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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter3 - Wave propagation in planor waveguides"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.1 : Page 45"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"range of propagation constant is 1.10880e+07 to 1.1014e+07 m**-1\n",
"number of modes are 4.0\n"
]
}
],
"source": [
"from math import pi, sqrt\n",
"#range of propagation constants and maximum no. of modes\n",
"n1=1.5##core refractive index\n",
"n2=1.49##cladding refrative index\n",
"t=9.83##thickness of guided layer in micro meter\n",
"h=0.85##wavelength in µm\n",
"b1=((2*pi*n1)/(h*10**-6))##phase propagation constant in m**-1\n",
"b2=((2*pi*n2)/(h*10**-6))##phase propagation constant in m**-1\n",
"m=((4*t)/h)*(sqrt(n1**2-n2**2))##number of modes\n",
"print \"range of propagation constant is %0.5e\"%(b1),\" to %0.4e\"%(b2),\" m**-1\"\n",
"print\"number of modes are\",round(m/2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.2 : Page 51"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"thicknes of the slab should not be greater than 0.794 µm\n"
]
}
],
"source": [
"from math import sqrt\n",
"#thickness\n",
"n1=3.6##core refractive index\n",
"n2=3.56##cladding refrative index\n",
"h=0.85##wavelength in µm\n",
"a=((h/(2*sqrt(n1**2-n2**2))))##thickness in µm\n",
"print \"thicknes of the slab should not be greater than %0.3f\"%(a),\" µm\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.3 : Page 52"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"part (a)\n",
"number of modes are : 5.0\n",
"part (b)\n",
"m \tuma(rad) \tum(m**-1) \twma(rad) \twm(m**-1) \tbm((wma/v)**2] \t\n",
"\n",
"0 1.30644 2.5845e+05 4.8263 9.5476e+05 0.93077\n",
"1 2.59574 5.1350e+05 4.27342 8.4538e+05 0.72974\n",
"2 3.83747 7.5914e+05 3.20529 6.3408e+05 0.41053\n",
"3 4.9063 9.7058e+05 0.963466 1.9060e+05 0.03709\n"
]
}
],
"source": [
"from math import pi, sqrt\n",
"#no. of modes\n",
"print \"part (a)\"\n",
"n1=1.5##core refractive index\n",
"n2=1.48##cladding refrative index\n",
"t=10.11##thickness of guided layer in micro meter\n",
"h=1.55##wavelength in µm\n",
"b1=((2*pi*n1)/(h*10**-6))##phase propagation constant in m**-1\n",
"b2=((2*pi*n2)/(h*10**-6))##phase propagation constant in m**-1\n",
"m=((2*pi*t)/h)*(sqrt(n1**2-n2**2))##number of modes\n",
"print \"number of modes are : \",round(m/2)\n",
"\n",
"print \"part (b)\"\n",
"t1=10.11##thickness of guided layer in micro meter\n",
"t=t1/2#\n",
"h=1.55##wavelength in µm\n",
"b1=((2*pi*n1)/(h*10**-6))##phase propagation constant in m**-1\n",
"b2=((2*pi*n2)/(h*10**-6))##phase propagation constant in m**-1\n",
"mo=(((2*pi*t1)/h)*(sqrt(n1**2-n2**2)))/2##number of modes\n",
"uma0=1.30644## for m=0 from the curve\n",
"uma1=2.59574## for m=1 from the curve\n",
"uma2=3.83747## for m=2 from the curve\n",
"uma3=4.9063## for m=3 from the curve\n",
"wma0=4.8263## for m=0 from the curve\n",
"wma1=4.27342## for m=1 from the curve\n",
"wma2=3.20529## for m=2 from the curve\n",
"wma3=0.963466## for m=3 from the curve\n",
"um0=uma0/(t*10**-6)##in m**-1\n",
"um1=uma1/(t*10**-6)##in m**-1\n",
"um2=uma2/(t*10**-6)##in m**-1\n",
"um3=uma3/(t*10**-6)##in m**-1\n",
"wm0=wma0/(t*10**-6)##in m**-1\n",
"wm1=wma1/(t*10**-6)##in m**-1\n",
"wm2=wma2/(t*10**-6)##in m**-1\n",
"wm3=wma3/(t*10**-6)##in m**-1\n",
"bm0=((wm0*t*10**-6)/mo)**2##for m=0 \n",
"bm1=((wm1*t*10**-6)/mo)**2##for m=1\n",
"bm2=((wm2*t*10**-6)/mo)**2##for m=2 \n",
"bm3=((wm3*t*10**-6)/mo)**2##for m=3\n",
"m0=sqrt((bm0*(b1**2-b2**2))+b2**2)##for m=0 in m**-1\n",
"m1=sqrt((bm1*(b1**2-b2**2))+b2**2)##for m=1 in m**-1\n",
"m2=sqrt((bm2*(b1**2-b2**2))+b2**2)##for m=2 in m**-1\n",
"m3=sqrt((bm3*(b1**2-b2**2))+b2**2)##for m=3 in m**-1\n",
"params = [\"m\", \"uma(rad)\", \"um(m**-1)\", \"wma(rad)\", \"wm(m**-1)\", \"bm((wma/v)**2]\" ]\n",
"for x in params:\n",
" print x,'\\t',\n",
"\n",
"print '\\n'\n",
"a = range(0,4)\n",
"b = [uma0, uma1, uma2, uma3]\n",
"c = [um0, um1, um2, um3]\n",
"d = [wma0, wma1, wma2, wma3]\n",
"e = [wm0, wm1, wm2, wm3]\n",
"f = [bm0, bm1, bm2, bm3]\n",
"from numpy import nditer\n",
"for k,l,m,n,o,p in nditer([a,b,c,d,e,f]) :\n",
" print k,' ',l,' %0.4e'%m,' ',n,' %0.4e'%o,' %0.5f'%p\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 3.4 : Page 56"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"G factor is 0.5622\n"
]
}
],
"source": [
"from math import sin, cos, pi\n",
"#G factor\n",
"d=0.793##in micro meter\n",
"v=pi/2##point of intersection\n",
"ua=0.934##\n",
"wa=1.262##\n",
"Y=(wa*(1+(sin(ua*pi/180))*(cos(ua*pi/180))/ua))\n",
"G=(1+((cos(ua*pi/180))**2)/Y)**(-1)\n",
"print \"G factor is %0.4f\"%G\n",
"#answer is wrong in the textbook"
]
}
],
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