# Chapter 3 : Transmission characteristics of optical fibers¶

## Example 3.1, page 89¶

In [1]:
import math

#Variable declaration
Pi=120*10**-6                                      #mean i/p power in uW
Po=3*10**-6                                        #mean o/p power in uW
L=8                                                #length of fibre in Km
a1=2                                               #loss in dB
L1=10                                              #length of fibre in Km
loss=9                                             #loss in dB

#Calculation
SA=10*math.log10(Pi/Po)                             #overall signal attenuation
a=SA/L                                              #signal attenuation per kilometer
al=a1*L1
SA1=al+loss                                         #signal attenuation for the 10KM link
P=10**(2.9)                                         #i/o power ratio, 2.9 is numeric value

#Result
print'Overall signal attenuation = ',round(SA),'dB'
print'Signal attenuation per kilometer = ',round(a),'dB Km^-1'
print'Overall signal attenuation for the 10KM link  = ',round(SA1),'dB'
print'Numeric value for i/o power ratio = %.1f' %P

Overall signal attenuation =  16.0 dB
Signal attenuation per kilometer =  2.0 dB Km^-1
Overall signal attenuation for the 10KM link  =  29.0 dB
Numeric value for i/o power ratio = 794.3


## Example 3.2, page 96¶

In [20]:
import math

#Variable declaration
Tf=1400                                        #tempreture in kelvin
K=1.381*10**-23                                #Boltzmann’s constant
Bc=7*10**-11                                   #isothermal compressibility
n=1.46                                         #refractive index
p=0.286                                        #refractive index
h1=0.63*10**-6                                 #wavelength
h2=10**-6                                      #wavelength
h3=1.3*10**-6                                  #wavelength
L=10**3                                        #length in km

#Calculation
a=(8*math.pi**3*n**8*p**2*Bc*K*Tf)/3
yr=a/h1**4                                     #Rayleigh scattering coefficient
Lk=math.exp(-yr*L)                             #transmission loss factor
At=10*math.log10(Lk**-1)                       #attenuation due to Rayleigh scattering
yr1=a/h2**4                                    #Rayleigh scattering coefficient
Lk1=math.exp(-yr1*L)                           #transmission loss factor
At1=10*math.log10(Lk1**-1)                     #attenuation due to Rayleigh scattering
yr2=a/h3**4                                    #Rayleigh scattering coefficient
Lk2=math.exp(-yr2*L)                           #transmission loss factor
At2=10*math.log10(Lk2**-1)                     #attenuation due to Rayleigh scattering

#Result
print'Attenuation due to Rayleigh scattering (in 0.63 μm)= %.1f dB km^-1'%(At)
print'Attenuation due to Rayleigh scattering (in 1.0 μm)= %.1f dB km^-1'%(At1)
print'Attenuation due to Rayleigh scattering (in 1.30 μm)= %.1f dB km^-1'%(At2)

Attenuation due to Rayleigh scattering (in 0.63 μm)= 5.2 dB
Attenuation due to Rayleigh scattering (in 1.0 μm)= 0.8 dB
Attenuation due to Rayleigh scattering (in 1.30 μm)= 0.3 dB


## Example 3.3, page 99¶

In [19]:
#Variable declaration
d=6                                                 #diameter in μm
h=1.3                                               #wavelength in μm
adb=0.5                                             #attenuation in dB
v=0.6

#Calculation

#result
print'Threshold optical power for SBS = %.1f mW'%(Pb*1000)
print 'Threshold optical power for SRS = %.2f W'%Pr

Threshold optical power for SBS = 80.3 mW
Threshold optical power for SRS = 1.38 W


## Example 3.4, page 101¶

In [36]:
import math

#Variable declaration
n1=1.5                                                 #refractive index
h=0.82*10**-6                                          #operating wavelength
delta=0.03                                             #relative refractive index difference
delta1=0.003                                           #relative refractive index difference
h1=1.55*10**-6                                         #operating wavelength
a=4*10**-6                                             #radius of core

#Calculation
n2=(n1**2)-(2*delta*n1**2)                               #refractive index
Rc=(3*n1**2*h)/(4*math.pi*(n1**2-n2)**0.5)               #multimode fiber critical radius of curvature
n21=(n1**2)-(2*delta1*n1**2)                             #refractive index
hc=(2*math.pi*a*n1*math.sqrt(2*delta1))/(2.405)          #cutoff wavelength for the single-mode fiber
b=20*h1/math.sqrt(0.043)
c=(2.748-(0.996*h1/hc))**-3
Rcs=b*c                                                  #critical radius of curvature for the single-mode

#Result
print'Multimode fiber critical radius of curvature = %.2f um'%(Rc*10**6)      #value given in the textbook is wrong
print'Single-mode fiber critical radius of curvature = %.2f um'%(Rcs*10**3)     #value given in the textbook is wrong

Multimode fiber critical radius of curvature = 1.20 um
Single-mode fiber critical radius of curvature = 0.05 um


## Example 3.5, page 109¶

In [51]:
import math

#Variable declaration
t=0.1*10**-6                           #total pulse time
d=15                                   #distance in Km

#Calculation
Bt=1/(2*t)                              #Maximum Bandwidth
D=t/d                                   #Pulse Dispersion
Bop=Bt*d                                #Bandwidth-length product

#Result
print'Maximum Bandwidth = %d Mhz'%(Bt/10**6)
print'Pulse Dispersion = %.2f ns per Km'%(D*10**9)
print'Bandwidth-length product = %d Mhz Km'%(Bop/10**6)

Maximum Bandwidth = 5 Mhz
Pulse Dispersion = 6.67 ns per Km
Bandwidth-length product = 75 Mhz Km


## Example 3.6, page 111¶

In [55]:
import math

#Variable declaration
b=0.025                                  #material dispersion
c=2.998                                  #speed of light (x 10^8)
h=85*10**6                                #wavelength dispersion parameter

#Calculation
M=b/(c*h)                                 #Material dispersion parameter
s=M*20                                    #RMS pulse broadening (1 Km)

#Result
print'Material dispersion parameter = %.1f ps n/m K/m'%(M*10**12)
print'RMS pulse broadening (1 Km) = %.2f ns K/m'%(s*10**9)

Material dispersion parameter = 98.1 ps n/m K/m
RMS pulse broadening (1 Km) = 1.96 ns K/m


## Example 3.7, page 112¶

In [66]:
import math

#Variable declaration
h=0.85*10**-6                        #wavelength
b=0.0012                             #relative spectral width
M=98.1*10**-12                       #material dispersion parameter

#Calculation
sh=b*h                               #relative spectral width
sm=sh*M*10**9                        #RMS pulse braodening

#Result
print'RMS pulse braodening (1 Km) = %.2f ns K/m'%(sm*10**9)

RMS pulse braodening (1 Km) = 0.10 ns K/m


## Example 3.8, page 117¶

In [7]:
import math

#Variable declaration
n1=1.5                                               #core refractive index
delt=0.01                                            #relative refractive index difference
c=2.998*10**8                                        #speed of light

#Calculation
Ts=(L*n1*delt)/c                                      #Delay difference
sc=(L*n1*delt)/(2*math.sqrt(3)*c)                     #RMS pulse broadening
Bt=1/(2*Ts)
Btm=0.2/sc                                            #Maximum bit rate using RMS pulse broadening
Bop=Btm*L                                             #Bandwidth-length product

#Result
print'(a) Delay difference = %d ns' %(Ts*10**9)
print'(b) RMS pulse broadening = %.1f ns' %(sc*10**9)
print'(c) Maximum bit rate using RMS pulse broadening = %.1f Mbit/s'%(Btm/10**6)
print'(d) Bandwidth-length product = %.1f Mhz km'%(Bop/10**9)

(a) Delay difference = 300 ns
(b) RMS pulse broadening = 86.7 ns
(c) Maximum bit rate using RMS pulse broadening = 2.3 Mbit/s
(d) Bandwidth-length product = 13.8 Mhz km


## Example 3.9, page 121¶

In [18]:
import math

#Variable declaration
sc=86.7                                              #RMS pulse broadening
L=10**3                                              #for 1 Km
n1=1.5                                               #core refractive index
delt=0.01                                            #relative refractive index difference
c=3*10**8                                            #speed of light

#Calculation
d=sc/L1                                              #for multimode step index fiber
sg=(L*n1*delt**2)/(20*math.sqrt(3)*c)                #gradient index fiber

#Result
print'RMS pulse broadening for multimode step index fiber = %.1f ns K/m'%(d)
print'RMS pulse broadening for gradient index fiber = %.1f ps K/m'%(sg*10**12)

RMS pulse broadening for multimode step index fiber = 14.5 ns K/m
RMS pulse broadening for gradient index fiber = 14.4 ps K/m


## Example 3.10, page 125¶

In [17]:
import math

#Variable declaration
sh=50                                        #rms spectral width
L=1                                          #1 Km
M=250*10**-12                                #material dispersion parameter
L1=10**3
NA=0.3                                       #numerical aperture
n1=1.45                                      #refractive index
c=2.998*10**8                                #speed of light

#Calculation
sm=sh*L*M                                      #rms pulse broadening
ss=(L1*NA**2)/(4*math.sqrt(3)*n1*c)            #rms pulse broadening per kilometer
st=math.sqrt(sm**2+ss**2)                      #total rms pulse broadening per kilometer
Bop=0.2/st                                     #bandwidth–length product

#Result
print'(a) Total RMS pulse broadening per Km = %.1f ns K/m'%(st*10**9)
print'(b) Bandwidth length product = %.1f Mhz Km'%(Bop*10**-6)

(a) Total RMS pulse broadening per Km = 32.4 ns K/m
(b) Bandwidth length product = 6.2 Mhz Km


## Example 3.11, page 131¶

In [15]:
#Variable declaration
h=1280                                     #wavelength in nm
S0=0.09*10**-12                            #dispersion slope
h0=1310                                    #zero dispersion wavlength in nm
h1=1550                                    #wavelength in nm
Dm=13.5*10**-12                            #material dispersion wavelength in m
Dp=0.4*10**-12                             #profile dispersion wavelength in m

#Calculation
a=h*S0/4
b=1-((h0*h**-1)**4)
Dt=a*b
Dt1=(h1*S0/4)*(1-(h0*h1**-1)**4)
Dw=Dt1-(Dm+Dp)

#Result
print'Total first order dispersion (1280 nm) = %.1f nm^-1 km^-1'%(Dt*10**12)
print'Total first order dispersion (1550 nm) = %.1f ps n/m K/m'%(Dt1*10**12)
print'Waveguide dispersion at wavelength 1.55um = %.1f ps n/m K/m'%(Dw*10**12)

Total first order dispersion (1280 nm) = -2.8 nm^-1 km^-1
Total first order dispersion (1550 nm) = 17.1 ps n/m K/m
Waveguide dispersion at wavelength 1.55um = 3.2 ps n/m K/m


## Example 3.12, page 143¶

In [2]:
import math

#Variable declaration
h=0.9*10**-6                               #peak wavelength
Lb=0.09                                    #beat length
s=10**-9                                   #spectral linewidth

#Calculation
Bf=h/Lb                                   #modal birefringence
Lbc=h**2/(Bf*s)                             #coherence length
Bxy=(2*math.pi)/Lb                        #difference between propagation constant

#Result
print'Modal birefringence, Bf = %.1f x 10^-5' %(Bf*10**5)
print'Coherence length, Lf = %.1f m' %Lbc
print'Difference between propagation constant = %.1f' %Bxy

Modal birefringence, Bf = 1.0 x 10^-5
Coherence length, Lf = 81.0 m
Difference between propagation constant = 69.8


## Example 3.13, page 144¶

In [1]:
#Variable declaration
h=1.3*10**-6                                 #fibers operating wavelength
Ls=0.7*10**-3                                #beat length
L=80                                         #beat length

#Calculation
Bf=h/Ls                                      #Fiber birefringence (0.7mm)
Bf1=h/L                                      #Fiber birefringence (80m)

#Result
print'Fiber birefringence (0.7mm) = %.2f x 10^-3'%(Bf*1000)
print'Fiber birefringence (80m) = %.2f x 10^-8'%(Bf1*10**8)

Fiber birefringence (0.7mm) = 1.86 x 10^-3
Fiber birefringence (80m) = 1.62 x 10^-8


## Example 3.14, page 150¶

In [1]:
import math

#Variable declaration
L=3.5*10**3                             #length of fiber
a=2*10**-3                              #tanh(h*L)

#Calculation
h=a/L                                   #mode coupling parameter

#Result
print'Mode coupling parameter = %.1f x 10^-7 m^-1'%(h*10**7)

Mode coupling parameter = 5.7 x 10^-7 m^-1

In [ ]: