11: Laser

Example number 11.1, Page number 33

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=590*10**-9;    #wavelength of sodium D line(m)
h=6.626*10**-34;   #planck's constant
c=3*10**8;     #velocity of light(m/s)
e=1.602*10**-19;  #charge of electron(eV)

#Calculation
E=h*c/lamda;   #energy of 1st excited state(J)
E=E/e;   #energy of 1st excited state(eV)

#Result
print "energy of 1st excited state is",round(E,1),"eV"

energy of 1st excited state is 2.1 eV

Example number 11.2, Page number 34

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=250+273;   #temperature(K)
lamda=590*10**-9;    #wavelength of sodium D line(m)
h=6.626*10**-34;   #planck's constant
c=3*10**8;     #velocity of light(m/s)
k=1.38*10**-23;   #boltzmann constant

#Calculation
a=h*c/(k*T*lamda);
N2byN1=math.exp(-a);    #ratio between atoms in 1st excited state and ground state

#Result
print "ratio between atoms in 1st excited state and ground state is",round(N2byN1*10**21,2),"*10**-21"

ratio between atoms in 1st excited state and ground state is 5.33 *10**-21

Example number 11.3, Page number 34

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=250+273;   #temperature(K)
lamda=590*10**-9;    #wavelength of sodium D line(m)
h=6.626*10**-34;   #planck's constant
c=3*10**8;     #velocity of light(m/s)
k=1.38*10**-23;   #boltzmann constant

#Calculation
a=h*c/(k*T*lamda);
N2byN1=1/(math.exp(a)-1);    #ratio between stimulated emission and spontaneous emission

#Result
print "ratio between stimulated emission and spontaneous emission is",round(N2byN1*10**21,4),"*10**-21"

ratio between stimulated emission and spontaneous emission is 5.3298 *10**-21

Example number 11.4, Page number 35

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
n0=1.76;    #refractive index of ruby rod
new0=4.3*10**14;   #frequency(Hz)
deltav0=1.5*10**11;   #doppler broadening(Hz)
c=3*10**8;     #velocity of light(m/s)
tow21=4.3*10**-3;    #lifetime of spontaneous emission(s)
tow_photon=6*10**-9;   #lifetime of photon(s)

#Calculation
a=4*math.pi**2*new0**2*n0**3/(c**3);
N2_N1=a*tow21*deltav0/tow_photon;     #difference between excited state and ground state population(per m**3)

#Result
print "difference between excited state and ground state population is",round(N2_N1*10**-23,3),"*10**23 per m**3"

difference between excited state and ground state population is 1.584 *10**23 per m**3

Example number 11.5, Page number 35

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=300;   #temperature(K)
lamda=5000*10**-10;    #wavelength of light(m)
h=6.626*10**-34;   #planck's constant
c=3*10**8;     #velocity of light(m/s)
k=1.38*10**-23;   #boltzmann constant

#Calculation
a=h*c/(k*T*lamda);
N2byN1=1/(math.exp(a)-1);    #ratio between stimulated emission and spontaneous emission

#Result
print "ratio between stimulated emission and spontaneous emission is",round(N2byN1*10**42),"*10**-42"
print "answer varies due to rounding off errors"
print "spontaneous emission is more predominant than that of stimulated emission. for stimulating emission, N2>>N1. therefore there is no amplification possibility"

ratio between stimulated emission and spontaneous emission is 2.0 *10**-42
answer varies due to rounding off errors
spontaneous emission is more predominant than that of stimulated emission. for stimulating emission, N2>>N1. therefore there is no amplification possibility

Example number 11.6, Page number 36

In [22]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=632.8*10**-9;    #wavelength of laser beam(m)
h=6.626*10**-34;   #planck's constant
c=3*10**8;     #velocity of light(m/s)
P=2.3*10**-3;   #output power(W)

#Calculation
new=c/lamda;    #frequency of photon(Hz)
E=h*new;    #energy of photon(J)
El=P*60;   #energy emitted by laser(J/min)
n=El/E;    #number of photons emitted(photons/min)

#Result
print "number of photons emitted is",round(n*10**-17,3),"*10**17 photons/min"
print "answer varies due to rounding off errors"

number of photons emitted is 4.393 *10**17 photons/min
answer varies due to rounding off errors