# 12: Fiber Optics¶

## Example number 12.1, Page number 12.24¶

In [52]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.54;          #Core refractive index
n2=1.50;          #Cladding refractive index

#Calculation
NA=math.sqrt(n1**2-n2**2);    #numerical aperture
alpha_m=alpha_m*180/math.pi;    #acceptance angle(degrees)

#Result
print "acceptance angle is",round(alpha_m,2),"degrees"
print "answer in the book varies due to rounding off errors"

acceptance angle is 20.41 degrees
answer in the book varies due to rounding off errors


## Example number 12.2, Page number 12.24¶

In [53]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.5;          #Core refractive index
n2=1.45;          #Cladding refractive index

#Calculation
delta=(n1-n2)/n1;    #fractional index change
NA=n1*math.sqrt(2*delta);     #numerical aperture
alpha_m=alpha_m*180/math.pi;    #acceptance angle(degrees)
thetac=math.asin(n2/n1)*180/math.pi;     #critical angle(degrees)

#Result
print "numerical aperture is",round(NA,3)
print "acceptance angle is",round(alpha_m,1),"degrees"
print "critical angle is",int(thetac),"degrees"

numerical aperture is 0.387
acceptance angle is 22.8 degrees
critical angle is 75 degrees


## Example number 12.3, Page number 12.25¶

In [54]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.53;          #Core refractive index
p=2.5;      #percentage(%)

#Calculation
n2=n1*(100-p)/100;     #Cladding refractive index
thetac=math.asin(n2/n1)*180/math.pi;     #critical angle(degrees)

#Result
print "critical angle is",round(thetac,2),"degrees"

critical angle is 77.16 degrees


## Example number 12.4, Page number 12.25¶

In [55]:
#importing modules
import math
from __future__ import division

#Variable declaration
delta=0.018;      #fractional difference
n1=1.50;          #Core refractive index

#Calculation
NA=round(n1*math.sqrt(2*delta),2);     #numerical aperture
alpha_m=alpha_m*180/math.pi;    #acceptance angle(degrees)
n2=n1-(delta*n1);        #Cladding refractive index
thetac=math.asin(n2/n1)*180/math.pi;     #critical angle(degrees)

#Result
print "numerical aperture is",NA
print "acceptance angle is",round(alpha_m,2),"degrees"
print "critical angle is",round(thetac,1),"degrees"

numerical aperture is 0.28
acceptance angle is 16.26 degrees
critical angle is 79.1 degrees


## Example number 12.5, Page number 12.26¶

In [56]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=50*10**-6;     #diameter(m)
lamda=1*10**-6;    #wavelength(m)
NA=0.2;     #numerical aperture

#Calculation
NSI=4.9*(d*NA/lamda)**2;     #total number of guided modes
NGI=NSI/2;      #number of modes of graded index fibre

#Result
print "total number of guided modes is",NSI
print "number of modes of graded index fibre is",NGI

total number of guided modes is 490.0
number of modes of graded index fibre is 245.0


## Example number 12.6, Page number 12.26¶

In [57]:
#importing modules
import math
from __future__ import division

#Variable declaration
delta=0.05;      #fractional difference
n1=1.5;          #Core refractive index

#Calculation
NA=n1*math.sqrt(2*delta);     #numerical aperture

#Result
print "numerical aperture is",round(NA,2)

numerical aperture is 0.47


## Example number 12.7, Page number 12.27¶

In [58]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=5*10**-6;     #diameter(m)
lamda=1*10**-6;    #wavelength(m)
NA=0.092;     #numerical aperture

#Calculation
N=4.9*(d*NA/lamda)**2;     #number of modes that can be propagated

#Result
print "number of modes that can be propagated is",int(N)

number of modes that can be propagated is 1


## Example number 12.8, Page number 12.27¶

In [59]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.53;          #Core refractive index
n2=1.50;          #Cladding refractive index
lamda=1*10**-6;     #wavelength(m)

#Calculation
NA=math.sqrt(n1**2-n2**2);    #numerical aperture
Vn=2*math.pi*a*NA/lamda;      #V number
N=Vn**2/2;      #maximum number of modes

#Result
print "V number is",round(Vn,1)
print "maximum number of modes is",round(N,1)
print "answer in the book varies due to rounding off errors"

V number is 94.7
maximum number of modes is 4485.7
answer in the book varies due to rounding off errors


## Example number 12.9, Page number 12.27¶

In [60]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=0.85*10**-6;    #wavelength(m)
NA=0.3;   #numerical aperture

#Calculation
N=4*math.pi**2*a**2*NA**2/lamda**2;    #number of propagating modes

#Result
print "number of propagating modes is",int(N)
print "answer in the book is wrong"

number of propagating modes is 49177
answer in the book is wrong


## Example number 12.10, Page number 12.28¶

In [61]:
#importing modules
import math
from __future__ import division

#Variable declaration
NA=0.2;   #numerical aperture
n2=1.59;          #Cladding refractive index
n0=1.33;     #refractive index

#Calculation
n1=round(math.sqrt(NA**2+n2**2),4);     #Core refractive index
NA1=math.sqrt(n1**2-n2**2)/n0;         #numerical aperture
alpha_m=alpha_m*180/math.pi;    #acceptance angle(degrees)

#Result
print "Core refractive index is",n1
print "acceptance angle is",round(alpha_m,3),"degrees"

Core refractive index is 1.6025
acceptance angle is 8.638 degrees


## Example number 12.11, Page number 12.29¶

In [62]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;    #velocity of light(m/sec)
h=6.63*10**-34;    #plank's constant(Js)
lamda=680*10**-9;    #wavelength(m)
P=4*10**-3;    #power(W)

#Calculation
delta_E=c*h/lamda;    #energy(J)
N=P/delta_E;     #number of photons

#Result
print "number of photons is",round(N/10**15,3),"*10**15"

number of photons is 13.675 *10**15


## Example number 12.12, Page number 12.29¶

In [64]:
#importing modules
import math
from __future__ import division

#Variable declaration
delta=0.0005;     #fractional difference
n1=1.5;          #Core refractive index

#Calculation
n2=n1-(delta*n1);          #Cladding refractive index
NA=n1*math.sqrt(2*delta);     #numerical aperture
thetac=math.asin(n2/n1)*180/math.pi;     #critical angle(degrees)

#Result
print "Cladding refractive index is",n2
print "numerical aperture is",round(NA,4)
print "critical angle is",round(thetac,1),"degrees"

Cladding refractive index is 1.49925
numerical aperture is 0.0474
critical angle is 88.2 degrees


## Example number 12.13, Page number 12.29¶

In [65]:
#importing modules
import math
from __future__ import division

#Variable declaration
alpha=2.2;     #attenuation coefficient(dB/km)
L1=2;    #distance(km)
L2=6;    #distance(km)

#Calculation
x1=-alpha*L1/10;
x2=-alpha*L2/10;
P1=10**x1;         #fraction of initial intensity after 2km
P2=10**x2;         #fraction of initial intensity after 5km

#Result
print "fraction of initial intensity after 2km is",round(P1,3)
print "fraction of initial intensity after 5km is",round(P2,3)

fraction of initial intensity after 2km is 0.363
fraction of initial intensity after 5km is 0.048


## Example number 12.14, Page number 12.30¶

In [66]:
#importing modules
import math
from __future__ import division

#Variable declaration
L=0.5;      #distance(km)
Pout=1;    #output power(W)
Pin=85/100;    #input power(W)

#Calculation
alpha=10*math.log10(Pout/Pin)/L;     #attenuation coefficient(dB/km)

#Result
print "attenuation coefficient is",round(alpha,2),"dB/km"

attenuation coefficient is 1.41 dB/km


## Example number 12.15, Page number 12.30¶

In [67]:
#importing modules
import math
from __future__ import division

#Variable declaration
L=10;      #distance(km)
Pout=2;    #output power(W)
Pin=100;    #input power(W)

#Calculation
alpha=10*math.log10(Pin/Pout)/L;     #attenuation coefficient(dB/km)
o_alpha=round(alpha,1)*L;      #overall signal attenuation

#Result
print "attenuation coefficient is",round(alpha,1),"dB/km"
print "overall signal attenuation is",int(o_alpha),"dB"

attenuation coefficient is 1.7 dB/km
overall signal attenuation is 17 dB