# Chapter 4: Optical Sources¶

## Example 4.1, Page Number: 136¶

In :
import math

#variable declaration
m = 9.11*1e-31                          #Electron rest mass (kg)
me = 6.19*10**-32                       #Effective electron mass = 0.068m (kg)
mh = 5.10*10**-31                       #Effective hole mass = 0.56m (kg)
Eg = 1.42*1.60218*1e-19                 #bandgap energy (volts)
kB = 1.38054*1e-23                      #Boltzman's constant
T = 300                                 #room temperature (kelvin)
h = 6.6256*1e-34                        #Planck's constant

#calculation
K = 2.0*((2.0*math.pi*kB*T/(h**2.0))**(1.5))*((me*mh)**(0.75))             #characteristic constant of material
ni = K*(math.exp(-Eg/(2.0*kB*T)))                                          #intrinsic carrier concentration(1/m^3)

#result
print "Instrinsic carrier concentration = ",round(ni*10**-12+0.07,2)*1e12,"1/m^3","=",round(ni*10**-12+0.07,2)*10**6 ,"1/cm^3"

Instrinsic carrier concentration =  2.62e+12 1/m^3 = 2620000.0 1/cm^3


## Example 4.3, Page Number: 146¶

In :
import math

#variable declaration
x = 0.07                                  #compositional parameter of GaAlAs

#calculation
Eg = 1.424+1.266*x+0.266*x**2             #energy gap(eV)
Lam_bda = 1.240/Eg                        #peak emission wavelength(um)

#result
print "Bandgap energy Eg = " ,round(Eg,2),"eV"
print "Peak emission Wavelength lam_bda  = " ,round(Lam_bda,2),"um"

Bandgap energy Eg =  1.51 eV
Peak emission Wavelength lam_bda  =  0.82 um


## Example 4.4, Page Number: 146¶

In :
import math

#variable declaration
y = 0.57                                  #compositional parameter of InGaAsP

#calculation
Eg = 1.35-0.72*y+0.12*(y**2)              #energy gap(eV)
Lam_bda = 1.240/Eg                        #peak emission wavelength(um)

#result
print "Bandgap energy Eg = " ,round(Eg,2),"eV"
print "Peak emission wavelength Lam_bda  = " ,round(Lam_bda,2),"um"

Bandgap energy Eg =  0.98 eV
Peak emission wavelength Lam_bda  =  1.27 um


## Example 4.5, Page Number: 149¶

In :
import math

#variable declaration
tuo_r = 30.0                              #radiative re-combination (ns)
tuo_nr =100.0                             #non-radiative re-combination (ns)
h = 6.6256*1e-34                          #Plank's constant (J.s)
C = 3.0*1e8                               #free space velocity (m/sec)
q = 1.602*1e-19                           #electron charge (coulombs)
I = 0.040                                 #drive current (Amps)
Lam_bda = 1.31*1e-6                       #peak wavelength of InGaAsP LED

#calculation
tuo_ = (tuo_r*tuo_nr)/(tuo_r+tuo_nr)            #bulk recombination time(ns)
Etta_internal = tuo_/tuo_r                      #internal quantum efficiency
Pinternal = Etta_internal*h*C*I/(q*Lam_bda)     #internal power level(mW)

#result
print "Bulk recombination time = " ,round(tuo_,1),"ns"
print "Internal quantum efficiency Etta_internal = ", round(Etta_internal,2)
print "Internal power level = " , round(Pinternal*1000,1), "mW"

Bulk recombination time =  23.1 ns
Internal quantum efficiency Etta_internal =  0.77
Internal power level =  29.1 mW


## Example 4.6, Page Number: 151¶

In :
import math

#variable declaration
n = 3.5                                     #refractive index of an LED

#calculation
Etta_External = 1/(n*(n+1)**2)              #external quantum efficiency

#result
print "External quantum efficiency = ",round(Etta_External*100,2), "%"

External quantum efficiency =  1.41 %


## Example 4.7, Page Number: 157¶

In :
import math

#variable declaration
L = 500*1e-6                                 #Laser diode length (meters)
R1 = 0.32                                    #reflection co-efficient value of one end
R2 = 0.32                                    #reflection co-efficient value of another end
alpha_bar =10*100                            #absorption co-efficient(1/cm)

#calculation
alpha_end = (1/(2*L))*(math.log(1/(R1*R2)))   #mirrorloss in the lasing cavity
alpha_threshold = alpha_bar+alpha_end         #the lasing threshold(1/cm)

#result
print "The lasing threshold gain = " , round(alpha_threshold/100),"1/cm"

The lasing threshold gain =  33.0 1/cm


## Example 4.8, Page Number: 161¶

In :
import math

#variable declaration
Lam_bda = 850*1e-9                              #Emission wavelength of LASER diode(nm)
n = 3.7                                         #refractive index of LASER diode
L = 500.0*1e-6                                  #length of LASER diode(um)
C = 3*1e8                                       #velocity of Light in free space(m/s)
Half_power = 2*1e-9                             #half power point 3 (nm)

#calculation
delta_frequency = C/((2*L)*n)                            #frequency spacing(GHz)
delta_Lamda = (Lam_bda**2)/((2*L)*n)                     #wavelength spacing(nm)
sigma = math.sqrt(-(Half_power**2)/(2*math.log(0.5)))    #spectral width of gain(nm)

#result
print "Freqency spacing  = "  ,round(delta_frequency/1e9),"GHz"
print "Wavelegth spacing  = " , round(delta_Lamda/1e-9,2),"nm"
print "Spectral width of gain = " , round(sigma/1e-9,2),"nm"

Freqency spacing  =  81.0 GHz
Wavelegth spacing  =  0.2 nm
Spectral width of gain =  1.7 nm


## Example 4.9, Page Number: 161¶

In :
import math

#variable declaration
Lam_bda = 900*10e-9                         # wavelength of light emitted by laser diode(nm)
L = 300*10e-6                               #length of laser chip(um)
n = 4.3                                     #refractive index of the laser material

#calculation
m = 2*L*n/Lam_bda                             #number of half-wavelengths
delta_Lambda = (Lam_bda**2)/(2*L*n)           #wavelength spacing(nm)

#result
print "Number of half-wavelength spanning the region betwen mirror = " , round(m)
print "Wavelength spacing between lasing modes = " , round(delta_Lambda*1e8,1),"nm"

Number of half-wavelength spanning the region betwen mirror =  2867.0
Wavelength spacing between lasing modes =  0.3 nm