Chapter 4: Optical sources and transmitter circuits¶

Example 4.1 , Page no:67¶

In :
import math
from __future__ import division

#initialisation of variables
tau_r=12*10**-9;  #radiative recombination time in s
tau_nr=35*10**-9;  #non-radiative recombination time in s
n1=3.5;  #refractive index of semiconductor
n2=1;  #refractive index of air
d=0.4*10**-6;  #active later thickness in m
V=8;  #recombination velocity

#CALCULATIONS
eta_int=1/(1+(tau_r/tau_nr));  #internal quantum efficiency
tau=1/((tau_r**-1)+(tau_nr**-1)+(2*V/d));  #total recombination time in s
f=math.sqrt(3)/(2*3.14*tau);  #bandwidth in Hz
F3=((n1-n2)**2/(n1+n2)**2);  #fresnel reflection
eta_ext=eta_int*(1-F3);  #external quantum efficiency

#RESULTS
print"internal quantum efficiency=",round(eta_int,5);  #The answers vary due to round off error
print"total recombination time =",round(tau*1e9,5),"ns";  #multiplication by 1e9 to convert unit from s to ns//The answers vary due to round off error
print"bandwidth =",round(f*1e-6,5),"MHz";  #multiplication by 1e-6 to convert unit from Hz to MHz///The answers vary due to round off error
print"fresnel reflection=",round(F3,5);  #The answers vary due to round off error
print"external quantum efficiency=",round(eta_ext,5);  #The answers vary due to round off error
internal quantum efficiency= 0.74468
total recombination time = 6.58307 ns
bandwidth = 41.89598 MHz
fresnel reflection= 0.30864
external quantum efficiency= 0.51484

Example 4.2 , Page no:67¶

In :
import math
from __future__ import division

#initialisation of variables
lambda1=1.3;  #wavelength of laser in um
w=5;  #active layer width in um
d=2;  #active layer thickness in um
n1=3.5;  #refractive index of core

#CALCULATIONS
k0=2*3.14/lambda1;  #propagation constant
row=0.3;  #confinement factor
neff=math.sqrt(n2**2+row);  #effective refractive index
D=k0*d*(math.sqrt(n1**2-n2**2));  #normalized thickness
W=k0*w*(math.sqrt(neff**2-n2**2));  #normalized width// the answer given in textbook is wrong
Wlat=w*(math.sqrt(2*math.log(2)))*(0.32+2.1*(W**-1.5));  #Full width lateral at half maximum in um/ the answer given in textbook is wrong
Wtra=d*(math.sqrt(2*math.log(2)))*(0.32+2.1*(D**-1.5));  #Full width transverse at half maximum in um/ the answer given in textbook is wrong

#RESULTS
print"Normalized thickness=",round(D,5);  #The answers vary due to round off error
print"Normalized width =",round(W,5);  #multiplication by 1e9 to convert unit from s to ns/// the answer given in textbook is wrong
print"Full width lateral at half maximum =",round(Wlat,5),"um";  #multiplication by 1e-6 to convert unit from Hz to MHz//// the answer given in textbook is wrong
print"Full width transverse at half maximum =",round(Wtra,5),"um";  #multiplication by 1e-6 to convert unit from Hz to MHz//// the answer given in textbook is wrong
Normalized thickness= 2.55438
Normalized width = 13.22961
Full width lateral at half maximum = 2.14078 um
Full width transverse at half maximum = 1.96484 um

Example 4.3 , Page no:68¶

In :
import math
from __future__ import division

#initialisation of variables
Eg=1.3;  #band gap energy in eV
l=0.4;  #cavity length in mm
R1=0.5;  #reflectivities on ends
R2=0.5;  #reflectivities on ends
alpha=3;  #loss coefficient in /mm
current_density=30*10**5;  #current density in amp/m^2
area=0.2*0.5*10**-6;  #laser active area in m^2

#CALCULATIONS
lambda1=1.24/Eg;  #emission wavelength in um
gth=alpha+(1/(2*l))*math.log(1/(R1*R2));  #Threshold Gain
threshold_current=current_density*area;  #threshold current in A

#RESULTS
print"Emission wavelength =",round(lambda1,5),"nm";  #multiplication by 1e3 to convert unit from um to nm
print"Threshold Gain=",round(gth,5),"/mm";
print"Threshold current =",round(threshold_current*1e3,5),"mA";  #for converting unit from A to mA
Emission wavelength = 0.95385 nm
Threshold Gain= 4.73287 /mm
Threshold current = 300.0 mA

Example 4.4 , Page no:68¶

In :
import math
from __future__ import division

#initialisation of variables
lamda=0.85*10**-6;  #wavelength of operation in m
delta_lamda=36*10**-9;  #spectral width in m

#CALCULATIONS
fractional_width=delta_lamda/lamda;  #fractional width

#RESULTS
print"Fractional width=", round(fractional_width*100,5),"percent";  #multiplication by 100 to represent information in percentage
Fractional width= 4.23529 percent