11: Lasers

Example number 11.1, Page number 249

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
h = 6.626*10**-34;     #Planck's constant(Js)
c = 3*10**8;     #Speed of light in free space(m/s)
k = 1.38*10**-23;     #Boltzmann constant(J/K)
T = 300;     #Temperature at absolute scale(K)
lamda1 = 5500;     #Wavelength of visible light(A)
lamda2 = 10**-2;     #Wavelength of microwave(m)

#Calculation
lamda1 = lamda1*10**-10;     #Wavelength of visible light(m)
rate_ratio = math.exp(h*c/(lamda1*k*T))-1;    #Ratio of spontaneous emission to stimulated emission
rate_ratio1 = math.exp(h*c/(lamda2*k*T))-1;     #Ratio of spontaneous emission to stimulated emission
rate_ratio1 = math.ceil(rate_ratio1*10**5)/10**5;     #rounding off the value of rate_ratio1 to 5 decimals

#Result
print "The ratio of spontaneous emission to stimulated emission for visible region is",rate_ratio
print "The ratio of spontaneous emission to stimulated emission for microwave region is", rate_ratio1

The ratio of spontaneous emission to stimulated emission for visible region is 8.19422217477e+37
The ratio of spontaneous emission to stimulated emission for microwave region is 0.00482

Example number 11.2, Page number 250

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

#Variable declaration
e = 1.6*10**-19;   #Energy equivalent of 1 eV(J/eV)
h = 6.626*10**-34;    #Planck's constant(Js)
c = 3*10**8;    #Speed of light in free space(m/s)
lamda = 690;    #Wavelength of laser light(nm)
E_lower = 30.5;    #Energy of lower state(eV)

#Calculation
lamda = lamda*10**-9;     #Wavelength of laser light(m)
E = h*c/lamda;    #Energy of the laser light(J)
E = E/e;     #Energy of the laser light(eV)
E_ex = E_lower + E;    #Energy of excited state of laser system(eV)
E_ex = math.ceil(E_ex*10**2)/10**2;     #rounding off the value of E_ex to 2 decimals

#Result
print "The energy of excited state of laser system is",E_ex, "eV"

The energy of excited state of laser system is 32.31 eV

Example number 11.3, Page number 250

In [7]:
#importing modules
import math
from __future__ import division
import numpy as np

#Variable declaration
h = 6.626*10**-34;     #Planck's constant(Js)
k = 1.38*10**-23;      #Boltzmann constant(J/K)

#Calculation
#Stimulated Emission = Spontaneous Emission <=> exp(h*f/(k*T))-1 = 1 i.e.
#f/T = log(2)*k/h = A
A =  np.log(2)*k/h;     #Frequency per unit temperature(Hz/K)
A = A/10**10;
A = math.ceil(A*10**3)/10**3;     #rounding off the value of A to 3 decimals

#Result
print "The stimulated emission equals spontaneous emission iff f/T =",A,"*10**10 Hz/k"

The stimulated emission equals spontaneous emission iff f/T = 1.444 *10**10 Hz/k

Example number 11.4, Page number 250

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda = 500;     #Wavelength of laser light(nm)
f = 15;     #Focal length of the lens(cm)
d = 2;      #Diameter of the aperture of source(cm)
P = 5;      #Power of the laser(mW)

#Calculation
P =  P*10**-3;    #Power of the laser(W)
lamda = lamda*10**-9;      #Wavelength of laser light(m)
d = d*10**-2;      #Diameter of the aperture of source(m)
f = f*10**-2;      #Focal length of the lens(m)
a = d/2;    #Radius of the aperture of source(m)
A = math.pi*lamda**2*f**2/a**2;     #Area of the spot at the focal plane, metre square
I = P/A;     #Intensity at the focus(W/m**2)
I = I/10**7;
I = math.ceil(I*10**4)/10**4;     #rounding off the value of I to 1 decimal

#Result
print "The area of the spot at the focal plane is",A, "m**2"
print "The intensity at the focus is",I,"*10**7 W/m**2"

The area of the spot at the focal plane is 1.76714586764e-10 m**2
The intensity at the focus is 2.8295 *10**7 W/m**2

Example number 11.5, Page number 251

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
h = 6.626*10**-34;     #Planck's constant(Js)
c = 3*10**8;     #Speed of light in free space(m/s)
lamda = 1064;    #Wavelength of laser light(nm)
P = 0.8;    #Average power output per laser pulse(W)
dt = 25;    #Pulse width of laser(ms)

#Calculation
dt = dt*10**-3;       #Pulse width of laser(s)
lamda = lamda*10**-9;     #Wavelength of laser light(m)
E = P*dt;   #Energy released per pulse(J)
E1 = E*10**3;
N = E/(h*c/lamda);    #Number of photons in a pulse

#Result
print "The energy released per pulse is",E1,"*10**-3 J"
print "The number of photons in a pulse is", N

The energy released per pulse is 20.0 *10**-3 J
The number of photons in a pulse is 1.07053023443e+17

Example number 11.6, Page number 251

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda = 693;     #Wavelength of laser beam(nm)
D = 3;       #Diameter of laser beam(mm)
d = 300;    #Height of a satellite above the surface of earth(km)

#Calculation
D = D*10**-3;    #Diameter of laser beam(m)
lamda = lamda*10**-9;     #Wavelength of laser beam(m)
d = d*10**3;     #Height of a satellite above the surface of earth(m)
d_theta = 1.22*lamda/D;    #Angular spread of laser beam(rad)
dtheta = d_theta*10**4;
dtheta = math.ceil(dtheta*10**2)/10**2;     #rounding off the value of dtheta to 2 decimals
a = d_theta*d;      #Diameter of the beam on the satellite(m)
a = math.ceil(a*10)/10;     #rounding off the value of a to 1 decimal

#Result
print "The height of a satellite above the surface of earth is",dtheta,"*10**-4 rad"
print "The diameter of the beam on the satellite is",a, "m"

The height of a satellite above the surface of earth is 2.82 *10**-4 rad
The diameter of the beam on the satellite is 84.6 m
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