Chapter5 - Single mode fibers

Example 5.1 : Page 86

In [2]:
from __future__ import division
from math import pi, sqrt
#w and wp
n=1.46#core refractive index
d=0.003#differnce in core-cladding refrative index
a=4#core radius in micro meter
h1=1.30# inmicro meter
h2=1.55#in micro meter
v1=((2*pi*(a*10**-6))*n*sqrt(2*(d)))/(h1*10**-6)#normalised frequency parameter
v2=((2*pi*(a*10**-6))*n*sqrt(2*(d)))/(h2*10**-6)#normalised frequency parameter
w1=(a*10**-6)*(0.65+((1.619)/(v1)**(3/2))+(2.879/(v1)**6))#in meter
wp1=w1-(a*10**-6)*(0.016+((1.567)/(v1)**7))#in micro meter
w2=(a*10**-6)*(0.65+((1.619)/(v2)**(3/2))+(2.879/(v2)**6))#in meter
wp2=w2-(a*10**-6)*(0.016+((1.567)/(v2)**7))#in micro meter
print " w = %0.4f"%(w1*10**6),"and wp = %0.4f"%(wp1*10**6),"micro meter when wavelength is 1.30 micro meter"
print " w = %0.4f"%(w2*10**6),"and wp = %0.4f"%(wp2*10**6),"micro meter when wavelength is 1.55 micro meter"

 w = 4.7086 and wp = 4.6184 micro meter when wavelength is 1.30 micro meter
 w = 5.5109 and wp = 5.3570 micro meter when wavelength is 1.55 micro meter

Example 5.2 : Page 88

In [3]:
from __future__ import division
from math import pi, sqrt
#difference between propogation constant and modal birefringence
print "part (a)"
bl=10#beat length in cm
h=1#in micro meter
db=((2*pi)/(bl*10**-2))#in m**-1
print "difference between propogation constant = %0.2f m**-1"%db
print "part (b)"
mb=db*((h*10**-6)/(2*pi))#modal birefringence
print "modal birefringence = %0.e"%mb
#answer is approximately equal to the answer in the book

part (a)
difference between propogation constant = 62.83 m**-1
part (b)
modal birefringence = 1e-05

Example 5.3 : Page 93

In [4]:
from __future__ import division
from math import pi, sqrt
#waveguide dispersion factor
n=1.45#core refractive index
d=0.003#differnce in core-cladding refrative index
n2=1.45*(1-d)#cladding refractive index
d1=8.2#core diameter in micro meter
a=d1/2#core radius in micro meter
h1=1.30# inmicro meter
h2=1.55#in micro meter
v1=(2*pi*a*n*sqrt(2*d))/h1#normalised frequency parameter
v2=((2*pi*(a))*n*sqrt(2*(d)))/(h2)#normalised frequency parameter
v1dv=0.080+0.549*(2.834-v1)**2#
v2dv=0.080+0.549*(2.834-v2)**2#
c=3*10**8# in m/s
dw1=-((n2*d*v1dv)/(c*h1))*10**12#waveguide dispersion factor in ps nm**-1 km**-1
dw2=-((n2*d*v2dv)/(c*h2))*10**12#waveguide dispersion factor in ps nm**-1 km**-1
print " waveguide dispersion factor = %0.3f"%(dw1),"ps nm**-1 km**-1 at wavelength 1.3 micro meter"
print " waveguide dispersion factor = %0.3f"%(dw2),"ps nm**-1 km**-1 at wavelength 1.55 micro meter"

 waveguide dispersion factor = -3.149 ps nm**-1 km**-1 at wavelength 1.3 micro meter
 waveguide dispersion factor = -5.537 ps nm**-1 km**-1 at wavelength 1.55 micro meter

Example 5.4 : Page 95

In [5]:
from __future__ import division
from math import pi, sqrt
#diameter of the core
c=3*10**8#in m/s
dm=6#material dispersion in ps nm**-1 km**-1
h=1.55#in micro meter
n1=1.45#core refrative index
d=0.005#differnce
n2=n1*(1-d)#cladding refrative index
x=((-dm/(((-n2*d)/(c*h))*10**12))-0.080)/0.549#
v=-(sqrt(x)-2.834)#
d=((v*h)/(pi*n1*sqrt(2*d)))#diameter in micro meter
print "diameter of the core = %0.2f micro meter"%d

diameter of the core = 7.10 micro meter

Example 5.5 : Page 100

In [6]:
#splice loss
h1=1.30#in micro meter
wp1=4.6155#in micro meter
h2=1.55#in micro meter
wp2=5.355#in micro meter
sl1=4.34*(1/wp1)**2#splice loss in dB
sl2=4.34*(1/wp2)**2#splice loss in dB
print "splice loss = %0.2f dB when wavelength is 1.30 micro meter"%sl1
print "splice loss = %0.2f dB when wavelength is 1.55 micro meter"%sl2

splice loss = 0.20 dB when wavelength is 1.30 micro meter
splice loss = 0.15 dB when wavelength is 1.55 micro meter