path: root/Solid_State_Physics_by_Dr._M._Arumugam/Chapter13_YE4TWNG.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 13: Fiber Optics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 1, Page number 13.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "critical angle is 78.5 degrees\n",
      "numerical aperture is 0.3\n",
      "acceptance angle is 17.4 degrees\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "n2=1.47;              #refractive index of cladding\n",
    "n1=1.5;    #refractive index of core\n",
    "\n",
    "#Calculation\n",
    "phi_c=math.asin(n2/n1);     #critical angle(radian)\n",
    "phi_c=phi_c*180/math.pi;    #critical angle(degrees)\n",
    "NA=math.sqrt(n1**2-n2**2);     #numerical aperture\n",
    "phi_max=math.asin(NA);       #acceptance angle(radian)\n",
    "phi_max=phi_max*180/math.pi;    #acceptance angle(degrees)\n",
    "\n",
    "#Result\n",
    "print \"critical angle is\",round(phi_c,1),\"degrees\"\n",
    "print \"numerical aperture is\",round(NA,1)\n",
    "print \"acceptance angle is\",round(phi_max,1),\"degrees\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 2, Page number 13.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total number of guided modes is 490\n",
      "number of modes propagated inside fibre is 245\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d=50*10**-6;     #diameter(m)\n",
    "NA=0.2;      #numerical aperture(m)\n",
    "lamda=1*10**-6;    #wavelength(m)\n",
    "\n",
    "#Calculation\n",
    "N=4.9*(d*NA/lamda)**2;     #total number of guided modes\n",
    "Nf=N/2;                    #number of modes propagated inside fibre\n",
    "\n",
    "#Result\n",
    "print \"total number of guided modes is\",int(N)\n",
    "print \"number of modes propagated inside fibre is\",int(Nf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3, Page number 13.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total number of guided modes is 1\n",
      "it is a single mode propagation\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d=5*10**-6;     #diameter(m)\n",
    "n2=1.447;              #refractive index of cladding\n",
    "n1=1.45;    #refractive index of core\n",
    "lamda=1*10**-6;    #wavelength(m)\n",
    "\n",
    "#Calculation\n",
    "NA=math.sqrt(n1**2-n2**2);      #numerical aperture\n",
    "N=4.9*(d*NA/lamda)**2;     #total number of guided modes\n",
    "\n",
    "#Result\n",
    "print \"total number of guided modes is\",int(N)\n",
    "print \"it is a single mode propagation\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 4, Page number 13.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerical aperture is 0.46\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "n1=1.46;    #refractive index of core\n",
    "delta=0.05;    #refractive index difference\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 5, Page number 13.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V number is 94.72\n",
      "maximum number of modes is 4486\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=50;\n",
    "n2=1.5;              #refractive index of cladding\n",
    "n1=1.53;    #refractive index of core\n",
    "lamda0=1;    #wavelength(micro m)\n",
    "\n",
    "#Calculation\n",
    "V_number=round(2*math.pi*a*math.sqrt(n1**2-n2**2)/lamda0,2);     #V number\n",
    "n=V_number**2/2;     #maximum number of modes\n",
    "\n",
    "#Result\n",
    "print \"V number is\",V_number\n",
    "print \"maximum number of modes is\",int(round(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 6, Page number 13.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total number of modes is 49178\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=100*10**-6;\n",
    "NA=0.3;      #numerical aperture(m)\n",
    "lamda=850*10**-9;    #wavelength(m)\n",
    "\n",
    "#Calculation\n",
    "V_number=round(2*math.pi**2*a**2*NA**2/lamda**2);     #number of modes\n",
    "\n",
    "#Result\n",
    "print \"total number of modes is\",int(2*V_number)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 7, Page number 13.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cutoff wavelength is 1.315 micro m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=25*10**-6;\n",
    "n1=1.48;    #refractive index of core\n",
    "delta=0.01;    #refractive index difference\n",
    "V=25;     #Vnumber\n",
    "\n",
    "#Calculation\n",
    "lamda=2*math.pi*a*n1*math.sqrt(2*delta)/V;      #cutoff wavelength(m)\n",
    "\n",
    "#Result\n",
    "print \"cutoff wavelength is\",round(lamda*10**6,3),\"micro m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 8, Page number 13.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "maximum value of core radius is 9.95 micro m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "V=2.405;     #Vnumber\n",
    "lamda=1.3;    #wavelength(micro m)\n",
    "NA=0.05;      #numerical aperture(m)\n",
    "\n",
    "#Calculation\n",
    "amax=V*lamda/(2*math.pi*NA);     #maximum value of core radius(micro m)\n",
    "\n",
    "#Result\n",
    "print \"maximum value of core radius is\",round(amax,2),\"micro m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 9, Page number 13.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "acceptance angle for meridional rays is 17.46 degrees\n",
      "acceptance angle for skew rays is 25.104 degrees\n",
      "answer for acceptance angle for skew rays given in the book is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "NA=0.3;      #numerical aperture(m)\n",
    "gama=45*math.pi/180;     #angle(radian)\n",
    "\n",
    "#Calculation\n",
    "thetaa=math.asin(NA);       #acceptance angle for meridional rays(radian)\n",
    "thetaa=thetaa*180/math.pi;  #acceptance angle for meridional rays(degrees)\n",
    "thetaas=math.asin(NA/math.cos(gama));     #acceptance angle for skew rays(radian)\n",
    "thetaas=thetaas*180/math.pi;   #acceptance angle for skew rays(degrees)\n",
    "\n",
    "#Result\n",
    "print \"acceptance angle for meridional rays is\",round(thetaa,2),\"degrees\"\n",
    "print \"acceptance angle for skew rays is\",round(thetaas,3),\"degrees\"\n",
    "print \"answer for acceptance angle for skew rays given in the book is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 10, Page number 13.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerical aperture is 0.303\n",
      "acceptance angle is 17.633 degrees\n",
      "answer for angle given 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",
    "delta=0.0196;         #relative refractive index difference\n",
    "n1=1.53;              #refractive index of core\n",
    "\n",
    "#Calculation\n",
    "NA=n1*math.sqrt(2*delta);     #numerical aperture\n",
    "theta=math.asin(NA);          #acceptance angle(radian)\n",
    "theta=theta*180/math.pi;      #acceptance angle(degrees)\n",
    "\n",
    "#Result\n",
    "print \"numerical aperture is\",round(NA,3)\n",
    "print \"acceptance angle is\",round(theta,3),\"degrees\"\n",
    "print \"answer for angle given in the book varies due to rounding off errors\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 11, Page number 13.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "core radius is 1.548 micro m\n",
      "answer given in the book is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "n2=1.465;             #refractive index of cladding\n",
    "n1=1.480;             #refractive index of core\n",
    "lamda=850*10**-9;     #wavelength(m)\n",
    "\n",
    "#Calculation\n",
    "delta=(n1**2-n2**2)/(2*n1**2);         #relative refractive index difference\n",
    "a=2.405*lamda*10**6/(2*math.pi*n1*math.sqrt(2*delta));     #core radius(micro m)\n",
    "\n",
    "#Result\n",
    "print \"core radius is\",round(a,3),\"micro m\"\n",
    "print \"answer given in the book is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 12, Page number 13.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total number of reflections per metre is 2321\n",
      "total distance travelled by light is 1.0067 m\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "n2=1.49;             #refractive index of cladding\n",
    "n1=1.5;              #refractive index of core\n",
    "a=25;                #core radius(micro m)\n",
    "\n",
    "#Calculation\n",
    "phic=math.asin(n2/n1);                  #angle(degrees)\n",
    "l=2*a*math.tan(phic);                   #fibre length covered in 1 reflection(micro m)\n",
    "n=10**6/l;                              #total number of reflections per metre\n",
    "d=1/math.sin(phic);                     #total distance travelled by light(m)\n",
    "\n",
    "#Result\n",
    "print \"total number of reflections per metre is\",int(n)\n",
    "print \"total distance travelled by light is\",round(d,4),\"m\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 13, Page number 13.22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total number of modes is 309\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "alpha=1.85;          #index profile\n",
    "a=25;                #core radius(micro m)\n",
    "NA=0.21;             #numerical aperture\n",
    "lamda=1.3;           #wavelength(micro m)\n",
    "\n",
    "#Calculation\n",
    "n=(alpha*2*math.pi**2*a**2*NA**2)/(lamda**2*(alpha+2));     #number of modes\n",
    "N=2*n;               #total number of modes\n",
    "\n",
    "#Result\n",
    "print \"total number of modes is\",int(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 14, Page number 13.22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "signal attenuation per unit length is 1.7 dB km-1\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;        #transmission distance(km)\n",
    "Pi=100;      #optical power(micro W)\n",
    "Po=2;        #optical power output(micro W)\n",
    "\n",
    "#Calculation\n",
    "sa=round(10*math.log10(Pi/Po)/L,1);     #signal attenuation per unit length(dB km-1)\n",
    "osa=sa*L;                    #overall signal attenuation(dB)\n",
    "\n",
    "#Result\n",
    "print \"signal attenuation per unit length is\",sa,\"dB km-1\"\n",
    "print \"overall signal attenuation is\",int(osa),\"dB\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 15, Page number 13.23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dispersion is 1343.3 ns\n",
      "bandwidth length product is 7.44 *10**6 Hz-km\n",
      "answer for bandwidth given in the book is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "L=10;        #transmission distance(km)\n",
    "n1=1.55;     #refractive index of core\n",
    "delta=0.026;  #relative refractive index difference\n",
    "C=3*10**5;    \n",
    "\n",
    "#Calculation\n",
    "deltaT=L*n1*delta/C;    #dispersion(s)\n",
    "blp=L/deltaT;           #bandwidth length product(Hz-km)\n",
    "\n",
    "#Result\n",
    "print \"dispersion is\",round(deltaT*10**9,1),\"ns\"\n",
    "print \"bandwidth length product is\",round(blp/10**6,2),\"*10**6 Hz-km\"\n",
    "print \"answer for bandwidth given in the book is wrong\""
   ]
  }
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