半导体激光器半高宽(FWHM)计算

一、问题描述

Estimate the spot size (FWHM) in the lateral and transverse directions for a 1.3-um semiconductor laser whose active region is 0.2-um thick and 1-um wide. Assume u2=3.5and u1=3.2.

二、问题分析

单模半导体激光器的线宽通常定义为输出信号光谱的半高宽(FWHM)：full width at half maximum,功率函数峰值3dB处相距的频率宽度即为FWHM。

1.首先考虑TE模，即只考虑y方向，由书本第二章式2.5.10:

求其通解可以得到式2.5.14：

偶模：

奇模：

其中，

为包层折射率，为有源区折射率，为有效折射率，<

附：

1.TE-mode

%%TEmode FWHM

clear all

clc

d=0.2; %um

w=1; %um

u1=3.2;

u2=3.5;

lamada=1.3;

k0=2*pi/lamada;

D=k0*sqrt((u2^2-u1^2))*d;

GamaT=D^2/(2+D^2);

ue=sqrt(u1^2+GamaT*(u2^2-u1^2));

lamda=1.3; %um

k0=2*pi/lamda;

k=k0*sqrt(u2*u2-ue*ue);

gamma=k0*sqrt(ue*ue-u1*u1);

Ae=1.6;

Be=Ae*0.882;

y=-1:0.0005:1;

phi_y=zeros(1,length(y));

for i=1:length(y)

if (abs(y(i))<=d/2)

phi_y(i)=(Ae*cos(k*y(i))).^2;

else

phi_y(i)=(Be*exp(-gamma*(abs(y(i))-d/2))).^2;

end

end

figure

plot(y,phi_y)

xlabel(Thickness d (um));

ylabel((pih_y)^2)

title(Transverse Modes FWHM)

hold on

grid on

phi_mid=max(phi_y)/2;

y_mid=zeros(1,2);

for i=1:(length(y)-1)/2

if (abs(phi_y(i)-phi_mid)<0.01)

y_mid(1)=y(i);

end

end

for i=(length(y)+1)/2:length(y)

if (abs(phi_y(i)-phi_mid)<0.01)

y_mid(2)=y(i);

end

end

plot(y_mid(1),phi_mid,gp,y_mid(2),phi_mid,rp)

fwhmvalue=abs(y_mid(2)-y_mid(1)) % um

2.TM-mode

%%TMmode FWHM

clear all

clc

d=0.2; %um

clc

clf

w=1; %um

u1=3.2;

u2=3.5;

lamada=1.3;

k0=2*pi/lamada;

D=k0*sqrt((u2^2-u1^2))*d;

GamaT=D^2/(2+D^2);

ue=sqrt(u1^2+GamaT*(u2^2-u1^2));

lamda=1.3; %um

k0=2*pi/lamda;

k=1.4745;

gamma=k0*sqrt(ue*ue-u1*u1)

Ae=1.6;

Be=Ae*0.745;

x=-3:0.0005:3;

phi_x=zeros(1,length(x));

for i=1:length(x)

if (abs(x(i))<=w/2)

phi_x(i)=(Ae*cos(k*x(i))).^2;

else

phi_x(i)=(Be*exp(-gamma*(abs(x(i))-w/2))).^2;

end

end

figure

plot(x,phi_x)

xlabel(Width d (um));

ylabel((pih_x)^2)

title(Lateral Modes FWHM)

hold on

grid on

phi_mid=max(phi_x)/2;

x_mid=zeros(1,2);

for i=1:(length(x)-1)/2

if (abs(phi_x(i)-phi_mid)<0.01)

x_mid(1)=x(i);

end

end

for i=(length(x)+1)/2:length(x)

if (abs(phi_x(i)-phi_mid)<0.01)

x_mid(2)=x(i);

end

end

plot(x_mid(1),phi_mid,gp,x_mid(2),phi_mid,rp)

fwhmvalue=abs(x_mid(2)-x_mid(1)) % um

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