# Chapter 5 : Optical fiber connection: joints, couplers and isolators¶

## Example 5.1, page 220¶

In :
import math

#Variable declaration
n1=1.5                                 #core refractive index
n=1.0                                  #refractive index of medium

#Calculation
r=((n1-n)/(n1+n))**2                   #magnitude of the Fresnel reflection at the fiber–air interface
Loss=-10*math.log10(1-r)               #loss in decibels at the single interface
Loss1=2*Loss                           #total loss

#Result
print'Total loss due to Fresnel reflection = %.2f dB'%Loss1         #loss due to fresnel resolution = 0.18X2 dB

Total loss due to Fresnel reflection = 0.35 dB


## Example 5.2, page 224¶

In :
import math

#Variable declaration
n1=1.5                                   #refractive index
y=5                                      #lateral offset of the fiber core axes in um

#Calculation
b=(16*n1**2)/(math.pi*(1+n1)**4)
c=math.acos(y*(2*a)**-1)
e=(y*a**-1)
f=math.sqrt(1-(y*(2*a)**-1)**2)
n=b*((2*c)-(e*f))                                             #coupling efficiency
Loss=-10*math.log10(n)                                         #insertion loss
na=(math.pi**-1)*((2*c)-(e*f))
Loss1=-10*math.log10(na)

#Result
print'(a) Insertion loss = %.3f dB'%Loss
print'(b) Insertion loss = %.2f dB'%Loss1

(a) Insertion loss = 0.945 dB
(b) Insertion loss = 0.59 dB


## Example 5.3, page 226¶

In :
import math

#Variable declaration
y=3                               #lateral misalignment in um

#Calculation
Lt=0.85*(y*a**-1)                     #misalignment loss for guided modes
n=1-Lt                            #coupling efficiency
Loss=-10*math.log10(n)            #insertion loss
Lt1=0.75*(y*a**-1)                    #both guided and leaky modes
n1=1-Lt1                          #coupling efficiency
Loss1=-10*math.log10(n1)          #insertion loss

#Result
print'(a) Uniform illumination of all guided modes only = %.2f dB'%Loss
print'(b) Uniform illumination of all guided and leaky modes = %.2f dB'%Loss1

(a) Uniform illumination of all guided modes only = 0.47 dB
(b) Uniform illumination of all guided and leaky modes = 0.41 dB


## Example 5.4, page 227¶

In :
import math

#Variable declaration
NA=0.2                                  #numerical aperture
n1=1.48                                 #core refractive index
NA1=0.4                                 #numerical aperture

#Calculation
na=((16*(n1)**2)/((1+n1)**4))*(1-(ang/(math.pi*NA)))               #angular coupling efficiency
Loss=-10*math.log10(na)                                            #insertion loss
na1=((16*(n1)**2)/((1+n1)**4))*(1-(ang/(math.pi*NA1)))             #angular coupling efficiency
Loss1=-10*math.log10(na1)                                          #insertion loss

#Result
print'Insertion loss at a joint (NA = 0.2) = %.2f dB'%Loss
print'Insertion loss at a joint (NA = 0.4) = %.2f dB'%Loss1         #in textbook, value is not calculated

Insertion loss at a joint (NA = 0.2) = 0.98 dB
Insertion loss at a joint (NA = 0.4) = 0.64 dB


## Example 5.5, page 231¶

In :
import math

#Variable declaration
V=2.4                                          #normalized frequency
NA=0.1                                         #numerical aperture
n1=1.46                                        #core refractive index
y=1                                            #lateral misalignment in um

#Calculation
w=a*(0.65+(1.62/V**1.5)+(2.88/V**6))/(2**0.5)  #normalized spot size
Tl=2.17*(y/w)**2                               #loss due to the lateral offset
Ta=2.17*((teta*w*n1*V)/(a*NA))**2              #loss due to angular misalignment
Tt=Tl+Ta                                       #total insertion loss

#Result
print'Total insertion loss = %.2f dB'%Tt

Total insertion loss = 0.72 dB


## Example 5.6, page 232¶

In :
import math

#Variable declaration

#Calculation
Loss=-10*math.log10(4*((w02/w01)+(w01/w02))**(-2))      #intrinsic loss

#Result
print'Intrinsic loss  = %.2f dB'%Loss

Intrinsic loss  = 0.35 dB


## Example 5.7, page 262¶

In :
import math

#Variable declaration
p1=60                                         #input port power
p2=0.004                                      #output port power
p3=26                                         #output port power
p4=27.5                                       #output port power

#Calculation
xloss=10*math.log10(p1/(p3+p4))              #Excess Loss
iloss1=10*math.log10(p1*p3**-1)                  #Insertion Loss at input
iloss2=10*math.log10(p1/p4)                  #Insertion Loss at output
cross=10*math.log10(p2/p1)                   #Crosstalk ratio
srat=((p3/(p3+p4))*100)                      #Split ratio

#Result
print'Excess Loss = %.1f dB'%xloss
print'Insertion Loss at input = %.2f dB'%iloss1
print'Insertion Loss at output = %.2f dB'%iloss2
print'Crosstalk ratio = %.1f dB'%cross
print'Split ratio = %.1f percent'%srat

Excess Loss = 0.5 dB
Insertion Loss at input = 3.63 dB
Insertion Loss at output = 3.39 dB
Crosstalk ratio = -41.8 dB
Split ratio = 48.6 percent


## Example 5.8, page 266¶

In :
import math

#Variable declaration
N=32                                           #total no of ports
pi=10**3                                       #optical power at input in micro-watt
pj=14                                          #optical power at input in micro-watt

#Calculation
sloss=10*math.log10(N)                               #splitting loss
xloss=10*math.log10(pi*(pj*N)**-1)                   #excess loss
tloss=sloss+xloss                                    #total loss
iloss=10*math.log10(pi*pj**-1)                       #insertion loss

#Result
print'Total loss = %.2f dB'%tloss
print'Insertion loss = %.2f dB'%iloss

Total loss = 18.54 dB
Insertion loss = 18.54 dB


## Example 5.9, page 268¶

In :
import math

#Variable declaration
p=16                                       #output ports
l=0.2                                      #excess loss with split ratio of 50%
l1=0.1                                     #splice loss

#Calculation
m=math.log(p)/math.log(2)                  #no of stages
xloss=(4*l)+(3*l1)                         #excess loss
sloss=10*math.log10(p)                     #split loss
iloss=sloss+xloss                          #insertion loss

#Result
print'Insertion loss = %.2f dB'%iloss

Insertion loss = 13.14 dB


## Example 5.10, page 277¶

In :
#Variable declaration
h=1.55*10**-6                      #optical signal wavelength
N=1.46                             #refractive index

#Calculation
v=h/(2*N)                           #grating period of the FBG

#Result
print'Grating period of FBG = %.2f um'%(v*10**6)

Grating period of FBG = 0.53 um

In :