12: Holography and Fibre Optics

Example number 12.1, Page number 271

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1 = 1.43;    #Refractive index of fibre core
n2 = 1.4;     #Refractive index of fibre cladding

#Calculation
#As sin (alpha_c) = n2/n1, solving for alpha_c
alpha_c = math.asin(n2/n1);     #Critical angle for optical fibre(rad)
alpha_c = alpha_c*57.2957795;     #Critical angle for optical fibre(degrees)
alpha_c = math.ceil(alpha_c*10**3)/10**3;     #rounding off the value of alpha_c to 3 decimals
#AS cos(theta_c) = n2/n1, solving for theta_c
theta_c = math.acos(n2/n1);    #Critical propagation angle for optical fibre(rad)
theta_c = theta_c*57.2957795;     #Critical propagation angle for optical fibre(degrees)
theta_c = math.ceil(theta_c*10**2)/10**2;     #rounding off the value of theta_c to 2 decimals
NA = math.sqrt(n1**2 - n2**2);     #Numerical aperture for optical fibre
NA = math.ceil(NA*10**3)/10**3;     #rounding off the value of NA to 3 decimals

#Result
print "The critical angle for optical fibre is",alpha_c, "degrees"
print "The critical propagation angle for optical fibre is",theta_c, "degrees"
print "Numerical aperture for optical fibre is",NA

The critical angle for optical fibre is 78.244 degrees
The critical propagation angle for optical fibre is 11.76 degrees
Numerical aperture for optical fibre is 0.292

Example number 12.2, Page number 271

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

#Variable declaration
n1 = 1.45;    #Refractive index of fibre core
n2 = 1.4;     #Refractive index of fibre cladding

#Calculation
NA = math.sqrt(n1**2 - n2**2);     #Numerical aperture for optical fibre
NA = math.ceil(NA*10**4)/10**4;     #rounding off the value of NA to 4 decimals
#As sin(theta_a) = sqrt(n1^2 - n2^2), solving for theta_a
theta_a = math.asin(math.sqrt(n1**2 - n2**2));     #Half of acceptance angle of optical fibre(rad)
theta_a = theta_a*57.2957795;     #Half of acceptance angle of optical fibre(degrees)
theta_accp = 2*theta_a;     #Acceptance angle of optical fibre(degrees)
theta_accp = math.ceil(theta_accp*10**2)/10**2;     #rounding off the value of theta_accp to 2 decimals
Delta = (n1 - n2)/n1;       #Relative refractive index difference
Delta = math.ceil(Delta*10**4)/10**4;     #rounding off the value of Delta to 4 decimals

#Result
print "Numerical aperture for optical fibre is", NA
print "The acceptance angle of optical fibre is",theta_accp, "degrees"
print "Relative refractive index difference is", Delta

Numerical aperture for optical fibre is 0.3775
The acceptance angle of optical fibre is 44.36 degrees
Relative refractive index difference is 0.0345

Example number 12.3, Page number 271

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1 = 1.55;     #Refractive index of fibre core
n2 = 1.53;     #Refractive index of fibre cladding
n0 = 1.3;      #Refractive index of medium

#Calculation
NA = math.sqrt(n1**2 - n2**2);     #Numerical aperture for optical fibre
NA = math.ceil(NA*10**4)/10**4;     #rounding off the value of NA to 4 decimals
#n0*sin(theta_a) = sqrt(n1^2 - n2^2) = NA, solving for theta_a
theta_a = math.asin(math.sqrt(n1**2 - n2**2)/n0);     #Half of acceptance angle of optical fibre(rad)
theta_a = theta_a*57.2957795;    #Half of acceptance angle of optical fibre(degrees)
theta_accp = 2*theta_a;     #Acceptance angle of optical fibre(degrees)

#Result
print "Numerical aperture for step index fibre is",NA
print "The acceptance angle of step index fibre is",int(theta_accp), "degrees"

Numerical aperture for step index fibre is 0.2482
The acceptance angle of step index fibre is 22 degrees

Example number 12.4, Page number 271 Theoritical proof

Example number 12.5, Page number 272

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

#Variable declaration
alpha = 2;      #Power loss through optical fibre(dB/km)
P_in = 500;     #Poer input of optical fibre(micro-watt)
z = 10;        #Length of the optical fibre(km)

#Calculation
#As alpha = 10/z*log10(P_in/P_out), solving for P_out
P_out = P_in/10**(alpha*z/10);      #Output power in fibre optic communication(micro-Watt)

#Result
print "The output power in fibre optic communication is",P_out, "micro-Watt"

The output power in fibre optic communication is 5.0 micro-Watt
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