# Chapter 3: Fibre Optics And Applications¶

## Example 1, Page No: 3.40¶

In :
# Finding Numerical aperture

import math;

# Variable Declaration
n1      = 1.6;      # Refractive index of core
n2      = 1.5;      # Refractive index of cladding

# Calculations
NA      = math.sqrt(n1**2 - n2**2);        # Numerical Aperture of optical fiber

# Result
print 'Numerical Aperture of the optical fiber = %3.4f' %NA;

Numerical Aperture of the optical fiber = 0.5568


## Example 2, Page No: 3.40¶

In :
# Finding Numerical aperture and acceptance Angle

import math;

# Variable declaration
n1      = 1.55;      # Refractive index of core
n2      = 1.5;       # Refractive index of cladding

# Calculations
NA      = math.sqrt(n1**2 - n2**2);        # Numerical Aperture of optical fiber
im      = math.asin(NA);                   # Acceptance angle
im_d    = im*180/math.pi                   # radian to degree conversion

# Result
print 'Numerical Aperture of the optical fiber = %3.4f'%NA,' Acceptance angle = %3.2f' %im_d,'degrees ';

Numerical Aperture of the optical fiber = 0.3905  Acceptance angle = 22.99 degrees


## Example 3, Page No: 3.41¶

In :
# Finding Refractive index of cladding

import math;

# Variable declaration
NA      = 0.26;      # Numerical aperture
n1      = 1.5 ;      # Refractive index of core
d       = 100*10^-6; # diameter of the core in m

# Calculations
n2      = math.sqrt( n1**2 - NA**2);       # Refractive index of cladding

# Result
print 'Refractive index of cladding = %3.4f' %n2;

Refractive index of cladding = 1.4773


## Example 4, Page No: 3.41¶

In :
# Finding Numerical aperture

import math;

# variable Declaration
n1      = 1.54;      # Refractive index of core
n2      = 1.5;      # Refractive index of cladding

# Calculations
NA      = math.sqrt(n1**2 - n2**2);        # Numerical Aperture of optical fiber

# Result
print 'Numerical Aperture of the optical fiber = %3.4f' %NA

Numerical Aperture of the optical fiber = 0.3487


## Addl_Example 1, Page No: 3.42¶

In :
# Finding Refractive index, Acceptance angle, Maximum number of modes that fibre allows

import math;

# Variable Declaration
n1      = 1.5;       # Refractive index of core
NA      = float(0.26);      # Numerical aperture
d       = 100*10**-6  # core diameter
lamda   = float(10**-6);     # wavelength in m

# Calculations
n2      = math.sqrt( n1**2 - NA**2);       # Refractive index of cladding
im      = math.asin(NA);                   # Acceptance angle
im_d    = im*180/math.pi                   # radian to degree conversion
N       = 4.9*(d*NA/lamda)**2;              # maximum no of modes

# Result
print ' Refractive index of cladding n2 = %3.4f' %n2,'\n Acceptance angle = %3.2f' %im_d, 'degrees','\n Maximum number of modes that fibre allows = %d '%N;

 Refractive index of cladding n2 = 1.4773
Acceptance angle = 15.07 degrees
Maximum number of modes that fibre allows = 3312


## Addl_Example 2, Page No: 3.43¶

In :
 # Finding Numerical aperture and Critical angle

import math;

# Varible Declaration
delta       = 0.02;         # relative refractive index
n1          = 1.48;         # refractive index of core

# Calculations
NA          = n1*(2*delta)**0.5;           # Numerical aperture
n2          = math.sqrt( n1**2 - NA**2);   # Refractive index of cladding
cri_ang     = math.asin(n2/n1);            # critical angle
cri_ang_d   = cri_ang*180/math.pi;         # critical angle in degrees

# Result
print ' Numerical Aperture = %3.3f'%NA,'\n The Critical angle = %3.2f' %cri_ang_d,' degrees';

 Numerical Aperture = 0.296
The Critical angle = 78.46  degrees


## Addl_Example 3, Page No: 3.43¶

In :
# Finding Refractive Index

import math

# Variable declaration
delta       = 0.015;        # relative refractive index
NA          = 0.27;         # Numerical aperture

# Calculations
# we know that NA = n1*sqrt(2*Δ)
n1          = NA/math.sqrt(2*delta)          # refractive index of core
n2          = math.sqrt( n1**2 - NA**2);     #  Refractive index of cladding

# Result
print ' Refractive index of the core = %3.3f' %n1,'\n Refractive index of the cladding = %3.3f\n' %n2;

 Refractive index of the core = 1.559
Refractive index of the cladding = 1.535



## Addl_Example 4, Page No: 3.44¶

In :
# No. of total modes propagating in a multimode step index fibre

import math;

# variable Declaration
NA      = 0.25;        # Numerical aperture
d       = 60*10**-6       # core diameter
lamda   = 2.7*10**-6;     # wavelength in m

# calculations
N       = 4.9*(d*NA/lamda)**2;       # no of modes for step index fibre

# Result
print 'No. of total modes propagating in a multimode step index fibre = %d' %N;

No. of total modes propagating in a multimode step index fibre = 151


## Addl_Example 5, Page No: 3.44¶

In :
# Finding No. of total modes propagating in the fibre
import math;

# Variable Declaration
NA      = 0.25;          # Numerical aperture
d       = 6*10**-6        # core diameter
lamda   = 1.5*10**-6;     # wavelength of laser source
n1      = 1.47;          # refractive index of core
n2      = 1.43           # refractive index of cladding

# calculations
NA      = math.sqrt( n1**2 - n2**2);       # Numerical Aperture
N       = 4.9*(d*NA/lamda)**2;      # no of modes for step index fibre

# Result
print 'No. of total modes propagating in the fibre = %d' %N;

No. of total modes propagating in the fibre = 9