{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#12: Fiber Optics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.1, Page number 12.24"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"acceptance angle is 20.41 degrees\n",
"answer in the book varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n1=1.54; #Core refractive index\n",
"n2=1.50; #Cladding refractive index\n",
"\n",
"#Calculation\n",
"NA=math.sqrt(n1**2-n2**2); #numerical aperture\n",
"alpha_m=math.asin(NA); #acceptance angle(radian)\n",
"alpha_m=alpha_m*180/math.pi; #acceptance angle(degrees)\n",
"\n",
"#Result\n",
"print \"acceptance angle is\",round(alpha_m,2),\"degrees\"\n",
"print \"answer in the book varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.2, Page number 12.24"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"numerical aperture is 0.387\n",
"acceptance angle is 22.8 degrees\n",
"critical angle is 75 degrees\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n1=1.5; #Core refractive index\n",
"n2=1.45; #Cladding refractive index\n",
"\n",
"#Calculation\n",
"delta=(n1-n2)/n1; #fractional index change\n",
"NA=n1*math.sqrt(2*delta); #numerical aperture\n",
"alpha_m=math.asin(NA); #acceptance angle(radian)\n",
"alpha_m=alpha_m*180/math.pi; #acceptance angle(degrees)\n",
"thetac=math.asin(n2/n1)*180/math.pi; #critical angle(degrees)\n",
"\n",
"#Result\n",
"print \"numerical aperture is\",round(NA,3)\n",
"print \"acceptance angle is\",round(alpha_m,1),\"degrees\"\n",
"print \"critical angle is\",int(thetac),\"degrees\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.3, Page number 12.25"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"critical angle is 77.16 degrees\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n1=1.53; #Core refractive index\n",
"p=2.5; #percentage(%)\n",
"\n",
"#Calculation\n",
"n2=n1*(100-p)/100; #Cladding refractive index\n",
"thetac=math.asin(n2/n1)*180/math.pi; #critical angle(degrees)\n",
"\n",
"#Result\n",
"print \"critical angle is\",round(thetac,2),\"degrees\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.4, Page number 12.25"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"numerical aperture is 0.28\n",
"acceptance angle is 16.26 degrees\n",
"critical angle is 79.1 degrees\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"delta=0.018; #fractional difference\n",
"n1=1.50; #Core refractive index\n",
"\n",
"#Calculation\n",
"NA=round(n1*math.sqrt(2*delta),2); #numerical aperture\n",
"alpha_m=math.asin(NA); #acceptance angle(radian)\n",
"alpha_m=alpha_m*180/math.pi; #acceptance angle(degrees)\n",
"n2=n1-(delta*n1); #Cladding refractive index\n",
"thetac=math.asin(n2/n1)*180/math.pi; #critical angle(degrees)\n",
"\n",
"#Result\n",
"print \"numerical aperture is\",NA\n",
"print \"acceptance angle is\",round(alpha_m,2),\"degrees\"\n",
"print \"critical angle is\",round(thetac,1),\"degrees\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.5, Page number 12.26"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"total number of guided modes is 490.0\n",
"number of modes of graded index fibre is 245.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=50*10**-6; #diameter(m)\n",
"lamda=1*10**-6; #wavelength(m)\n",
"NA=0.2; #numerical aperture\n",
"\n",
"#Calculation\n",
"NSI=4.9*(d*NA/lamda)**2; #total number of guided modes\n",
"NGI=NSI/2; #number of modes of graded index fibre\n",
"\n",
"#Result\n",
"print \"total number of guided modes is\",NSI\n",
"print \"number of modes of graded index fibre is\",NGI"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.6, Page number 12.26"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"numerical aperture is 0.47\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"delta=0.05; #fractional difference\n",
"n1=1.5; #Core refractive index\n",
"\n",
"#Calculation\n",
"NA=n1*math.sqrt(2*delta); #numerical aperture\n",
"\n",
"#Result\n",
"print \"numerical aperture is\",round(NA,2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.7, Page number 12.27"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of modes that can be propagated is 1\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=5*10**-6; #diameter(m)\n",
"lamda=1*10**-6; #wavelength(m)\n",
"NA=0.092; #numerical aperture\n",
"\n",
"#Calculation\n",
"N=4.9*(d*NA/lamda)**2; #number of modes that can be propagated\n",
"\n",
"#Result\n",
"print \"number of modes that can be propagated is\",int(N)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.8, Page number 12.27"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"V number is 94.7\n",
"maximum number of modes is 4485.7\n",
"answer in the book varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n1=1.53; #Core refractive index\n",
"n2=1.50; #Cladding refractive index\n",
"a=50*10**-6; #radius(m)\n",
"lamda=1*10**-6; #wavelength(m)\n",
"\n",
"#Calculation\n",
"NA=math.sqrt(n1**2-n2**2); #numerical aperture\n",
"Vn=2*math.pi*a*NA/lamda; #V number\n",
"N=Vn**2/2; #maximum number of modes\n",
"\n",
"#Result\n",
"print \"V number is\",round(Vn,1)\n",
"print \"maximum number of modes is\",round(N,1)\n",
"print \"answer in the book varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.9, Page number 12.27"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of propagating modes is 49177\n",
"answer in the book is wrong\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=100*10**-6; #radius(m)\n",
"lamda=0.85*10**-6; #wavelength(m)\n",
"NA=0.3; #numerical aperture\n",
"\n",
"#Calculation\n",
"N=4*math.pi**2*a**2*NA**2/lamda**2; #number of propagating modes\n",
"\n",
"#Result\n",
"print \"number of propagating modes is\",int(N)\n",
"print \"answer in the book is wrong\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.10, Page number 12.28"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Core refractive index is 1.6025\n",
"acceptance angle is 8.638 degrees\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"NA=0.2; #numerical aperture\n",
"n2=1.59; #Cladding refractive index\n",
"n0=1.33; #refractive index\n",
"\n",
"#Calculation\n",
"n1=round(math.sqrt(NA**2+n2**2),4); #Core refractive index\n",
"NA1=math.sqrt(n1**2-n2**2)/n0; #numerical aperture\n",
"alpha_m=math.asin(NA1); #acceptance angle(radian)\n",
"alpha_m=alpha_m*180/math.pi; #acceptance angle(degrees)\n",
"\n",
"#Result\n",
"print \"Core refractive index is\",n1\n",
"print \"acceptance angle is\",round(alpha_m,3),\"degrees\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.11, Page number 12.29"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of photons is 13.675 *10**15\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"c=3*10**8; #velocity of light(m/sec)\n",
"h=6.63*10**-34; #plank's constant(Js)\n",
"lamda=680*10**-9; #wavelength(m)\n",
"P=4*10**-3; #power(W)\n",
"\n",
"#Calculation\n",
"delta_E=c*h/lamda; #energy(J)\n",
"N=P/delta_E; #number of photons\n",
"\n",
"#Result\n",
"print \"number of photons is\",round(N/10**15,3),\"*10**15\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.12, Page number 12.29"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cladding refractive index is 1.49925\n",
"numerical aperture is 0.0474\n",
"critical angle is 88.2 degrees\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"delta=0.0005; #fractional difference\n",
"n1=1.5; #Core refractive index\n",
"\n",
"#Calculation\n",
"n2=n1-(delta*n1); #Cladding refractive index\n",
"NA=n1*math.sqrt(2*delta); #numerical aperture\n",
"thetac=math.asin(n2/n1)*180/math.pi; #critical angle(degrees)\n",
"\n",
"#Result\n",
"print \"Cladding refractive index is\",n2\n",
"print \"numerical aperture is\",round(NA,4)\n",
"print \"critical angle is\",round(thetac,1),\"degrees\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.13, Page number 12.29"
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"fraction of initial intensity after 2km is 0.363\n",
"fraction of initial intensity after 5km is 0.048\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"alpha=2.2; #attenuation coefficient(dB/km)\n",
"L1=2; #distance(km)\n",
"L2=6; #distance(km)\n",
"\n",
"#Calculation\n",
"x1=-alpha*L1/10; \n",
"x2=-alpha*L2/10;\n",
"P1=10**x1; #fraction of initial intensity after 2km\n",
"P2=10**x2; #fraction of initial intensity after 5km\n",
"\n",
"#Result\n",
"print \"fraction of initial intensity after 2km is\",round(P1,3)\n",
"print \"fraction of initial intensity after 5km is\",round(P2,3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.14, Page number 12.30"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"attenuation coefficient is 1.41 dB/km\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"L=0.5; #distance(km)\n",
"Pout=1; #output power(W)\n",
"Pin=85/100; #input power(W)\n",
"\n",
"#Calculation\n",
"alpha=10*math.log10(Pout/Pin)/L; #attenuation coefficient(dB/km)\n",
"\n",
"#Result\n",
"print \"attenuation coefficient is\",round(alpha,2),\"dB/km\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 12.15, Page number 12.30"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"attenuation coefficient is 1.7 dB/km\n",
"overall signal attenuation is 17 dB\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"L=10; #distance(km)\n",
"Pout=2; #output power(W)\n",
"Pin=100; #input power(W)\n",
"\n",
"#Calculation\n",
"alpha=10*math.log10(Pin/Pout)/L; #attenuation coefficient(dB/km)\n",
"o_alpha=round(alpha,1)*L; #overall signal attenuation\n",
"\n",
"#Result\n",
"print \"attenuation coefficient is\",round(alpha,1),\"dB/km\"\n",
"print \"overall signal attenuation is\",int(o_alpha),\"dB\""
]
}
],
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