# Chapter 5 Fiber optics¶

## Example 5.1 Page no 184¶

In [1]:
#Given
u1 =1.48                    #refractive index of cladding
u2 =1.5                     #refractive index of core
u =1

#Calculation
import math
theta = math.asin (u1/u2)*180/3.14
Fr =((u2 -u1)/u2)*100
A= math.asin ( math.sqrt (u2**2- u1**2) )
NA=math.sin(A)

#Result
print"(i) Critical angle is",round(theta,2),"degree"
print"(ii)Fractional refractive index is",round(Fr,2),"% of light"
print"(iv) Numerical aperture is",round(NA,2)

(i) Critical angle is 80.67 degree
(ii)Fractional refractive index is 1.33 % of light
(iii) Acceptance angle is 0.25 radian
(iv) Numerical aperture is 0.24


## Example 5.2 Page no 184¶

In [54]:
#Given
uf=1.5
A1=0.005
u=1.45

#Calculation
import math
uc=uf*(1-A1)
x=uc/uf
A=math.asin(x)*180/3.14
X=math.sqrt((uf**2)-(uc**2))
A11=math.asin(X)*180/3.14
Na=X

#Result
print"(a) Refractive index is",round(uc,2)
print"(b) Critical internal reflacting angle is",round(A,2),"Degree"
print"(c) Acceptance angle is",round(A11,4),"Degree"
print"(d) Numerical aperature is",round(Na,4)

(a) Refractive index is 1.49
(b) Critical internal reflacting angle is 84.31 Degree
(c) Acceptance angle is 8.6204 Degree
(d) Numerical aperature is 0.1498


## Example 5.3 Page no 185¶

In [3]:
#Given
NA =0.22                         # Numerical Aperatur e
Fr =0.012

#Calculation
import math
u1=NA/ math.sqrt (Fr *(2 - Fr))
u2= math.sqrt (u1**2- NA**2)

#result
print"Refractive index of core is",round(u1,2)

Refractive index of core is 1.42
Refractive index of clad is 1.41


## Example 5.4 Page no 185¶

In [6]:
#Given
u1 =1.62                     #refractive index of core
u2 =1.52                       # refractive index of clad

#Calculation
import math
A= math.asin ( math.sqrt (u1**2- u2**2) )*180/3.14
NA=math.sin(A*3.14/180.0)

#Result
print"Acceptance length is",round(A,2),"Degree"
print"Numerical aperature is",round(NA,4)

Acceptance length is 34.1 Degree
Numerical aperature is 0.5604


## Example 5.5 Page no 185¶

In [60]:
#Given
Na=0.20
u=1.59
uw=1.33

#Calculation
import math
uc=math.sqrt(Na**2+u**2)
NA=(math.sqrt(uc**2-u**2))/uw
A= math.asin(NA)*180/3.14

#Result
print"Acceptance angle is", round(A,1),"Degree"

Acceptance angle is 8.7 Degree


## Example 5.6 Page no 186¶

In [73]:
#Given
uc=1.45
uf=1.5
ua=1

#Calculation
import math
a=math.asin(uc/uf)*180/3.14
NA=math.sqrt(uf**2-uc**2)
N=math.asin(NA)*180/3.14

#Result
print"Critical angle is",round(a,1) ,"Degree"
print"Acceptance angle is",round(N,2),"Degree"
print"Nemerical aperature is",round(NA,3)

Critical angle is 75.2 Degree
Acceptance angle is 22.6 Degree
Nemerical aperature is 0.384


## Example 5.7 Page no 186¶

In [80]:
#Given
w=0.850                             #micro m
NA=0.22
a=50/2.0                            #micro m

#Calculation
import math
V=2*math.pi*a*NA/w
N=V**2/4.0

#Result
print"V numver is", round(V,2)
print"Number of modes is",round(N,2)

V numver is 40.66
Number of modes is 413.23


## Example 5.8 Page no 187¶

In [84]:
#Given
NA=0.16
uc=1.45
d=0.6                    #M
w=9*10**-7

#Calculation
import math
V=math.pi*d*NA/w

#Result
print"Normalized frequency is",round(V*10**-5,2),"*10**5"

Normalized frequency is 3.35 *10**5


## Example 5.9 Page no 187¶

In [93]:
#Given
uc=1.52
d=29*10**-6
a=0.007
w=1.3*10**-6

#Calculation
import math
u=uc-(uc*a)
V=(math.pi*d/w)*math.sqrt(uc**2-u**2)
N=V**2/2.0

#Result
print"(i) The fiber V-number is",round(V,2)
print"(ii) The number of modes is",round(N,0),"Modes"

(i) The fiber V-number is 12.58
(ii) The number of modes is 79.0 Modes


## Example 5.10 Page no 187¶

In [97]:
#Given
uf=1.48
uc=1.46
w=0.82                        #micro m
a=25

#Calculation
import math
V=2*math.pi*a*math.sqrt(uf**2-uc**2)/w
N=V**2/2.0

print"Number of modes is", round(N,0)

Number of modes is 1079.0


## Example 5.11 Page no 188¶

In [110]:
#Given
uf=1.48
u=1.46
c=3*10**8

#Calculation
a=(uf-u)/uf
af=uf*1000*a/(c*(1-a))
t=af*20

#Result
print"Dispersion per kilometer  of length is", round(af*10**9,1),"ns"
print"Total dispersion is",round(t*10**6,2),"ms"

Dispersion per kilometer  of length is 67.6 ns
Total dispersion is 1.35 ms


## Example 5.12 Page no 188¶

In [3]:
#Given
a=40                            #ps/nm-Km
w=1.5                            #nm
b=20                             #Km

#Calculation
A=a*w*b

#Result
print"Material dispersion is",A*10**-3,"ns"

Material dispersion is 1.2 ns


## Example 5.13 Page no 188¶

In [5]:
#Given
d=6.6                        #ps/nm-Km
w=1.5                          #nm
l=20                            #Km

#Calculation
import math
A=d*w*l

#Result
print"Wavelength dispersion is",A,"ps"

Wavelength dispersion is 198.0 ps


## Example 5.14 Page no 188¶

In [15]:
#Givem
uc=1.5
c=3.0*10**5                       #Km/s
z=6

#Calculation
u=uc/100.0
a=(uc*z/c)*(uc/(uc-u)-1)

#Result
print"Delay difference is", round(a*10**8,1),"m sec"

Delay difference is 30.3 m sec


## Example 5.15 Page no 189¶

In [21]:
#Given
a=3.5                        #db/Km
P1=0.5                       #mW
L=4
b=25.11

#Calculation
import math
N=a*L
P0=P1/b

#Result
print "Power level is",round(P0*10**3,1),"micro W"

Power level is 19.9 micro W


## Example 5.16 Page no 189¶

In [32]:
#Given
uc=1.558
a=0.026
z=10**3                        #m
c=3*10**8

#Calculation
D=uc*a*z/(c*(1-a))
D1=D*10

#Result
print"Dispersion/Km is",round(D*10**8,1),"n sec"
print"Total dispersion in 10 Km is",round(D1*10**8,1),"n sec"

Dispersion/Km is 13.9 n sec
Total dispersion in 10 Km is 138.6 n sec


## Example 5.17 Page no 189¶

In [37]:
#Given
uc=1.5
a=0.026
c=3*10**8

#Calculation
A=(uc*a**2*1000)/(8*c)

#Result
print"Maximum dispersion is",round(A*10**9,2),"ns/Km"

Maximum dispersion is 0.42 ns/Km