Chapter 3- Optical Fiber Fabrication

Example1: PgNo-83

In [1]:
import math

# variable declaration
n1=1.50 # core refractive index
n2=1.48 # cladding refractive index
y=1.3*math.pow(10,(-6))
m=1000 # the no. of models

# Calculations
v=math.sqrt(2*m)
a=(v*y)/(2*math.pi*(math.sqrt(pow(n1,2)-math.pow(n2,2)))*math.pow(10,6)) # core radius in micrometer

# Results
print ('%s %.2e %s' %(" core radius= ",a ,"micrometer"))

 core radius=  3.79e-11 micrometer

Example2: PgNo-83

In [2]:
import math

# Variable declaration
n1=1.505 # core refractive index
n2=1.502 # cladding refractive index

# Calculations
n_m=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture
y=1.3*math.pow(10,(-6))
v=2.4
a=(v*y)/(2*math.pi*(math.sqrt(math.pow(n1,2)-math.pow(n2,2))))*math.pow(10,6)# core radius in micrometer

# Results
print ('%s %.2f'%(" numerical aperture= ",n_m))
print ('%s %.3f %s' %("\n core radius= ",a,"micrometer"))

 numerical aperture=  0.09

 core radius=  5.228 micrometer

Example3: PgNo-84

In [3]:
import math
# Variable declaration

n1=1.5 # core refractive index
dl=0.01 # index difference
m=0 # for the dominant mode
v=0 # for the dominant mode
y=1.3 # in micrometer
a=5.0 # radius in micrometer

# Calculations
k=(2*math.pi)/y
b=math.pow(k,2)*math.pow(n1,2)-(2*k*n1*math.sqrt(2*dl))/a
B=math.sqrt(b) # propagation constant in rad/um

# Results
print ('%s %.3f %s' %(" propagation constant= ",B,"rad/um"))

 propagation constant=  7.221 rad/um

Example4: PgNo-86

In [4]:
# Printing the results
b=1/2 # propagtion constant
print (" normalised propagtion constant")
print ("\n B=(pow((b/k),2)-pow(n2,2))/(pow(n1,2)-pow(n2,2))")
print ("\n thus when b=1/2")
print ("\n B=k*sqrt(pow(n2,2)+b*(pow(n1,2)-pow(n2,2))")
print ("\n B=k*sqrt(pow(n1,2)-pow(n2,2)/2)")
print ("\n which gives its rms value")

 normalised propagtion constant

 B=(pow((b/k),2)-pow(n2,2))/(pow(n1,2)-pow(n2,2))

 thus when b=1/2

 B=k*sqrt(pow(n2,2)+b*(pow(n1,2)-pow(n2,2))

 B=k*sqrt(pow(n1,2)-pow(n2,2)/2)

 which gives its rms value

Example5: PgNo-87

In [5]:
import math

# Variable declaration
n1=3.6 #core refractive index
n2=3.3 # cladding refractive index
d=2.0 # thickness in um
y=0.8 # wavelength in um

# Calculations
m=(2*d*math.sqrt(math.pow(n1,2)-math.pow(n2,2))/y) # total no. of models allowed
M=math.ceil(m) # total no. of models allowed

print " Total no. of models allowed= ",int(M)

 Total no. of models allowed=  8

Example6: PgNo-88

In [6]:
import math

# Initialisation of variables
n1=1.48 # core refractive index
a=40*(math.pow(10,-6)) #core radius in meter
dl=0.015 # index difference
y=0.85*(math.pow(10,-6)) # wavelength in um

# Calculations
v=(2*math.pi*a*n1*math.sqrt(2*dl))/y # normalised frequency
M=math.pow(v,2)/2
m=math.ceil(M) # the total no. of guided  modes

# Results
print ('%s %.2f' %(" normalised frequency= ",v))
print "\n The total no. of guided  modess = ",int(m)

 normalised frequency=  75.80

 The total no. of guided  modess =  2873

Example7: PgNo-89

In [7]:
import math

# Initialisation of variables
n1=1.46 # core refractive index
dl=0.015 # index difference
a=30*(math.pow(10,-6))# core radius in meter
y=0.85*(math.pow(10,-6)) #wavelength in um

# calcualtions
n2=n1-(n1*dl)# cladding refractive index
v=(2*math.pi*a*n1*math.sqrt(2*dl))/y # normalised frequency
M=math.pow(v,2)/2 # the total no. of guided  modes

# Results
print ('%s %.2f' %(" Cladding refractive index= ",n2))
print ('%s %.3f'%("\n Normalised frequency= ",v))
print "\n The total no. of guided  modes = ",int(M)

 Cladding refractive index=  1.44

 Normalised frequency=  56.078

 The total no. of guided  modes =  1572

Example8: PgNo-91

In [8]:
import math

# Initialisation of variables
n1=1.5 # core refractive index
dl=0.01 # index difference
M=1100 # the total no. of guided  modes
y=1.3*(math.pow(10,-6)) # wavelength in um
v=math.sqrt(2*M)# normalised frequency

# Calculations
a=(v*y)/(2*math.pi*n1*math.sqrt(2*dl))*math.pow(10,6) #core radius in meter

# Results
print ('%s %.2f' %(" Normalised frequency= ",v))
print ('%s %.2f %s' %("\n The diameter of the fiber core = ",2*a,"um"))

 Normalised frequency=  46.90

 The diameter of the fiber core =  91.50 um

Example9: PgNo-91

In [9]:
import math

# Initialisation of variables
n1=1.45 # core refractive index
n_m=0.16 # numerical aperture

# Calculations
a=30*math.pow(10,-6) # core radius in micrometer
y=0.5*(math.pow(10,-6)) # wavelength in um
v=(2*math.pi*a*n_m)/y #normalised frequency

# Results
print ('%s %.2f' %(" Normalised frequency= ",v))

 Normalised frequency=  60.32

Example10: PgNo-93

In [10]:
import math

# Initialisation of variables
n1=3.6 # core refractive index
n2=3.56 # cladding refractive index
y=0.85*(math.pow(10,-6))# wavelength in um
m=1
n=0
v_c=2.405 # for planner guide

# Calculations
a=(v_c*y)/(2*math.pi*math.sqrt(math.pow(n1,2)-math.pow(n2,2)))# core radius in micrometer

print ('%s %.2f %s' %("The max thickness= ",a*pow(10,6),"um"))

The max thickness=  0.61 um

Example11: PgNo-94

In [11]:
import math

# variable declaration
n1=1.5 #core refractive index
y=1.3*(math.pow(10,-6)) # wavelength in um
M=1100 #  total no. of models
dl=0.01 # index difference

# Calculations
v=math.sqrt(2*M)
V=math.ceil(v)
a=(V*y)/(2*math.pi*n1*math.sqrt(2*dl))*math.pow(10,6) # core radius in micrometer
a1=math.ceil(a)# core radius in micrometer

# Results
print ('%s %.2f %s' %("The core diameter= ",2*a1,"um"))

The core diameter=  92.00 um

Example12: PgNo-96

In [12]:
import math

# Initialisation of variables
n1=1.45 # core refractive index
dl=0.015 # index difference

# Calculations
y=0.85*(math.pow(10,-6)) # wavelength in meter
v=2.4*math.pow((1+(2/2)),(0.5))# Max normalised frequency
a=(v*y)/(2*math.pi*n1*math.pow((2*dl),(0.5))) # Max core radius in m
d=2*a # The max core diameter in meter

# Results
print ('%s %.3f %s'%(" The max core diameter in meter= ",d*pow(10,6),"um"))

 The max core diameter in meter=  3.657 um

Example13: PgNo-98

In [13]:
import math

# Variable Initialisation
n1=1.48 #core refractive index
n2=1.46 # cladding refractive index
a=2.5   # radius in um
y=0.85  # wavelength in um
dl=(n1-n2)/n1 # index difference
v=(2*math.pi*a*n1*math.pow((2*dl),(0.5)))/y #the normaised frequency
M=(v*v)/2 # number of modes
print " The number of modes= ",int(M)

 The number of modes=  10

Example14: PgNo-101

In [14]:
import math

# Initialisation of variables
a=25 # radius in um
y=1.3 # wavelength in um
v=26.6 # the normaised frequency
NA=(v*y)/(2*math.pi*a) #Numerical aperture
a_c=math.pi*math.pow((NA),2)
M=(v*v)/2

# Results
print ('%s %.3f' %(" The number of modes= ", NA))
print ('%s %.3f' %("\n The number of modes= ", a_c))
print ("\n Answer in textbook is wrong")
print "\n The number of modes= ",int(M)

 The number of modes=  0.220

 The number of modes=  0.152

 Answer in textbook is wrong

 The number of modes=  353

Example15: PgNo-103

In [15]:
import math

# Declaration of variables
n1=1.49 # core refractive index
n2=1.47 # cladding refractive index
a=2  # radius in um
dl=(n1-n2)/n1 # index difference
v_c=2.405

# calculations
y_c=(2*math.pi*a*n1*math.pow((2*dl),(0.5)))/v_c # cut off wavelength in um
Y=1.31 # wavelength in um
A=(v_c*Y)/(2*math.pi*n1*math.pow((2*dl),(0.5))) # min core radius in um

# Results
print ('%s %.3f %s' %(" The cut off wavelength = ",y_c,"um"))
print ('%s %.3f %s' %("\n The min core radius = ",A,"um"))

 The cut off wavelength =  1.276 um

 The min core radius =  2.054 um

Example16: PgNo-105

In [16]:
import math

# Initialisation of variables
a=25 # radius in um
NA=0.3 # Numerical aperture
y=1 # wavelength in um
v=(2*math.pi*a*NA)/y # the normalised frequency
V=47.1 # the normalised frequency
M=(V*V)/4 # The mode volume

# Results
print ('%s %.2f' %(" The normalised frequency = ",v))
print "\n The mode volume = ",int(M),"guided modes"

 The normalised frequency =  47.12

 The mode volume =  554 guided modes

Example17: PgNo-107

In [17]:
import math

# variable declaration
n1=1.46 # core refractive index
a=4.5   # radius in um
dl=0.0025 # relative index difference
v_c=2.405

# calculations
y_c=(2*math.pi*a*n1*math.pow((2*dl),(0.5)))/v_c # cut off wavelength in um

print ('%s %.3f %s' %(" The cut off wavelength = ",y_c,"um"))

 The cut off wavelength =  1.214 um

Example18: PgNo-109

In [18]:
import math

# Initialisation of variables
n1=1.5 #core refractive index
n2=1.45 # cladding refractive index
a=50 # radius in um
y=1.3 #operating wavelength in um

# calculations
NA=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture
N_A=0.38 
v=(2*math.pi*a*N_A)/y # cut of numbers
M=math.pow(v,2)/2 # number of modes

print ('%s %.2f'%(" The cut of numbers = ",v))
print "\n The number of modes = ",int(M)

 The cut of numbers =  91.83

 The number of modes =  4216

Example19: PgNo-111

In [19]:
import math

# Variable initialisation
n1=1.53 # core refractive index
n2=1.5 # cladding refractive index
y=1.5 # operating wavelength in um

# calculation
NA=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture
a=(2.405*y)/(2*math.pi*NA)# max radius in um

print ('%s %.2f %s' %(" The max core radius = ",a,"um"))

 The max core radius =  1.90 um

Example20: PgNo-112

In [20]:
import math

# variable declaration
a=25 # max radius in um
y=0.8 # operating wavelength in um
NA=0.343 # numerical aperture
v=(2*math.pi*a*NA)/y # v-number
M=math.pow(v,2)/2 #number of modes

print ('%s %.6f' %(" The v-number = ",v))
print "\n The number of modes = ",int(M)

 The v-number =  67.347893

 The number of modes =  2267

Example21: PgNo-114

In [21]:
import math

# Initialisation of variables
n1=1.5 #core refractive index
NA=0.38 # numerical aperture
v=75 # v-number
y=1.3 # operating wavelength in um
a=(v*y)/(2*math.pi*NA) # core radius in um
n2=math.sqrt(math.pow(n1,2)-math.pow(NA,2))# cladding refractive index

# Results
print ('%s %.2f %s' %(" The core radius = ",a,"um"))
print ('%s %.2f' %("\n The cladding refractive index = ", n2))
print ("\n answer in textbook is wrong ")

 The core radius =  40.84 um

 The cladding refractive index =  1.45

 answer in textbook is wrong

Example22: PgNo-117

In [22]:
import math

#Initialisation of variables
y=1.2 # operating wavelength in um
w=5 # spot size in um
x=(2*y)/(math.pi*w) # the divergence angle in degree

# results
print ('%s %.3f %s' %(" The divergence angle = ",x,"degree"))

 The divergence angle =  0.153 degree

Example23: PgNo-119

In [23]:
import math

# Initialisation of variables
n1=1.46 # core refractive index
a=4.5 # core radius in um
dl=0.0025 # relative index difference
NA=n1*(math.sqrt(2*dl)) # numerical aperture
v=2.405
y=(2*math.pi*a*NA)/(v) # cut off wavelength in um

print ('%s %.3f %s' %(" The cut off wavelength = ",y,"um"))

 The cut off wavelength =  1.214 um

Example24: PgNo-121

In [24]:
import math

# variable declaration
n1=1.5 # core refractive index
n2=1.47 # cladding refractive index
y1=0.87 # operating wavelength in um
y2=1.5 # operating wavelength in um
a=25.0 # max radius in um

# Calculations
NA=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture
v1=(2*math.pi*a*NA)/y1
v2=(2*math.pi*a*NA)/y2
al=2.0 # parabolic index profile for GRIN
M1=(al/(al+2))*(math.pow(v1,2)/2)# number of modes
M2=(al/(al+2))*(math.pow(v2,2)/2)# number of modes

# Results
print " The number of modes at 870 nm = ",int(M1),"um"
print "\n The number of modes = ",int(M2),"um"

 The number of modes at 870 nm =  726 um

 The number of modes =  244 um

Example25: PgNo-122

In [25]:
import math

# Initialisation of variables
n1=1.5 # core refractive index
n2=1.46 # cladding refractive index
v=2.4 # cut off parameter
y=0.85 # operating wavelength in um

# Calculations
NA=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture
a=(v*y)/(2*math.pi*NA)# max radius in um
w=v*a # spot size
x=(2*y)/(3.4*w) # divergence angle in degree
d=50 # distance in meter
w_s=(y*d)/(math.pi*w) # spot size at 50 meter

# Results
print ('%s %.2f %s' %(" The numerical aperture = ",NA,"um"))
print ('%s %.2f %s' %("\n The max core radius = ",a,"um"))
print ('%s %.2f %s' %("\n The spot size = ",w,"um"))
print ('%s %.3f %s' %("\n The divergence angle = ",x,"degree"))
print ('%s %.2f %s' %("\n The spot size at 50 meter = ",w_s,"m"))

 The numerical aperture =  0.34 um

 The max core radius =  0.94 um

 The spot size =  2.26 um

 The divergence angle =  0.221 degree

 The spot size at 50 meter =  5.97 m

Example26: PgNo-124

In [26]:
import math

# Initialisation of variables
n1=1.53 # core refractive index
n2=1.50 # cladding  refractive index
y=1.2  # wavelength in um
v=2.405
a=(v*y)/(2*math.pi*(math.sqrt(math.pow(n1,2)-math.pow(n2,2)))) #core radius in micrometer

print ('%s %.3f %s' %(" The max diameter= ",2*a,"um"))

 The max diameter=  3.047 um

Example27: PgNo-127

In [27]:
import math
# Initialisation of variables
n1=1.47 # core refractive index
n2=1.46 # cladding  refractive index
y=1.3   # wavelength in um
dl=(n1-n2)/n1 # fractional refractive index diff

# calculations
NA=math.sqrt(math.pow(n1,2)-math.pow(n2,2))
v=2.405
a=(v*y)/(2*math.pi*(math.sqrt(math.pow(n1,2)-math.pow(n2,2))))# largest core radius in micrometer
n_eff=n1-(NA/(2*math.pi*(a/y))) # fractional refractive index

# Results
print ('%s %.2f %s' %(" The largest core radius = ",a,"um"))
print ('%s %.2f' %("\n The fractional refractive index= ",n_eff))

 The largest core radius =  2.91 um

 The fractional refractive index=  1.46

Example28: PgNo-130

In [28]:
import math

# initialisation of variables
n1=1.50 # core refractive index
n2=1.48 # cladding  refractive index
NA=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture
a=25 # core radius in um
y=0.85 # wavelength in um
v=(2*math.pi*a*NA)/y #cut off parameter
M=math.pow(v,2)/2 # number of modes

# Results
print ('%s %.3f' %(" The cut off parameter = ",v))
print "\n The number of modes = ",int(M)

 The cut off parameter =  45.115

 The number of modes =  1017

Example29: PgNo-132

In [29]:
import math

# initialisation of variables
n1=1.50 # core refractive index
a=25    # core radius in um
y=1.5   # wavelength in um
v=2.405

# Calculations
NA=(v*y)/(2*math.pi*a) # numerical aperture
D=math.pow((NA/n1),2)/(2) # max value of D
n2=n1-(D*n1) # cladding refractive index

# Results
print ('%s %.6f' %(" The max value of D = ",D))
print ('%s %.2f' %("\n The cladding refractive index = ",n2))

 The max value of D =  0.000117

 The cladding refractive index =  1.50

Example30: PgNo-133

In [30]:
import math
# variable declaration
n1=1.52 #core refractive index
n2=1.48 #cladding  refractive index
a=45    # core radius in um
y=0.85  # wavelength in um

# Calculations
dl=(n1-n2)/n1 # relative refractive index
x=(math.asin(n2/n1))*(180/math.pi) # critical angle in degree
NA=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) #numerical aperture
a_c=(math.asin(NA))*(180/math.pi) #acceptance angle in degree
a_s=math.pi*(math.pow(n1,2)-math.pow(n2,2))# solid acceptance angle
v=(2*math.pi*a*0.34)/y # normalise v-number
M=math.pow(v,2)/2 # number of guided modes
a1=5 # for single mode step fiber
v1=(2*math.pi*a1*0.34)/y
M1=math.pow(v1,2)/2
R=int(M)-int(M1)# reduction in modes

# Results
print ('%s %.4f' %(" The max value of D = ",dl))
print ('%s %.2f %s' %("\n The critical angle = ",x,"degree"))
print ('%s %.2f %s' %("\n The acceptance angle = ",2*a_c,"degree"))
print ('%s %.2f %s' %("\n The solid acceptance angle = ",a_s,"degree"))
print ('%s %.2f ' %("\n The numerical aperture = ",NA))
print ('%s %.2f ' %("\n The normalise v-number = ",v))
print "\n The number of guided modes = ",int(M)
print "\n The reduction in modes = ",R

 The max value of D =  0.0263

 The critical angle =  76.83 degree

 The acceptance angle =  40.54 degree

 The solid acceptance angle =  0.38 degree

 The numerical aperture =  0.35 

 The normalise v-number =  113.10 

 The number of guided modes =  6395

 The reduction in modes =  6317

Example31: PgNo-135

In [31]:
import math
# Initialisation of variables

n1=1.46 #core refractive index
a=45/2 #max radius in um
y=0.85 # operating wavelength in um
NA=0.17 # numerical aperture
v=(2*math.pi*a*NA)/y #normalised frequency
M=math.pow(v,2)/2 # number of modes

# Results
print ('%s %.2f' %(" The normalised frequency = ",v))
print "\n The number of modes = ",int(M)

 The normalised frequency =  27.65

 The number of modes =  382