Chapter 9: Optical Fibers

Example 9.1,Page number 296

In [5]:
import math

#given

n2=1.35;            #refractive index
n1=1.4;             #refractive index
Wo=math.degrees(math.asin(n2/n1));    #in radians
print"Critical Angle,Wo =",round(Wo,4),"degree";
NA=sqrt(n1**2-n2**2);
print"Numerical Aperture,NA =",round(NA,4);
Wa=math.degrees(math.asin(NA));       #in radians
print"Angle of acceptance,Wa =",round(Wa,4),"degree";

Critical Angle,Wo = 74.6411 degree
Numerical Aperture,NA = 0.3708
Angle of acceptance,Wa = 21.7656 degree

Example 9.2,Page number 300

In [7]:
import math

#given

Po=8;           #in mW
Pi=50.;         #in mW
l=15;           #in km
TA=-10*math.log10(Po/Pi);
print"Total fibre Attenuation,L =",round(TA,4),"dB/",l,"km";
Alpha=TA/l;     
print"Alpha is =",round(Alpha,4),"dB/km";

Total fibre Attenuation,L = 7.9588 dB/ 15 km
Alpha is = 0.5306 dB/km

Example 9.3,Page number 300

In [9]:
import math

#given

Po=10.;            #in mW
Pi=150;            #in mW
Alpha=0.8;         #in dB/km
TA=-10*math.log10(Po/Pi);
print" Total fibre Attenuation,L =",round(TA,4),"dB";
l=TA/Alpha;
print" maximum length is,l =",round(l,4),"km";

#Round off Variations appear

 Total fibre Attenuation,L = 11.7609 dB
 maximum length is,l = 14.7011 km

Example 9.4,Page number 302

In [10]:
import math

#given

B=92*10**-12;         #in m**2/N
Tf=1550;              #in K
n=1.46;               #refractive index
p=0.29;
K=1.38*10**-23;       #in J/K
l=1;             #in km
L1=630;          #in nm
L2=1330;         #in nm
L3=1550;         #in nm
print"Rayleight scattering coefficient";
Y1=8*math.pi**3*n**8*p**2*B*K*Tf/3/(L1*10**-9)**4;
Y2=8*math.pi**3*n**8*p**2*B*K*Tf/3/(L2*10**-9)**4;
Y3=8*math.pi**3*n**8*p**2*B*K*Tf/3/(L3*10**-9)**4;  
print"for L1= 630nm, is","{0:.3e}".format(Y1);
print"for L2= 1330nm, is","{0:.3e}".format(Y2);
print"for L3= 1550nm, is","{0:.3e}".format(Y3);
#Misprinted answer

print"Rayleight scattering attenuation factor";
Fr1=math.e**-(Y1*l*10**3);
Fr2=math.e**-(Y2*l*10**3);
Fr3=math.e**-(Y3*l*10**3);
print"for Y1=  0.00179 is",round(Fr1,4);
print"for Y2=  0.00009 is",round(Fr2,4);
print"for Y3=  0.0000182 is",round(Fr3,4);


print"Rayleight scattering attenuation";
Ar1=10*math.log10(Fr1**-1);
Ar2=10*math.log10(Fr2**-1);
Ar3=10*math.log10(Fr3**-1);
print"for Ar1=  0.17 is",round(Ar1,4),"dB/km";
print"for Ar2=  0.91 is",round(Ar2,4),"dB/km";
print"for Ar3=  0.98 is",round(Ar3,4),"dB/km";
#For L3 answers in book are misprinted

Rayleight scattering coefficient
for L1= 630nm, is 1.793e-03
for L2= 1330nm, is 9.029e-05
for L3= 1550nm, is 4.895e-05
Rayleight scattering attenuation factor
for Y1=  0.00179 is 0.1664
for Y2=  0.00009 is 0.9137
for Y3=  0.0000182 is 0.9522
Rayleight scattering attenuation
for Ar1=  0.17 is 7.7886 dB/km
for Ar2=  0.91 is 0.3921 dB/km
for Ar3=  0.98 is 0.2126 dB/km

Example 9.5,Page number 304

In [12]:
import math

#given

L=850;          #in nm
L1=0.850;       #converted L in micrometer for using in given formula
A=0.5;          #in dB/km
d=5;            #in micrometer
Bw=1;           #in Gz
Po=4.4*10**-3*A*Bw*L1**2*d**2;
print"Po(Th) =",round(Po,4),"W";
print"Therefore,Po(Th) =",round(Po*1000,4),"mW";

Po(Th) = 0.0397 W
Therefore,Po(Th) = 39.7375 mW

Example 9.6,Page number 304

In [13]:
import math

#given

L=1330;         #in nm
L1=1.330;       #converted L in micrometer for using in given formula
A=0.5;          #in dB/km
d=5;            #in micrometer
Bw=1;           #in Gz
Po=4.4*10**-3*A*Bw*L1**2*d**2;
print"Po(Th) =",round(Po,4),"W";
print"Therefore,Po(Th) =",round(Po*1000,4),"mW";

Po(Th) = 0.0973 W
Therefore,Po(Th) = 97.2895 mW

Example 9.7,Page number 304

In [14]:
import math

#given

L=1550;         #in nm
L1=1.550;       #converted L in micrometer for using in given formula
A=0.5;          #in dB/km
d=5;            #in micrometer
Bw=1;           #in Gz
Po=4.4*10**-3*A*Bw*L1**2*d**2;
print"Po(Th) =",round(Po,4),"W";
print"Therefore,Po(Th) =",round(Po*1000,4),"mW";

Po(Th) = 0.1321 W
Therefore,Po(Th) = 132.1375 mW

Example 9.8,Page number 304

In [17]:
import math

#given

L=850;          #in nm
L1=0.850;       #converted L in micrometer for using in given formula
A=0.5;          #in dB/km
d=8;            #in micrometer
Bw=1;           #in Gz
Po=4.4*10**-3*A*Bw*L1**2*d**2;
print"Po(Th) =",round(Po,4),"W";
print"Therefore,Po(Th) =",round(Po*1000,4),"mW";

Po(Th) = 0.1017 W
Therefore,Po(Th) = 101.728 mW

Example 9.9,Page number 304

In [16]:
import math

#given

L=850;          #in nm
L1=0.850;       #converted L in micrometer for using in given formula
A=0.5;          #in dB/km
d=10;           #in micrometer
Bw=1;           #in Gz
Po=4.4*10**-3*A*Bw*L1**2*d**2;
print"Po(Th) =",round(Po,4),"W";
print"Therefore,Po(Th) =",round(Po*1000,4),"mW";

Po(Th) = 0.159 W
Therefore,Po(Th) = 158.95 mW

Example 9.10,Page number 305

In [18]:
import math

#given

L=850.;         #in nm
L1=L/1000;      #converted L in micrometer for using in given formula
A=0.4;          #in dB/km
d=5;            #in micrometer
Po=5.9*10**-2*A*L1*d**2;
print"Po(Th) =",round(Po,4),"W";
print"Therefore,Po(Th) =",round(Po*1000,4),"mW";

Po(Th) = 0.5015 W
Therefore,Po(Th) = 501.5 mW

Example 9.11,Page number 305

In [21]:
import math

#given

L=1330.;          #in nm
L1=L/1000;        #converted L in micrometer for using in given formula
A=0.4;            #in dB/km
d=5;              #in micrometer
Po=5.9*10**-2*A*L1*d**2;
print"Po(Th) =",round(Po,4),"W";
print"Therefore,Po(Th) =",round(Po*1000,4),"mW";  #unit in book is wrong

Po(Th) = 0.7847 W
Therefore,Po(Th) = 784.7 mW

Example 9.12,Page number 305

In [20]:
import math

#given

L=1550.;          #in nm
L1=L/1000;        #converted L in micrometer for using in given formula
A=0.4;            #in dB/km
d=5;              #in micrometer
Po=5.9*10**-2*A*L1*d**2;
print"Po(Th) =",round(Po,4),"W";
print"Therefore,Po(Th) =",round(Po*1000,4),"mW";   #unit in book is wrong

Po(Th) = 0.9145 W
Therefore,Po(Th) = 914.5 mW

Example 9.13,Page number 310

In [24]:
import math

#given

R=25;                #in nm
R1=25*10**-6;        #in m
L=1000;              #in nm
L1=10**-6;           #in m
NA=0.2;     
V=2*math.pi/L1*R1*NA;
print"Normalised frequency(V) =",round(V,4);
y=2.;                #for parabolic
Mmax=y/(y+2)*(V**2)/2;
print"Maximum number of modes is equal to =",round(Mmax,4);   #answer mistake in book

Normalised frequency(V) = 31.4159
Maximum number of modes is equal to = 246.7401

Example 9.14,Page number 313

In [26]:
import math

#given

Tp=0.25;             #in microsec
fB=0.529/Tp/10**-6;  #channel bitrate
fBw=fB;              #channel bandwidth = channel bitrate when zero ISI and RZ input data is modulated
print"Maximum operating bandwidth =",round(fBw*10**-6,4),"MHz";
L=50;            #in km
D=Tp*10**-6/L;   #Dispersion
print"Dispersion =",round(D*10**9,4),"ns/km";
fBwL=fBw*10**-6*L;            #bandwidth length product
print"Bandwidth length product(fBw*L) =",round(fBwL,4),"MHz/km";

Maximum operating bandwidth = 2.116 MHz
Dispersion = 5.0 ns/km
Bandwidth length product(fBw*L) = 105.8 MHz/km

Example 9.15,Page number 314

In [27]:
import math

#given

Tp=2;               #in microsec
fB=0.529/Tp/10**-6; #channel bit rate
fBw=fB;             #channel bandwidth = channel bitrate when zero ISI and RZ input data is modulated
print"Maximum operating bandwidth =",round(fBw*10**-6,4),"MHz";
L=50;            #in km
D=Tp*10**-6/L;   #Dispersion
print"Dispersion =",round(D*10**9,4),"ns/km";       #unit in book is wrong
fBwL=fBw*10**-6*L;            #bandwidth length product
print"Bandwidth length product(fBw*L) =",round(fBwL,4),"MHz/km";

Maximum operating bandwidth = 0.2645 MHz
Dispersion = 40.0 ns/km
Bandwidth length product(fBw*L) = 13.225 MHz/km

Example 9.16,Page number 314

In [29]:
import math

#given

Tp=5;                 #in microsec
fB=0.529/Tp/10**-6;   #channel bitrate
fBw=fB;               #channel bandwidth = channel bitrate when zero ISI and RZ input data is modulated
print"Maximum operating bandwidth =",round(fBw*10**-6,4),"MHz";
L=50;            #in km
D=Tp*10**-6/L;   #Dispersion
print"Dispersion =",round(D*10**6,4),"micro s/km";
fBwL=fBw*10**-6*L;            #bandwidth length product
print"Bandwidth length product(fBw*L) =",round(fBwL,4),"MHz/km";

Maximum operating bandwidth = 0.1058 MHz
Dispersion = 0.1 micro s/km
Bandwidth length product(fBw*L) = 5.29 MHz/km

Example 9.17,Page number 315

In [31]:
import math

#given

Slw=25;         #in nm
L=850;          #in nm         given
c=3*10**5;      #in km/s
ofmd=0.02;      #optical fiber material dispersion
Mdp=1./L/c*ofmd;         #answer mismatch due to differnt value chosen for calculation
print"Material Dispersion parameter Mdp =",round(Mdp*10**12,4),"ps/nm.km";
l=1;            #in km
dmd=Slw*l*Mdp;  #pulse chirping
print"pulse chirping dmd =",round(dmd*10**9,4),"ns/km";

Material Dispersion parameter Mdp = 78.4314 ps/nm.km
pulse chirping dmd = 1.9608 ns/km

Example 9.18,Page number 315

In [32]:
import math

#given

Slw=2;          #in nm
L=850;          #in nm         given
c=3*10**5;      #in km/s
ofmd=0.02;      #optical fiber material dispersion
Mdp=1./L/c*ofmd;   #answer mismatch due to differnt value chosen for calculation
print"Material Dispersion parameter Mdp =",round(Mdp*10**12,4),"ps/nm.km";
l=1;            #in km
dmd=Slw*l*Mdp;  #pulse chirping
print"pulse chirping dmd =",round(dmd*10**9,4),"ns/km";

Material Dispersion parameter Mdp = 78.4314 ps/nm.km
pulse chirping dmd = 0.1569 ns/km

Example 9.19,Page number 325

In [34]:
import math

#given

fb1=2.5;        #in Gb/s
D1=20;          #in ps/nm.km
D2=5;           #in ps/nm.km
fb2=D1/D2*fb1;      
print" fb2 =",fb2,"Gb/s";
#Values of D1 and D2 are conflicted in question ,however solution is correct 

 fb2 = 10.0 Gb/s

Example 9.20,Page number 325

In [35]:
import math

#given

fb1=2.5;            #in Gb/s
DV1=100;          #in GHz
DV2=50;          #in GHz
fb2=DV1/DV2*fb1;
print" fb2 =",fb2,"Gb/s";

 fb2 = 5.0 Gb/s

Example 9.21,Page number 332

In [36]:
import math

#given

L=400;          #in km
dAV=4;          #in ps/km
dTL=L*dAV;      #total chromatic dispersion
print"dTL =",round(dTL,4),"ps/nm.km";

dTL = 1600.0 ps/nm.km

Example 9.22,Page number 335

In [39]:
import math

#given

no=1;               #refractive index
n1=1.35;            #refractive index
Po=((n1-no)/(n1+no))**2;     #fresnal reflection
print" Po(refl)=",round(Po,4);
Lrefl=-10*math.log10(1-Po);      #attenuation loss
print"L(refl)=",round(Lrefl,4),"dB";

 Po(refl)= 0.0222
L(refl)= 0.0974 dB

Example 9.23,Page number 335

In [40]:
import math

#given

no=1;               #refractive index
n1=1.55;            #refractive index
Po=((n1-no)/(n1+no))**2;    #fresnal reflection
print"Fresnel reflective coefficient,Po(refl)=",round(Po,4);
Lrefl=-10*log10(1-Po);     #attenuation loss
print"Attenuation based on Fresnel reflective coefficient,L(refl)=",round(Lrefl,4),"dB";
Ltot=5*Lrefl;
print"Total link attenuation on Fresnel reflections,Ltotal =",round(Ltot,4),"dB";

Fresnel reflective coefficient,Po(refl)= 0.0465
Attenuation based on Fresnel reflective coefficient,L(refl)= 0.2069 dB
Total link attenuation on Fresnel reflections,Ltotal = 1.0344 dB

Example 9.24,Page number 336

In [57]:
import math

#given

n1=1;
n2=1.5;
a=25.;         #in micrometer
y=3.;          #in micrometer
Csim=16*(n1/n2)**2/math.pi/(1+(n1/n2))**4*(2*math.acos(y/2/a)-(y/a)*(1-(y/2/a)**2)**0.5); 

#lateral coupling coefficient
a=2*math.acos(y/2/a)-(y/a)*math.sqrt(1-(y/2./a)**2);
b=16*(n1/n2)**2/math.pi/(1+(n1/n2))**4;
print"Lateral coupling coefficient,Csim=",round(Csim,4);
Lsim=-10*math.log10(1-Csim);
print"Insertion Loss,Lsim=",round(Lsim,4),"dB";
#Answer wrong in book

Lateral coupling coefficient,Csim= 0.8512
Insertion Loss,Lsim= 8.2751 dB

Example 9.25,Page number 337

In [49]:
import math

#given

Alpha=2.;
a=25.;           #in micrometer
y=2.;            #in micrometer
Cgim=2/math.pi*(y/a)*(Alpha+2)/(Alpha+1);       #lateral coupling coefficient
print" Csim=",round(Cgim,4);
Lgim=-10*math.log10(1-Cgim);     #insertion loss
print" Insertion Loss,Lgim=",round(Lgim,4),"dB";

 Csim= 0.0679
 Insertion Loss,Lgim= 0.3054 dB

Example 9.26,Page number 339

In [52]:
import math

#given

n1=1.5;            #refractive index
n2=1.5;            #refractive index
W=2.5;             #in degree
NA1=0.3;
NA2=0.4;
Csim1=16*(n1/n2)**2/(1+(n1/n2)**4)*(1-n2*W/(180*NA1));   #angular coupling coefficient
#Answer wrong in book
print"Csim=",round(Csim1,4);
Lsim1=-10*math.log10(Csim1);
print"Insertion Loss,Lsim=",round(Lsim1,4),"dB";
Csim2=16*(n1/n2)**2/(1+(n1/n2)**4)*(1-n2*W/(180*NA2)); #angular coupling coefficient
#Answer wrong in book
print"Csim=",round(Csim2,4);
Lsim2=-10*math.log10(Csim2);
print"Insertion Loss,Lsim=",round(Lsim2,4),"dB";

Csim= 7.4444
Insertion Loss,Lsim= -8.7183 dB
Csim= 7.5833
Insertion Loss,Lsim= -8.7986 dB

Example 9.27,Page number 340

In [53]:
import math

#given

a=4;            #in micrometer
V=2.4;
aw=1;           #in degree
NA1=0.2;
n1=1.45;        #refractive index
y=1;            #in micrometer
omega=a*(0.65+1.62*V**-1.5+2.88*V**-6)/math.sqrt(2);
print"Normalised spot view (w)=",round(omega,4),"micrometer";
Lsml=2.17*(y/omega)**2;
print"Insertion loss due to lateral,Lsm=",round(Lsml,4),"dB";     #answer is wrong in book 
Lsmg=2.17*(aw*math.pi/180*omega*n1*V/a/NA1)**2;
print"Insertion loss due to angular,Lsm=",round(Lsmg,4),"dB";

print"Total Insertion loss,Lsmtotal=",round(Lsml+Lsmg,4),"dB";

Normalised spot view (w)= 3.1135 micrometer
Insertion loss due to lateral,Lsm= 0.2239 dB
Insertion loss due to angular,Lsm= 0.1213 dB
Total Insertion loss,Lsmtotal= 0.3451 dB

Example 9.28,Page number 340

In [56]:
import math

#given

a1=4.5;          #in micrometer
a2=4;            #in micrometer
V=2.1;
aw=1;            #in degree
NA=0.2;
n1=1.45;
y=1;             #in micrometer
w1=a1*(0.65+1.62*V**-0.5+2.88*V**-6)/math.sqrt(2);     #insertion loss
print"Wo1=",round(w1,4);
w2=a2*(0.65+1.62*V**-0.5+2.88*V**-6)/math.sqrt(2);     #insertion loss
print"Wo2=",round(w2,4);
Lintr=-10*math.log10(4*((w1/w2+w2/w1)**-2));           #toatl insertion loss at joint
print"Lintr=",round(Lintr,4),"dB";        #Answer wrong in book

Wo1= 5.7323
Wo2= 5.0954
Lintr= 0.0601 dB