Chapter 7: Optical Fibre Communication¶

Example 7.1, Page 206¶

In [1]:
from math import sqrt

#Variable declaration
NA = 0.24;#Numerical Aperture
delta = 0.014;

#Calculations & Results
n1 = (NA)/sqrt(2*delta);#Refractive index of first medium
print 'Refractive index of first medium is ',round(n1,4)
n2 = n1 - (delta*n1);#Refractive index of secong material
print 'Refractive index of secong material is ',round(n2,4)

Refractive index of first medium is  1.4343
Refractive index of secong material is  1.4142


Example 7.2, Page 207¶

In [2]:
from math import sqrt,asin,degrees

#Variable declaration
n1 = 1.49; # Refractive index of first medium
n2 = 1.44; # Refractive index of second medium

#Calculations & Results
def deg_to_dms(deg):
d = int(deg)
md = abs(deg - d) * 60
m = int(md)
sd = (md - m) * 60
sd=round(sd,2)
return [d, m, sd]

delta = (n1-n2)/n1; # Index difference
NA = n1* sqrt(2*delta);
print 'Numerical Aperture of fiber is',round(NA,3)
theta = degrees(asin(NA));
print 'Acceptance angle is ',deg_to_dms(theta),'degrees'

Numerical Aperture of fiber is 0.386
Acceptance angle is  [22, 42, 22.17] degrees


Example 7.3, Page 207¶

In [3]:
from math import sqrt,asin,degrees

#Variable declaration
NA = 0.15 ; # Numerical Aperture of fiber
n2 = 1.55; # Refractive index of cladding
n0w = 1.33; # Refractive index of water
n0a = 1; # Refractive index of air

#Calculations
def deg_to_dms(deg):
d = int(deg)
md = abs(deg - d) * 60
m = int(md)
sd = (md - m) * 60
sd=round(sd,2)
return [d, m, sd]

n1 = sqrt(NA**2 + n2**2);
NAW = (sqrt(n1**2 -n2**2))/n0w;
theta = degrees(asin(NAW));#Acceptance angle in water

#Result
print 'Acceptance angle in water is ',deg_to_dms(theta),'degrees'

Acceptance angle in water is  [6, 28, 32.55] degrees


Example 7.4, Page 216¶

In [4]:
from math import log10

#Variable declaration
l = 16; # Length of optical fiber in Km
Pi = 240e-6; # Mean optical length launched in optical fiber in Watts
Po = 6e-6; # Mean optical power at the output in watts

#Calculations&Results
alpha = 10*log10(Pi/Po);#Signal attenuation in fiber
print 'Signal attenuation in fiber',round(alpha),'dB'
alpha1 = alpha/l;#Signal attenuation per km of the fiber
print 'Signal attenuation per km of the fiber',round(alpha1),'dB/km'

Signal attenuation in fiber 16.0 dB
Signal attenuation per km of the fiber 1.0 dB/km


Example 7.5, Page 219¶

In [5]:
from math import pi,exp

#Variable declaration
Tf = 1400; # Fictive temperature of silicon in Kelvin
betai = 7e-11; # Isothermal compressibility square meter per newton
n = 1.46; # Refractive index of silicon
p = 0.286; # Photoelastic constant of silicon
lamda = 0.63e-6 # Wavelength in micrometer
kb = 1.38e-23 # Boltzmann constant in joule per kelvin
L = 1e3;

#Calculations
alphas = (8 * pi**3 * n**8 * p**2 * kb * Tf * betai)/(3 * lamda**4);#Rayleigh scattering coefficient
alphars = exp(-alphas * L);#Loss factor

#Results
print 'Rayleigh scattering coefficient is ',round(alphas/1e-3,2),'*10^-3 /m'
print 'Loss factor is',round(alphars,3)  #Answer varies due to rounding-off values

Rayleigh scattering coefficient is  1.2 *10^-3 /m
Loss factor is 0.302


Example 7.6, Page 222¶

In [6]:
#Variable declaration
alpha = 0.5; # Attenuation of single mode optical fibre in dB per km
lamda = 1.4; # Operating wavelength of optical fiber in micrometer
d = 8 # Diameter of fiber in micrometer
y = 0.6; # Laser source frequency width

#Calculations
pb = 4.4e-3 * d**2 * lamda**2 * alpha * y;#Threshold optical power in SBS
prs = 5.9e-2 * d**2 * lamda * alpha;#Threshold optical power in SRS

#Results
print 'Threshold optical power in SBS',pb/1e-3,'mW'
print 'Threshold optical power in SRS',prs,'W'

Threshold optical power in SBS 165.5808 mW
Threshold optical power in SRS 2.6432 W


Example 7.7, Page 225¶

In [7]:
from math import sqrt, pi

#Variable declaration
n1 = 1.50; # Refreactive index of forst medium
delta = 0.003; # Index difference
lamda = 1.6*1e-6; # Operating wavelength of fober in meter

#Calculations&Results
n2 = sqrt(n1**2-(2*delta*n1**2));#refractive index of cladding
#Substituting n2^2 = n1^2 - 2*delta*n1^2 in euation of Rc,
rc = (3*n1**2*lamda)/(4*pi*((2*delta*n1**2)**(3./2)));#The critical radius of curvature for which bending losses occur
print 'The critical radius of curvature for which bending losses occur is ',round(rc/1e-6,2),'um'

The critical radius of curvature for which bending losses occur is  547.92 um