# 4: Laser¶

## Example number 1, Page number 136¶

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;               #velocity of light(m/sec)
lamda=6943*10**-10;      #wavelength(m)
h=6.626*10**-34;         #planck's constant(Jsec)
Kb=1.38*10**-23;         #boltzmann constant
T=300;                   #temperature(K)

#Calculation
new=c/lamda;          #frequency(Hz)
a=h*new/(Kb*T);
N1byN2=math.exp(a);   #relative population

#Result
print "relative population is",round(N1byN2/10**30,3),"*10**30"
print "answer given in the book is wrong"

relative population is 1.081 *10**30
answer given in the book is wrong


## Example number 2, Page number 137¶

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

#Variable declaration
c=3*10**8;               #velocity of light(m/sec)
lamda=632.8*10**-9;      #wavelength(m)
h=6.626*10**-34;         #planck's constant(Jsec)
t=1;                     #time(sec)
P=2.3*10**-3;            #power(W)
sa=1*10**-6;             #spot area(m**2)

#Calculation
new=c/lamda;             #frequency(Hz)
n=P*t/(h*new);           #number of photons emitted(per sec)
Pd=P/sa;                 #power density(kW/m**2)

#Result
print "number of photons emitted is",round(n/10**15,2),"*10**15 photons/second"
print "power density is",Pd/10**3,"kW/m**2"

number of photons emitted is 7.32 *10**15 photons/second
power density is 2.3 kW/m**2


## Example number 3, Page number 137¶

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;               #velocity of light(m/sec)
e=1.6*10**-19;           #charge of electron(coulomb)
Eg=1.44*e;               #band gap energy(J)
h=6.626*10**-34;         #planck's constant(Jsec)

#Calculation
lamda=h*c/Eg;            #wavelength(m)

#Result
print "wavelength is",int(round(lamda*10**10)),"angstrom"

wavelength is 8628 angstrom


## Example number 4, Page number 137¶

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

#Variable declaration
lamda=1.55;              #peak emission wavelength(micro m)

#Calculation
Eg=1.24/lamda;           #band gap(eV)

#Result
print "band gap is",Eg,"eV"

band gap is 0.8 eV


## Example number 5, Page number 137¶

In [26]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;               #velocity of light(m/sec)
e=1.6*10**-19;           #charge of electron(coulomb)
lamda=6943*10**-10;      #wavelength(m)
h=6.6*10**-34;           #planck's constant(Jsec)
kb=1.38*10**-23;         #boltzmann constant
T=300;                   #temperature(K)

#Calculation
Uv=h*c/(e*lamda);        #energy(eV)
Uvj=Uv*e;                #energy(J)
x=Uvj/(kb*T);
NbyN0=math.exp(x);       #relative population of 2 states

#Result
print "relative population of 2 states is",int(NbyN0*10**-29),"*10**29"
print "answer given in the book is wrong"

relative population of 2 states is 8 *10**29
answer given in the book is wrong


## Example number 6, Page number 138¶

In [28]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=2.998*10**8;               #velocity of light(m/sec)
lamda=0.5*10**-9;            #wavelength(m)
h=6.626*10**-34;             #planck's constant(Jsec)
Kb=1.381*10**-23;            #boltzmann constant
T=1000;                      #temperature(K)

#Calculation
new=c/lamda;                 #operating frequency(Hz)
new=new/10**3;               #operating frequency(kHz)
new=round(new/10**14)*10**14;
x=h*new/(Kb*T);
B21byA21=1/(math.exp(x)-1);  #ratio of emission

#Result
print "ratio of emission is",round(B21byA21*10**13,1),"*10**-13"

ratio of emission is 3.1 *10**-13