Chapter Six : Laser II

Example 6.1, Page Number 252

In [1]:
lw=1.1*(10**11) #Fluorescent Linewidth in Hertz
l=0.1 #length of laser rod in meter
n=1.8 #given Refraction Index
c=3*(10**8) #Speed of light

ms=c/(2*l*n) #where ms is the mode seperation in hertz
ms=round(ms,0)
ps=1/ms #where ps is the Pulse seperation in seconds
Nm=lw/ms #where Nm is the Number of modes oscillating
Nm=round(Nm,0)
pd=(1/Nm)*ps #where pd is the pulse duration

print "The Mode Seperation is "+str(ms)+" Hertz"
print "The Pulse Seperation is %.2e seconds"%(ps)
print "The Number of Modes Oscillating is "+str(Nm)
print "The Pulse Duration is %.1e seconds"%(pd)

The Mode Seperation is 833333333.0 Hertz
The Pulse Seperation is 1.20e-09 seconds
The Number of Modes Oscillating is 132.0
The Pulse Duration is 9.1e-12 seconds

Example 6.2, Page Number 256

In [2]:
#In a typical Laser
N1=10**24 #in per meter cube
v=5*(10**14) #Frequency in hertz
vo=(10**-5) #Volume in per meter cube
h=6.63*(10**-34) #Plancks Constant

#Assuming Nf<<<<N1

E1=0.5*(h*v*N1*vo) #Where E is the Energy of the pulses
E1=round(E1,1)

print "The Energy of the Pulse is "+str(E1)+" J"

The Energy of the Pulse is 1.7 J

Example 6.3, Page Number 256

In [3]:
#Using the Energy of the pulses from the above example
E=1.657 #Energy of the pulses in Joules
l=0.1 #Cavity length in meter
r=0.8 #Mirror reflectance
c=3*(10**8) #Speed of light

tc=l/((1-r)*c) #where tc is the cavity lifetime

P=E/tc #where P is the pulse power

print "The Cavity Lifetime is %.1e seconds"%(tc)
print "The Pulse Power is "+str(P)+" W"

The Cavity Lifetime is 1.7e-09 seconds
The Pulse Power is 994200000.0 W

Example 6.4, Page Number 260

In [4]:
#Considering a He-Ne Laser
d=3*(10**-3) #Diameter in meter
l=633*(10**-9) #Wavelength of the laser

theta=l/d #where theta is the divergence of the beam
print "The Divergence of the Beam is "+str(theta)+" Radians"
#After Collimation

theta=theta/30 #Reduced by a factor of 30
print "After Collimation,The angle of Divergance is reduced to %.2e Radians"%(theta)

The Divergence of the Beam is 0.000211 Radians
After Collimation,The angle of Divergance is reduced to 7.03e-06 Radians

Example 6.5, Page Number 263

In [5]:
#Assuming all lights from a Sodium Lamp

l=589*(10**-9) #Given Wavelength in meter
lw=5.1*(10**11) #Given Linewidth in Hertz
c=3*(10**8) #Speed of light

#By equation 6.9

tc=1/lw #Where tc is the cavity lifetime

#By Equation 6.8
Lc=tc*c #Where Lc is the length of the Wave Train
Lc=round(Lc,4)
print "The Cavity lifetime is %.1e seconds"%(tc)
print "The Length of the Wave Train or the Coherance Length is "+str(Lc)+" meter"

print "Under Multi Modes,The Linewidth is about 1500 MHz and Coherance Length is 0.2 m"
print "Under Single Mode,The Linewidth is about 1Mhz and the Coherance Length is 300 m"

The Cavity lifetime is 2.0e-12 seconds
The Length of the Wave Train or the Coherance Length is 0.0006 meter
Under Multi Modes,The Linewidth is about 1500 MHz and Coherance Length is 0.2 m
Under Single Mode,The Linewidth is about 1Mhz and the Coherance Length is 300 m

Example 6.6, Page Number 266

In [6]:
P=10*(10**-3) #Given Power of the He-Ne Laser
F=1 #Given F Number
l=633*(10**-9) #Wavelength of the laser
PI=3.14
#From equation 6.10a

rs=(2/PI)*l*F #where rs is the radius of the focused spot

P1=(P*PI)/((2*l)**2) #Where P1 is the Power per unit area

print "The Radius of the Focused Spot is %.2e meter"%(rs)
print "The Power Per unit Area is "+str(P1)+" Watt per meter square"

The Radius of the Focused Spot is 4.03e-07 meter
The Power Per unit Area is 19591254064.9 Watt per meter square

Example 6.7, Page Number 266

In [7]:
from math import sqrt

#Given a Carbon Dioxide Laser Beam 
l=10.6*(10**-6) #Wavelength in meter
d=50*(10**-3) #diameter in meter
fl=200*(10**-3) #Focal Length
PI=3.14

#Using Equation 6.10
rs=wo=(l*fl)/(PI*(d/2)) #where rs is the radius of the focused spot

#Given that spot size can be toletated by 10 percent
dw=1.1
w=1
#using equation 6.11
z=((PI*(rs**2))*sqrt((dw**2)-(w**2)))/l #where z is the depth of focus

print "The Radius of the Focused spot is %.2e meter"%(rs)
print "The depth of the Focus is %.2e meter"%(z)

#Answer is misprinted in the book

The Radius of the Focused spot is 2.70e-05 meter
The depth of the Focus is 9.90e-05 meter