g*a*((N-N_tr)/(1+epsilon*N_p))*N_p) + (B_sp*T*R_sp) - (N_p/tau_p);

Pout = N_p*Vp*h*v*alpha_m*v_g;

how can I do that?

 

[mya246]

Hi mya, welcome to PF!

You need to be more specific. What equation are you trying to solve? What exactly is the problem you are having?

I need to plot the light-current characteristic of laser (Pout vs I) by solving using ode45.

dy(1)= ((ni*I)/(q*V))-(N/tau)-(v_g*a*((N-N_tr)/(1+epsilon*N_p))*N_p);
dy(2)= (T*v_g*a*((N-N_tr)/(1+epsilon*N_p))*N_p) + (B_sp*T*R_sp) - (N_p/tau_p);

Pout = N_p*Vp*h*v*alpha_m*v_g;

how can I do that?

 

[DrClaude]

I'm sorry, but this is not clear at all. You have dy(1) and dy(2), but I don't see any y(1) or y(2). And these are the derivatives with respect to what? And how does Pout relate to those ODEs?

 

[mya246]

I'm sorry, but this is not clear at all. You have dy(1) and dy(2), but I don't see any y(1) or y(2). And these are the derivatives with respect to what? And how does Pout relate to those ODEs?

sorry for that y(1) = N, y(2) = N_p. How can I plot the Pout vs current? Pout is related to N_p by solving the ODE

 

[DrClaude]

sorry for that y(1) = N, y(2) = N_p.
How can I plot the Pout vs current? Pout is related to N_p by solving the ODE

I'm sorry, but I'm still not clear on what you are solving. Are the derivatives with respect to time?

 

[reza 86]

rate equation

clc
clear all
close all
tau_s = 3e-9;
N0 = 1e24;
A =1e-12;
P0 = 1/(A*tau_s);
TSPAN = [0 10];
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') % carriers density in high laser level
subplot(2,1,2)
plot(T*tau_s ,Y(:,2)*P0)
title('photons density in activer region') % photons density in activer region
And this is the 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 ( try: from I0 to 3*I0 for example ...and see what happens!)
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))

 

[reza 86]

I hope that it would be helpful,

Can anyone help me by giving MATLAB code to simulate semiconductor laser rate equation by finite difference methord. i wrote a code but it is not working. please help me.

 

[reza 86]

qzsas