# Chapter 2 : Optical fiber waveguides¶

## Example 2.1, page 19¶

In :
import math

#Variable declaration
n1=1.50                   #core refractive index

#Calculation
phic=math.asin(n2/n1)*180/(math.pi)     #critical angle at core cladding
NA=math.sqrt(n1**2-n2**2)               #numerical aperture
phia=math.asin(NA)*180/math.pi          #acceptance angle in air

#Result
print'(a) Critical angle at the core-cladding = %.1f°'%phic
print'(b) NA for the fiber = %.2f'%NA
print'(c) Acceptance angle in air for the fiber = %.1f°'%phia

(a) Critical angle at the core-cladding = 78.5°
(b) NA for the fiber = 0.30
(c) Acceptance angle in air for the fiber = 17.4°


## Example 2.2, page 20¶

In :
import math

#Variable declaration
delta=0.01                           #relative refractive index = 1%
n1=1.46                               #core index

#Calculation
NA=n1*math.sqrt(2*delta)             #numerical aperture
zeta=math.pi*(NA)**2                 #solid acceptance angle
n12=1-delta                          #ratio of(n2/n1)
phic=math.asin(n12)*180/math.pi      #critical angle

#Result
print'Numerical aperture (NA) = %.2f'%NA
print'Critical angle at core-cladding = %.1f°'%phic

Numerical aperture (NA) = 0.21
Solid acceptance angle =  0.13 rad
Critical angle at core-cladding = 81.9°


## Example 2.3, page 23¶

In :
import math

#variable declaration
NA=0.4                                              #numerical aperture
y=50*math.pi/180                                    #angle between projection of the ray and radius of fibre of core (radians)

#Calculation
phia1=math.asin(NA)*180/math.pi                     #acceptance angle for meridional rays
phia2=math.asin(NA/(math.cos(y)))*180/math.pi       #acceptance angle for skew rays

#Result
print'Acceptance angle for meridional rays = %.1f°'%phia1
print'Acceptance angle for skew rays = %.1f°'%phia2
print"Therefore, acceptance angle for the skew rays is about 15° greater thanthe corresponding angle for meridional rays"

Acceptance angle for meridional rays = 23.6°
Acceptance angle for skew rays = 38.5°
Therefore, acceptance angle for the skew rays is about 15° greater thanthe corresponding angle for meridional rays


## Example 2.4, page 45¶

In :
import math

#variable declaration
n1=1.48                                              #core index
delta=1.5/100                                        #relative refractive index = 1.5%
h=0.85*10**-6                                        #operating wavelength

#Calculation
V=(2*math.pi*a*n1*math.sqrt(2*delta))/h              #normalized frequency for the fiber
Ms=(V**2)/2                                          #no of guided modes

#Result
print 'Normalised frequency, V = %.1f'%V
print'Total number of guided modes, Ms = %d'%round(Ms)

Normalised frequency, V = 75.8
Total number of guided modes, Ms = 2872


## Example 2.5, page 54¶

In :
import math

#variable declaration
NA=0.2                                            #numerical aperture
h=1*10**-6                                        #operating wavelength

#Calculation
V=(2*math.pi*a*NA)/h                             #normalized frequency for the fiber
Mg=(V**2)/4                                      #no of guided modes gor parabolic profile

#Result
print 'Normalised frequency, V = %.1f'%V
print'Total number of guided modes, Mg = %d'%round(Mg)

Normalised frequency, V = 31.4
Total number of guided modes, Mg = 247


## Example 2.6, page 55¶

In :
import math
#variable declaration
n1=1.48                                                         #core index
h=0.85*10**-6                                                   #operating wavelength
V=2.4                                                           #normalized frequency for the fiber
delta=1.5/100                                                   #relative refractive index (RRI)= 1.5%
delta1=delta/10                                               #RRI difference reduced by 10

#Calculation
d=2*a
d1=2*a1

#Result
print 'Maximum core diameter for relative refractive index of 1.5 percent  = ',round((d*10**6),2),"um"
print "Maximum core diameter for relative refractive index  = ",round(d1*10**6),"um"

Maximum core diameter for relative refractive index of 1.5 percent  =  2.53 um
Maximum core diameter for relative refractive index  =  8.0 um


## Example 2.7, page 2.7¶

In :
import math
#variable declaration
n1=1.5                                                          #core index
delta=0.01                                                      #relative refractive index (RRI)= 1%
h=1.3*10**-6                                                    #operating wavelength
alph=2

#Calculation
V=(2.4)*math.sqrt(1+(2/alph))                                   #normalized frequency for the fiber
d=2*a

#Result
print "Maximum core diameter for relative refractive index  = ",round(d*10**6,1),"um"

Maximum core diameter for relative refractive index  =  6.6 um


## Example 2.8, page 60¶

In :
import math
#Variable declaration
n1=1.46                                                        #core index
delta=0.25/100                                                 #relative refractive index (RRI)= 0.25%

#Calculation
hc=(2*math.pi*a*n1*math.sqrt(2*delta))/2.405                    #cutoff wavelength

#Result
print 'Fibre is single moded to a wavelength = ',round(hc*10**9),'nm'

Fibre is single moded to a wavelength =  1214.0 nm


## Example 2.10, page 69¶

In :
import math
#Variable declaration
wo=5.8*10**-6                                   #spot size
V=2.2                                         #normalized frequency

#Calculation
d=2*a

#Result
print'Fibre core diameter = ',round(d*10**6,1),"um"

Fibre core diameter =  9.9 um


## Example 2.11, page 73¶

In :
import math
#Variable declaration
h=1.30*10**-6                            #operating wavelength
hc=1.08*10**-6                            #cutoff wavelength
theta=12                                   #in angle (degree)

#Calculation
Veff=2.405*hc/h                                               #effective normalised frequency
wo=3.81*10**-6*(0.6043+(1.755*Veff**-1.5)+(2.78*Veff**-6))    #spot size

#Result
print 'Spot size = ',round(wo*10**6,2),'um'

Spot size =  4.84 um


## Example 2.12, page 74¶

In :
import math

#Variable declaration
wo=5.2*10**-6                                     #spot size
n1=1.485                                          #core index
hc=1.190*10**-6                                   #cutoff wavelength

#Calculation

ESI relative refractive index difference =  0.21 %