Chapter4 - Signal Degradation in fibers

Example 4.3.1, page 4-4

In [32]:
from __future__ import division
from numpy import sqrt, pi, log10
L=10        #fiber length in km
Pin=150*10**-6      #input power
Pout=5*10**-6       #output power
ln=20        #length of optical link
interval=1      #splices after interval of 1 km
l=1.2       #loss due to 1 splice
attenuation=10*log10(Pin/Pout) 
alpha=attenuation/L 
attenuation_loss=alpha*20 
splices_loss=(ln-interval)*l 
total_loss=attenuation_loss+splices_loss 
power_ratio=10**(total_loss/10) 
print "Signal attenuation is %.2f dBs.\nSignal attenuation is %.3f dB/Km.\nTotal loss in 20 Km fiber is %.2f dbs.\nTotal attenuation is %.2f dBs.\ninput/output ratio is %0.e." %(attenuation,alpha,attenuation_loss,total_loss,power_ratio) 
# Answer wrong for last part.

Signal attenuation is 14.77 dBs.
Signal attenuation is 1.477 dB/Km.
Total loss in 20 Km fiber is 29.54 dbs.
Total attenuation is 52.34 dBs.
input/output ratio is 2e+05.

Example 4.6.1, page 4-12

In [10]:
from numpy import exp
beta_c=8*10**-11      #isothermal compressibility
n=1.46      #refractive index
P=0.286     #photoelastic constat
k=1.38*10**-23  #Boltzmnn constant
T=1500      #temperature
L=1000      #length
lamda=1000*10**-9   #wavelength
gamma_r = 8*(3.14**3)*(P**2)*(n**8)*beta_c*k*T/(3*(lamda**4))       #computing coefficient
attenuation=exp(-gamma_r*L)         #computing attenuation
print "Attenuation due to Rayleigh scattering is %.3f." %(attenuation) 

Attenuation due to Rayleigh scattering is 0.794.

Example 4.6.2, page 4-12

In [17]:
beta_c=7*10**-11         #isothermal compressibility
n=1.46      #refractive index
P=0.29     #photoelastic constat
k=1.38*10**-23  #Boltzmnn constant
T=1400      #temperature
L=1000      #length
lamda=0.7*10**-6   #wavelength
gamma_r = 8*(3.14**3)*(P**2)*(n**8)*beta_c*k*T/(3*(lamda**4))       #computing coefficient
attenuation=exp(-gamma_r*L)         #computing attenuation
gamma_r=gamma_r
print "Raleigh Scattering corfficient is %.3e per meter" %(gamma_r) 
#Attenuation is not calcualted in textbook"
print "Attenuation due to Rayleigh scattering is %.3f" %(attenuation) 
#answer for Raleigh Scattering corfficient in the book is given as 0.804d-3, deviation of 0.003d-3

Raleigh Scattering corfficient is 8.074e-04 per meter
Attenuation due to Rayleigh scattering is 0.446

Example 4.7.1, page 4-17

In [19]:
d=5      #core diameter
alpha=0.4   #attenuation
B=0.5     #Bandwidth
lamda=1.4    #wavelength
PB=4.4*10**-3*d**2*lamda**2*alpha*B       #computing threshold power for SBS
PR=5.9*10**-2*d**2*lamda*alpha       #computing threshold power for SRS
PB=PB*10**3 
PR=PR*10**3 
print "Threshold power for SBS is %.1f mW.\nThreshold power for SRS is %.3f mW." %(PB,PR) 
#NOTE - Calculation error in the book while calculating threshold for SBS.
#Also, while calculating SRS, formula is taken incorrectly, 
#Bandwidth is multiplied in second step, which is not in the formula.") 

Threshold power for SBS is 43.1 mW.
Threshold power for SRS is 826.000 mW.

Example 4.8.1, page 4-18

In [22]:
n1=1.5      #refractive index of core
delta=0.03/100      #relative refractive index
lamda=0.82*10**-6       #wavelength
n2=sqrt(n1**2-2*delta*n1**2)       #computing cladding refractive index
Rc=(3*n1**2*lamda)/(4*3.14*(n1**2-n2**2)**1.5)      #computing critical radius
Rc=Rc*10**3 
print "Critical radius is %.f micrometer." %(Rc)  

Critical radius is 9 micrometer.

Example 4.8.2, page 4-20

In [24]:
n1=1.45      #refractive index of core
delta=3.0/100      #relative refractive index
lamda=1.5*10**-6       #wavelength
a=5*10**-6      #core radius
n2=sqrt(n1**2-2*delta*n1**2)       #computing cladding refractive index
Rc=(3*n1**2*lamda)/(4*3.14*(n1**2-n2**2)**0.5)      #computing critical radius for single mode
Rc=Rc*10**6 
print "Critical radius is %.2f micrometer" %(Rc) 
lamda_cut_off= 2*3.14*a*n1*sqrt(2*delta)/2.405 
RcSM= (20*lamda/(n1-n2)**1.5)*(2.748-0.996*lamda/lamda_cut_off)**-3       #computing critical radius for single mode
RcSM=RcSM*10**6 
print "Critical radius for single mode fiber is %.2f micrometer." %(RcSM) 
#Calculation error in the book.(2.748-0.996*lamda/lamda_cut_off)**-3  in this term raised to -3 is not taken in the book.

Critical radius is 2.12 micrometer
Critical radius for single mode fiber is 226.37 micrometer.

Example 4.13.1, page 4-28

In [26]:
lamda=1550*10**-9 
lamda0=1.3*10**-6 
s0=0.095 
Dt=lamda*s0/4*(1-(lamda0/lamda)**4)      #computing material dispersion
Dt=Dt*10**9 
print "Material dispersion at 1550 nm is %.1f ps/nm/km" %Dt
#answer in the book is wrong.

Material dispersion at 1550 nm is 18.6 ps/nm/km

Example 4.14.1, page 4-33

In [27]:
tau=0.1*10**-6      #pulse broadning
dist=20*10**3       #distance
Bopt=1/(2*tau)      #computing optical bandwidth
Bopt=Bopt*10**-6 
dispertion=tau/dist         #computing dispersion
dispertion=dispertion*10**12 
BLP=Bopt*dist       #computing Bandwidth length product
BLP=BLP*10**-3 
print "optical bandwidth is %d MHz.\nDispersion per unit length is %d ns/km.\nBandwidth length product is %d MHz.km." %(Bopt,dispertion,BLP) 

optical bandwidth is 5 MHz.
Dispersion per unit length is 5 ns/km.
Bandwidth length product is 100 MHz.km.

Example 4.15.1, page 4-34

In [29]:
RSW=0.0012      #relative spectral width
lamda=0.90*10**-6   #wavelength
L=1         #distance in km (assumed)
P=0.025     #material dispersion parameter
c=3*10**5       #speed of light in km/s
M=10**3*P/(c*lamda)      #computing material dispersion
sigma_lamda=RSW*lamda 
sigmaM=sigma_lamda*L*M*10**7         #computing RMS pulse broadning
sigmaB=25*L*M*10**-3 
print "Material dispersion parameter is %.2f ps/nm/km.\nRMS pulsr broadning when sigma_lamda is 25 is %.1f ns/km.\nRMS pulse broadning is %.2f ns/km." %(M,sigmaB,sigmaM) 
#answer in the book for RMS pulse broadning is wrong.

Material dispersion parameter is 92.59 ps/nm/km.
RMS pulsr broadning when sigma_lamda is 25 is 2.3 ns/km.
RMS pulse broadning is 1.00 ns/km.

Example 4.17.1, page 4-37

In [31]:
L=10         #length of optical link
n1=1.49      #refractive index
c=3*10**8       #speed of light
delta=1.0/100         #relative refractive index
delTS=L*n1*delta/c      #computing delay difference
delTS=delTS*10**12 
sigmaS=L*n1*delta/(2*sqrt(3)*c)     #computing rms pulse broadning
sigmaS=sigmaS*10**12 
B=1/(2*delTS)         #computing maximum bit rate
B=B*10**3 
B_acc=0.2/(sigmaS)      #computing accurate bit rate
B_acc=B_acc*10**3 
BLP=B_acc*L       #computing Bandwidth length product
print "Delay difference is %d ns.\nRMS pulse broadning is %.1f ns.\nBit rate is %.1f Mbit/s.\nAccurate bit rate is %.3f Mbits/s.\nBandwidth length product is %.1f MHz.km" %(delTS,sigmaS,B,B_acc,BLP) 
#answer for maximum bit rate is given as 1.008 Mb/s, deviation of 0.008 Mb/s.

Delay difference is 496 ns.
RMS pulse broadning is 143.4 ns.
Bit rate is 1.0 Mbit/s.
Accurate bit rate is 1.395 Mbits/s.
Bandwidth length product is 13.9 MHz.km