13: Fiber Optics

Example number 1, Page number 13.19

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

#Variable declaration
n2=1.47;              #refractive index of cladding
n1=1.5;    #refractive index of core

#Calculation
phi_c=math.asin(n2/n1);     #critical angle(radian)
phi_c=phi_c*180/math.pi;    #critical angle(degrees)
NA=math.sqrt(n1**2-n2**2);     #numerical aperture
phi_max=math.asin(NA);       #acceptance angle(radian)
phi_max=phi_max*180/math.pi;    #acceptance angle(degrees)

#Result
print "critical angle is",round(phi_c,1),"degrees"
print "numerical aperture is",round(NA,1)
print "acceptance angle is",round(phi_max,1),"degrees"

critical angle is 78.5 degrees
numerical aperture is 0.3
acceptance angle is 17.4 degrees

Example number 2, Page number 13.19

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

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

#Calculation
N=4.9*(d*NA/lamda)**2;     #total number of guided modes
Nf=N/2;                    #number of modes propagated inside fibre

#Result
print "total number of guided modes is",int(N)
print "number of modes propagated inside fibre is",int(Nf)

total number of guided modes is 490
number of modes propagated inside fibre is 245

Example number 3, Page number 13.19

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

#Variable declaration
d=5*10**-6;     #diameter(m)
n2=1.447;              #refractive index of cladding
n1=1.45;    #refractive index of core
lamda=1*10**-6;    #wavelength(m)

#Calculation
NA=math.sqrt(n1**2-n2**2);      #numerical aperture
N=4.9*(d*NA/lamda)**2;     #total number of guided modes

#Result
print "total number of guided modes is",int(N)
print "it is a single mode propagation"

total number of guided modes is 1
it is a single mode propagation

Example number 4, Page number 13.19

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

#Variable declaration
n1=1.46;    #refractive index of core
delta=0.05;    #refractive index difference

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

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

numerical aperture is 0.46

Example number 5, Page number 13.20

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=50;
n2=1.5;              #refractive index of cladding
n1=1.53;    #refractive index of core
lamda0=1;    #wavelength(micro m)

#Calculation
V_number=round(2*math.pi*a*math.sqrt(n1**2-n2**2)/lamda0,2);     #V number
n=V_number**2/2;     #maximum number of modes

#Result
print "V number is",V_number
print "maximum number of modes is",int(round(n))

V number is 94.72
maximum number of modes is 4486

Example number 6, Page number 13.20

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

#Variable declaration
a=100*10**-6;
NA=0.3;      #numerical aperture(m)
lamda=850*10**-9;    #wavelength(m)

#Calculation
V_number=round(2*math.pi**2*a**2*NA**2/lamda**2);     #number of modes

#Result
print "total number of modes is",int(2*V_number)

total number of modes is 49178

Example number 7, Page number 13.20

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=25*10**-6;
n1=1.48;    #refractive index of core
delta=0.01;    #refractive index difference
V=25;     #Vnumber

#Calculation
lamda=2*math.pi*a*n1*math.sqrt(2*delta)/V;      #cutoff wavelength(m)

#Result
print "cutoff wavelength is",round(lamda*10**6,3),"micro m"

cutoff wavelength is 1.315 micro m

Example number 8, Page number 13.20

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

#Variable declaration
V=2.405;     #Vnumber
lamda=1.3;    #wavelength(micro m)
NA=0.05;      #numerical aperture(m)

#Calculation
amax=V*lamda/(2*math.pi*NA);     #maximum value of core radius(micro m)

#Result
print "maximum value of core radius is",round(amax,2),"micro m"

maximum value of core radius is 9.95 micro m

Example number 9, Page number 13.21

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

#Variable declaration
NA=0.3;      #numerical aperture(m)
gama=45*math.pi/180;     #angle(radian)

#Calculation
thetaa=math.asin(NA);       #acceptance angle for meridional rays(radian)
thetaa=thetaa*180/math.pi;  #acceptance angle for meridional rays(degrees)
thetaas=math.asin(NA/math.cos(gama));     #acceptance angle for skew rays(radian)
thetaas=thetaas*180/math.pi;   #acceptance angle for skew rays(degrees)

#Result
print "acceptance angle for meridional rays is",round(thetaa,2),"degrees"
print "acceptance angle for skew rays is",round(thetaas,3),"degrees"
print "answer for acceptance angle for skew rays given in the book is wrong"

acceptance angle for meridional rays is 17.46 degrees
acceptance angle for skew rays is 25.104 degrees
answer for acceptance angle for skew rays given in the book is wrong

Example number 10, Page number 13.21

In [22]:
#importing modules
import math
from __future__ import division

#Variable declaration
delta=0.0196;         #relative refractive index difference
n1=1.53;              #refractive index of core

#Calculation
NA=n1*math.sqrt(2*delta);     #numerical aperture
theta=math.asin(NA);          #acceptance angle(radian)
theta=theta*180/math.pi;      #acceptance angle(degrees)

#Result
print "numerical aperture is",round(NA,3)
print "acceptance angle is",round(theta,3),"degrees"
print "answer for angle given in the book varies due to rounding off errors"

numerical aperture is 0.303
acceptance angle is 17.633 degrees
answer for angle given in the book varies due to rounding off errors

Example number 11, Page number 13.21

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

#Variable declaration
n2=1.465;             #refractive index of cladding
n1=1.480;             #refractive index of core
lamda=850*10**-9;     #wavelength(m)

#Calculation
delta=(n1**2-n2**2)/(2*n1**2);         #relative refractive index difference
a=2.405*lamda*10**6/(2*math.pi*n1*math.sqrt(2*delta));     #core radius(micro m)

#Result
print "core radius is",round(a,3),"micro m"
print "answer given in the book is wrong"

core radius is 1.548 micro m
answer given in the book is wrong

Example number 12, Page number 13.21

In [32]:
#importing modules
import math
from __future__ import division

#Variable declaration
n2=1.49;             #refractive index of cladding
n1=1.5;              #refractive index of core
a=25;                #core radius(micro m)

#Calculation
phic=math.asin(n2/n1);                  #angle(degrees)
l=2*a*math.tan(phic);                   #fibre length covered in 1 reflection(micro m)
n=10**6/l;                              #total number of reflections per metre
d=1/math.sin(phic);                     #total distance travelled by light(m)

#Result
print "total number of reflections per metre is",int(n)
print "total distance travelled by light is",round(d,4),"m"

total number of reflections per metre is 2321
total distance travelled by light is 1.0067 m

Example number 13, Page number 13.22

In [36]:
#importing modules
import math
from __future__ import division

#Variable declaration
alpha=1.85;          #index profile
a=25;                #core radius(micro m)
NA=0.21;             #numerical aperture
lamda=1.3;           #wavelength(micro m)

#Calculation
n=(alpha*2*math.pi**2*a**2*NA**2)/(lamda**2*(alpha+2));     #number of modes
N=2*n;               #total number of modes

#Result
print "total number of modes is",int(N)

total number of modes is 309

Example number 14, Page number 13.22

In [41]:
#importing modules
import math
from __future__ import division

#Variable declaration
L=10;        #transmission distance(km)
Pi=100;      #optical power(micro W)
Po=2;        #optical power output(micro W)

#Calculation
sa=round(10*math.log10(Pi/Po)/L,1);     #signal attenuation per unit length(dB km-1)
osa=sa*L;                    #overall signal attenuation(dB)

#Result
print "signal attenuation per unit length is",sa,"dB km-1"
print "overall signal attenuation is",int(osa),"dB"

signal attenuation per unit length is 1.7 dB km-1
overall signal attenuation is 17 dB

Example number 15, Page number 13.23

In [51]:
#importing modules
import math
from __future__ import division

#Variable declaration
L=10;        #transmission distance(km)
n1=1.55;     #refractive index of core
delta=0.026;  #relative refractive index difference
C=3*10**5;    

#Calculation
deltaT=L*n1*delta/C;    #dispersion(s)
blp=L/deltaT;           #bandwidth length product(Hz-km)

#Result
print "dispersion is",round(deltaT*10**9,1),"ns"
print "bandwidth length product is",round(blp/10**6,2),"*10**6 Hz-km"
print "answer for bandwidth given in the book is wrong"

dispersion is 1343.3 ns
bandwidth length product is 7.44 *10**6 Hz-km
answer for bandwidth given in the book is wrong