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{
"metadata": {
"name": "Chapter_2"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": "Chapter 2 : Optical fiber waveguides\n"
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.1, page 19"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n\n#Variable declaration\nn1=1.50 #core refractive index\nn2=1.47 #cladding refractive index\n\n#Calculation\nphic=math.asin(n2/n1)*180/(math.pi) #critical angle at core cladding\nNA=math.sqrt(n1**2-n2**2) #numerical aperture\nphia=math.asin(NA)*180/math.pi #acceptance angle in air\n\n#Result\nprint'(a) Critical angle at the core-cladding = %.1f\u00b0'%phic\nprint'(b) NA for the fiber = %.2f'%NA\nprint'(c) Acceptance angle in air for the fiber = %.1f\u00b0'%phia",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "(a) Critical angle at the core-cladding = 78.5\u00b0\n(b) NA for the fiber = 0.30\n(c) Acceptance angle in air for the fiber = 17.4\u00b0\n"
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.2, page 20"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n\n#Variable declaration\ndelta=0.01 #relative refractive index = 1%\nn1=1.46 #core index\n\n#Calculation\nNA=n1*math.sqrt(2*delta) #numerical aperture\nzeta=math.pi*(NA)**2 #solid acceptance angle\nn12=1-delta #ratio of(n2/n1)\nphic=math.asin(n12)*180/math.pi #critical angle\n\n#Result\nprint'Numerical aperture (NA) = %.2f'%NA\nprint'Solid acceptance angle = ',round((zeta),2),'rad'\nprint'Critical angle at core-cladding = %.1f\u00b0'%phic",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Numerical aperture (NA) = 0.21\nSolid acceptance angle = 0.13 rad\nCritical angle at core-cladding = 81.9\u00b0\n"
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.3, page 23"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n\n#variable declaration\nNA=0.4 #numerical aperture\ny=50*math.pi/180 #angle between projection of the ray and radius of fibre of core (radians)\n\n#Calculation\nphia1=math.asin(NA)*180/math.pi #acceptance angle for meridional rays\nphia2=math.asin(NA/(math.cos(y)))*180/math.pi #acceptance angle for skew rays\n\n#Result\nprint'Acceptance angle for meridional rays = %.1f\u00b0'%phia1\nprint'Acceptance angle for skew rays = %.1f\u00b0'%phia2\nprint\"Therefore, acceptance angle for the skew rays is about 15\u00b0 greater thanthe corresponding angle for meridional rays\"",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Acceptance angle for meridional rays = 23.6\u00b0\nAcceptance angle for skew rays = 38.5\u00b0\nTherefore, acceptance angle for the skew rays is about 15\u00b0 greater thanthe corresponding angle for meridional rays\n"
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.4, page 45"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n\n#variable declaration\nn1=1.48 #core index\na=40*10**-6 #radius of core\ndelta=1.5/100 #relative refractive index = 1.5%\nh=0.85*10**-6 #operating wavelength\n\n#Calculation \nV=(2*math.pi*a*n1*math.sqrt(2*delta))/h #normalized frequency for the fiber\nMs=(V**2)/2 #no of guided modes\n\n#Result\nprint 'Normalised frequency, V = %.1f'%V\nprint'Total number of guided modes, Ms = %d'%round(Ms)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Normalised frequency, V = 75.8\nTotal number of guided modes, Ms = 2872\n"
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.5, page 54"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n\n#variable declaration\nNA=0.2 #numerical aperture\na=25*10**-6 #radius of core\nh=1*10**-6 #operating wavelength\n\n#Calculation \nV=(2*math.pi*a*NA)/h #normalized frequency for the fiber\nMg=(V**2)/4 #no of guided modes gor parabolic profile\n\n#Result\nprint 'Normalised frequency, V = %.1f'%V\nprint'Total number of guided modes, Mg = %d'%round(Mg)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Normalised frequency, V = 31.4\nTotal number of guided modes, Mg = 247\n"
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.6, page 55"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n#variable declaration\nn1=1.48 #core index \nh=0.85*10**-6 #operating wavelength\nV=2.4 #normalized frequency for the fiber\ndelta=1.5/100 #relative refractive index (RRI)= 1.5%\ndelta1=delta/10 #RRI difference reduced by 10\n\n#Calculation\na=(V*h)/(2*math.pi*n1*math.sqrt(2*delta)) #radius of core\nd=2*a\na1=(V*h)/(2*math.pi*n1*math.sqrt(2*delta1)) #new radius of core\nd1=2*a1\n\n#Result\nprint 'Maximum core diameter for relative refractive index of 1.5 percent = ',round((d*10**6),2),\"um\"\nprint \"Maximum core diameter for relative refractive index = \",round(d1*10**6),\"um\"",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Maximum core diameter for relative refractive index of 1.5 percent = 2.53 um\nMaximum core diameter for relative refractive index = 8.0 um\n"
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.7, page 2.7"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n#variable declaration\nn1=1.5 #core index \ndelta=0.01 #relative refractive index (RRI)= 1%\nh=1.3*10**-6 #operating wavelength\nalph=2\n\n#Calculation\nV=(2.4)*math.sqrt(1+(2/alph)) #normalized frequency for the fiber\na=(V*h)/(2*math.pi*n1*math.sqrt(2*delta)) #radius of core\nd=2*a\n\n#Result\nprint \"Maximum core diameter for relative refractive index = \",round(d*10**6,1),\"um\"",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Maximum core diameter for relative refractive index = 6.6 um\n"
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.8, page 60"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n#Variable declaration\na=4.5*10**-6 #radius of core\nn1=1.46 #core index \ndelta=0.25/100 #relative refractive index (RRI)= 0.25%\n\n\n#Calculation \nhc=(2*math.pi*a*n1*math.sqrt(2*delta))/2.405 #cutoff wavelength\n\n\n#Result\nprint 'Fibre is single moded to a wavelength = ',round(hc*10**9),'nm'",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Fibre is single moded to a wavelength = 1214.0 nm\n"
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.10, page 69"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n#Variable declaration\nwo=5.8*10**-6 #spot size \nV=2.2 #normalized frequency\n\n#Calculation \na=wo/((0.65+1.619*V**(-1.5))+(2.879*V**-6)) #radius of the core\nd=2*a\n\n#Result\nprint'Fibre core diameter = ',round(d*10**6,1),\"um\"\n",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Fibre core diameter = 9.9 um\n"
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.11, page 73"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n#Variable declaration\nh=1.30*10**-6 #operating wavelength \nhc=1.08*10**-6 #cutoff wavelength\ntheta=12 #in angle (degree)\n\n#Calculation \naeff=3.832*h/(2*math.pi*math.sin(theta)) #effective core radius\nVeff=2.405*hc/h #effective normalised frequency\nwo=3.81*10**-6*(0.6043+(1.755*Veff**-1.5)+(2.78*Veff**-6)) #spot size\n\n#Result\nprint 'Spot size = ',round(wo*10**6,2),'um'",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Spot size = 4.84 um\n"
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2.12, page 74"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n\n#Variable declaration\nwo=5.2*10**-6 #spot size\nn1=1.485 #core index\nhc=1.190*10**-6 #cutoff wavelength\n\n#Calculation \naesi=1.820*wo #ESI core radius\nD=(0.293/n1**2)*(hc/aesi)**2 #ESI relative index difference\n\n#Result\nprint'ESI relative refractive index difference = ',round(D*10**2,2),'%'",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "ESI relative refractive index difference = 0.21 %\n"
}
],
"prompt_number": 22
}
],
"metadata": {}
}
]
}
|
