{
"metadata": {
"name": "",
"signature": "sha256:e126fa636efa72af4b20cd3702da45f085d125811e3d4b6de05ba5fde96d2c77"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2:Light propagation in optical ber"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.1 , Page no:30"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from __future__ import division\n",
"\n",
"#initialisation of variables\n",
"ncore=1.46; #refractive index of core\n",
"nclad=1; #refractive index of cladding\n",
"c=3e5; #velocity of light in Km/s\n",
"L=1; #length of path in Km\n",
"\n",
"#CALCULATIONS\n",
"NA=math.sqrt(ncore**2-nclad**2); #Numerical aperture\n",
"delt_tau_by_L=(NA**2)/(2*c*ncore); #multipath pulse broadening in s/Km\n",
"delt_tau=delt_tau_by_L*L; #bandwidth distance product Hz\n",
"BL=(1/delt_tau)*L; #bandwidth distance product Hz\n",
"#case-2\n",
"ncore1=1.465; #refractive index of core\n",
"nclad1=1.45; #refractive index of cladding\n",
"NA1=math.sqrt(ncore1**2-nclad1**2); #Numerical aperture\n",
"delt_tau_by_L1=(NA1**2)/(2*c*ncore1); #multipath pulse broadening in s/m\n",
"BL1=(1/delt_tau_by_L1)*L; #bandwidth distance product Hz\n",
"\n",
"#RESULTS\n",
"print\"Numerical aperture=\",round(NA,5); #The answers vary due to round off error\n",
"print\"\\nMultipath pulse broadening=\",round(delt_tau_by_L*1e9,5),\"ns/Km\"; #The answer provided in the textbook is wrong//multiplication by 1e9 to convert s/Km to ns/Km \n",
"print\"\\nBandwidth distance product=\",round(BL*1e-6,5),\"GHz \"; #The answer provided in the textbook is wrong//multiplication by 1e-6 to convert Hz to MHz\n",
"print\"\\n\\nNumerical aperture=\",round(NA1,5);\n",
"print\"\\nMultipath pulse broadening=\",round(delt_tau_by_L1*1e9,5),\"ns/Km\"; #The answer provided in the textbook is wrong//multiplication by 1e9 to convert s/Km to ns/Km \n",
"print\"\\nBandwidth distance product=\",round(BL1*1e-9,5),\"GHz \"; #The answer provided in the textbook is wrong//multiplication by 1e-6 to convert Hz to GHz"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Numerical aperture= 1.06377\n",
"\n",
"Multipath pulse broadening= 1291.78082 ns/Km\n",
"\n",
"Bandwidth distance product= 0.77413 GHz \n",
"\n",
"\n",
"Numerical aperture= 0.20911\n",
"\n",
"Multipath pulse broadening= 49.74403 ns/Km\n",
"\n",
"Bandwidth distance product= 0.0201 GHz \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.2 , Page no:30"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from __future__ import division\n",
"\n",
"#initialisation of variables\n",
"lamda1=0.7; #wavelength in um\n",
"lamda2=1.3; #wavelength in um\n",
"lamda3=2; #wavelength in um\n",
"\n",
"#CALCULATIONS\n",
"f_lambda1=(303.33*(lamda1**-1)-233.33); #equation for lambda1\n",
"f_lambda2=(303.33*(lamda2**-1)-233.33); #equation for lambda2\n",
"f_lambda3=(303.33*(lamda3**-1)-233.33); #equation for lambda3\n",
"\n",
"#RESULTS\n",
"print\"Material dispersion at Lambda 0.7um=\",round(f_lambda1,5);\n",
"print\"\\nMaterial dispersion at Lambda 1.3um=\",round(f_lambda2,5); #The answers vary due to round off error\n",
"print\"\\nMaterial dispersion at Lambda 2um=\",round(f_lambda3,5); #The answers vary due to round off error\n",
"print\"\\nIts is a standard silica fiber\";"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Material dispersion at Lambda 0.7um= 199.99857\n",
"\n",
"Material dispersion at Lambda 1.3um= 0.00077\n",
"\n",
"Material dispersion at Lambda 2um= -81.665\n",
"\n",
"Its is a standard silica fiber\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.3 , Page no:32"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from __future__ import division\n",
"\n",
"#initialisation of variables\n",
"ncore=1.505; #refractive index of core\n",
"nclad=1.502; #refractive index of cladding\n",
"V=2.4; #v no. for single mode \n",
"lambda1=1300e-9; #operating wavelength in m\n",
"\n",
"#CALCULATIONS\n",
"NA=math.sqrt(ncore**2-nclad**2); #numerical aperture\n",
"a=V*(lambda1)/(2*3.14*NA); #dimension of fiber core in m\n",
"\n",
"#RESULTS\n",
"print\"The numarical aperture =\",round(NA,5);\n",
"print\"\\n Dimension of fiber core =\",round(a*1e6,5),\"um\"; #multiplication by 1e6 to convert unit from m to um"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The numarical aperture = 0.09498\n",
"\n",
" Dimension of fiber core = 5.23079 um\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.4 , Page no:33"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from __future__ import division\n",
"\n",
"#initialisation of variables\n",
"V=2; #v no. for single mode \n",
"a=4; #radius of fiber in um\n",
"\n",
"#CALCULATIONS\n",
"w=a*(0.65+1.619*V**(-3/2)+2.87*V**-6); #effective mode radius in um\n",
"\n",
"#RESULTS\n",
"print\"Effective mode radius =\",round(w,5),\"um\";"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Effective mode radius = 5.06899 um\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.6 , Page no:34"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from __future__ import division\n",
"\n",
"#initialisation of variables\n",
"m=0; #for dominant mode\n",
"v=0; #for dominant mode\n",
"n1=1.5; #refractive index of core\n",
"delta=0.01; #core clad index difference\n",
"a=5; #fiber radius in um\n",
"lambda1=1.3; #wavelength of operation in um\n",
"\n",
"#CALCULATIONS\n",
"k0=(2*3.14/lambda1); #constant in /m\n",
"beta=math.sqrt((k0**2)*(n1**2)-(2*k0*n1*math.sqrt(2*delta)/a)); #propagation constant in rad/um\n",
"\n",
"#RESULTS\n",
"print\"Propagation constant=\",round(beta,5),\"rad/um\"; #The answers vary due to round off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Propagation constant= 7.21781 rad/um\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.8 , Page no:34"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from __future__ import division\n",
"\n",
"#initialisation of variables\n",
"M=1000; #modes supported\n",
"lambda1=1.3; #operating wavelength in um\n",
"n1=1.5; #refractive index of core\n",
"n2=1.48; #refractive index of cladding\n",
"\n",
"#CALCULATIONS\n",
"V=math.sqrt(2*M); #normalised frequency V no.\n",
"NA=math.sqrt(n1**2-n2**2); #numerical apperture\n",
"R=lambda1*V/(2*3.14*NA); #radius of fiber in um\n",
"\n",
"#RESULTS\n",
"print\"Core Radius=\",round(R,5),\"um\"; #The answer provided in the textbook is wrong"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Core Radius= 37.92063 um\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.9 , Page no:35"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from __future__ import division\n",
"\n",
"#initialisation of variables\n",
"lambda1=1.3; #wavelength of operation in um\n",
"n1=1.5; #refractive index of core\n",
"n2=1.48; #refractive index of cladding\n",
"k0=2*3.14/lambda1; #constant in /m\n",
"\n",
"#CALCULATIONS\n",
"#case-1\n",
"b=0.5; #normalized propagation constant\n",
"k0=2*3.14/lambda1; #constant\n",
"beta=k0*math.sqrt(n2**2+b*(n1**2-n2**2)); #propagation constant\n",
"\n",
"#case-2\n",
"#given \n",
"lambda1=1.3; #wavelength of operation in um\n",
"n1=1.5; #refractive index of core\n",
"n2=1.48; #refractive index of cladding\n",
"k0=2*3.14/lambda1; #constant in /m\n",
"b=0.5; #normalized propagation constant\n",
"k0=2*3.14/lambda1; #constant\n",
"b1=(((n1+n2)/2)**2-n2**2)/(n1**2-n2**2); #normalized propagation constant\n",
"\n",
"#case-3\n",
"#given \n",
"lambda1=1.3; #wavelength of operation in um\n",
"n1=1.5; #refractive index of core\n",
"n21=1.0; #refractive index of cladding\n",
"k0=2*3.14/lambda1; #constant in /m\n",
"b=0.5; #normalized propagation constant\n",
"k0=2*3.14/lambda1; #constant\n",
"beta1=k0*math.sqrt(n21**2+b*(n1**2-n21**2)); #propagation constant\n",
"\n",
"#RESULTS\n",
"print\"Propagation constant=\",round(beta,5),\"rad/um\"; #The answers vary due to round off error\n",
"print\"\\nPropagation constant=\",round(b1,5); #The answers vary due to round off error\n",
"print\"\\nPropagation constant=\",round(beta1,5),\"rad/um\"; #The answers vary due to round off error"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Propagation constant= 7.19801 rad/um\n",
"\n",
"Propagation constant= 0.49832\n",
"\n",
"Propagation constant= 6.15805 rad/um\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.10 , Page no:35"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"from __future__ import division\n",
"\n",
"#initialisation of variables\n",
"#case-1\n",
"n1=1.49; #refractive index of core\n",
"n2=1.46; #refractive index of cladding\n",
"c=3*10**5; #speed of light in Km/s\n",
"t1=n1/c; #time delay for one traveling along axis in s/Km\n",
"t2=(n1**2/n2)/c; #time delay for one traveling along path that is totally reflecting at the first interface in s/km\n",
"\n",
"#case-2\n",
"n11=1.47; #refractive index of core\n",
"n21=1.46; #refractive index of cladding\n",
"c1=3*10**5; #speed of light in Km/s\n",
"t11=n11/c1; #time delay for one traveling along axis in\n",
"t22=(n11**2/n21)/c1; #time delay for one traveling along path that is totally reflecting at the first interface\n",
"\n",
"\n",
"print\"time delay for traveling along axis =\",round(t1*1e6,5),\"us/Km\"; #multiplication by 1e6 to convert the unit from s/Km to us/Km\n",
"print\"\\ntime delay for traveling along path that is totally reflecting at the first interface =\",round(t2*1e6,5),\"us/Km\"; #multiplication by 1e6 to convert the unit from s/Km to us/Km\n",
"print\"\\ntime delay for traveling along axis =\",round(t11*1e6,5),\"us/Km\"; #multiplication by 1e6 to convert the unit from s/Km to us/Km\n",
"print\"\\ntime delay for traveling along path that is totally reflecting at the first interface =\",round(t22*1e6,5),\"us/Km\"; #multiplication by 1e6 to convert the unit from s/Km to us/Km\n",
"#The answer provided in the textbook is wrong it has got wrong unit"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"time delay for traveling along axis = 4.96667 us/Km\n",
"\n",
"time delay for traveling along path that is totally reflecting at the first interface = 5.06872 us/Km\n",
"\n",
"time delay for traveling along axis = 4.9 us/Km\n",
"\n",
"time delay for traveling along path that is totally reflecting at the first interface = 4.93356 us/Km\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}