Chapter Five : Lasers I

Example 5.1, Page Number 173

In [1]:
from math import exp

T=2000 # In Kelvin
v=5*(10**14) #Frequency In Hertz
h=6.6*(10**-34) #Plancks Constant
k=1.38*(10**-23) #Boltzman Constant

#From Equation 5.9b

R=exp((h*v)/(k*T))-1 
R=round(R,2)
print "The Ratio of rates of spontaneous & stimulated emission is "+str(R)

The Ratio of rates of spontaneous & stimulated emission is 155829.12

Example 5.2, Page Number 176

In [2]:
from math import exp
T=300 #Given Room Temperature in kelvin
l=550*(10**-9) #Average Wavelength of Visible Radiation
h=6.6*(10**-34) #Plancks Constant
c=3*(10**8) #Speed Of light
k=1.38*(10**-23) #Boltzman Constant
e=1.6*(10**-19) #Charge of a Electron

E=(h*c)/l #Where E is the given Energy Difference
E1=E/e
#From Equation 5.4 & given that g1=g2

N=exp((-1*E)/(k*T)) #Where N is the ratio of N2 and N1

print "The Given Energy Difference of the Two Levels is "+str(E1)+" eV"

print "The Relative Population of the Energy Levels is %.2e"%(N)

The Given Energy Difference of the Two Levels is 2.25 eV
The Relative Population of the Energy Levels is 1.72e-38

Example 5.3, Page Number 184

In [3]:
#For NdYAG
t=230*(10**-6) #Spontaneous Lifetime
l=1.06*(10**-6) #Wavelength in meter
n=1.82 #Refractive Index
w=3*(10**12) #Linewidth in Hertz
h=6.6*(10**-34) #Plancks Constant
PI=3.14
#From equation 5.8

B21=(l**3)/(8*PI*h*t*(n**3)) #Where B21 is the Einstein Coefficient

#From equation 5.18
k=1

kvs=(k*l*w)/(B21*h*n) #Small Signal Gain Coefficient per meter cube

print "Small Signal Gain Coefficient is %.2e /meter cube"%(kvs)

Small Signal Gain Coefficient is 5.11e+22 /meter cube

Example 5.4, Page Number 205

In [4]:
n2=3.6 #Refractive Index for GaAs
n1=1 #Refractive Index for Air
#From Fresnels Equation

R=((n2-n1)/(n2+n1))**2
R=round(R,2)

print "The Reflectance at a GaAs/Air Interface is "+str(R)

The Reflectance at a GaAs/Air Interface is 0.32

Example 5.5, Page Number 209

In [5]:
from math import log1p

#For GaAs Junction
l=0.84*(10**-6) #Wavelength in meter
w=1.45*(10**13) #Linewidth in Hertz
y=3.5*(10**3) #Loss Coefficient per meter
n=3.6 #Refractive Index for GaAs
q=1 #Quantam Efficiency
le=300*(10**-6)#length in meter
d=2*(10**-6) 
R=0.32 #Reflectance
c=3*(10**8) #Speed of light in m/s
e=1.6*(10**-19) #Charge of electron
#From Equation 5.17

v=c/l #Frequency

k=y+((1/(2*le))*log1p(1/(R*R)))#Where k is the threshold gain 
k=round(k,0)
#From Equation 5.39

J=(8*3.14*w*e*(n**2)*d*k*(v**2))/(c**2)
J=round(J,2)
print "The Threshold Gain is "+str(k)+" /m"
print "The Threshold Current Density is "+str(J)+" A/mm square"

The Threshold Gain is 7461.0 /m
The Threshold Current Density is 15972801.15 A/mm square

Example 5.6, Page number 225

In [6]:
i=10*(10**-3) #Current in ampere
V=2500 
P=5*(10**-3) #optical Output

E=P/(i*V) #Where E is the overall Power Efficiency
E=E*100
print "The Overall Power Efficiency is "+str(E)+" Percent"

The Overall Power Efficiency is 0.02 Percent