path: root/sample_notebooks/ShivaAmruthavakkula/Chapter_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1.1.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Divergence of a beam,page number:7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the divergence of the beam is 8.05960631817e-05 in radians\n",
      "the divergence of the beam is 0.00461781426568 in degrees\n"
     ]
    }
   ],
   "source": [
    "# '''Example 1.1.1 :Divergence of a beam '''\n",
    "\n",
    "import math\n",
    "\n",
    " #decalring variables\n",
    "Lambda=633*(10**-9)          #wavelength of laser\n",
    "s=10*10**-3                 #spot size of the laser\n",
    "w=s/2                       # waist radius\n",
    "\n",
    "#calculations\n",
    "\n",
    "theta_radians=(4*Lambda)/(math.pi*(2*w))\n",
    "num=math.pi*(w)\n",
    "theta_degrees=math.degrees(theta_radians)\n",
    "\n",
    "#results\n",
    "print \"the divergence of the beam is\",theta_radians,\"in radians\"\n",
    "print \"the divergence of the beam is\",theta_degrees,\"in degrees\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1.2.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Relative permittivity and refractive index n,Page number:8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Materials   EpsilonR squareroot(EpsilonR)\n",
      "\n",
      "------------------------------------------\n",
      "\n",
      "silicon \t11.9 \t3.44963766213 \n",
      "\n",
      "Diamond \t5.7 \t2.38746727726 \n",
      "\n",
      "GaAs    \t13.1 \t3.61939221417 \n",
      "\n",
      "SiO2    \t3.84 \t1.95959179423 \n",
      "\n",
      "Water   \t80 \t8.94427191 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "'''Example 1.2.1: relative permittivity and refractive index n'''\n",
    "\n",
    "\n",
    "import math\n",
    "\n",
    "numbers=[0,1,2,3,4]\n",
    "\n",
    "#declaring array variables\n",
    "materials=['silicon','Diamond','GaAs   ','SiO2   ','Water  ']       #declaring the materials\n",
    "relative_permittivity=[11.9,5.7,13.1,3.84,80]                       #declaring the relative permittivity at low frequencies\n",
    "\n",
    "#calculations\n",
    "refractive_index=[]                                                 #declaring result set                                                 \n",
    "for i in relative_permittivity:\n",
    "    t=math.sqrt(i)\n",
    "    refractive_index.append(t)\n",
    "    \n",
    "#Results and Table\n",
    "print \"Materials   EpsilonR squareroot(EpsilonR)\\n\"\n",
    "print \"------------------------------------------\\n\"\n",
    "for j in numbers:\n",
    "    print materials[j],\"\\t\",relative_permittivity[j],\"\\t\",refractive_index[j],\"\\n\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Example 1.3.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Relative permittivity and refractive index n,Page number-11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The phase velocity is  206896551.724\n",
      "The group velocity is  205479452.055\n"
     ]
    }
   ],
   "source": [
    "'''Example 1.3.2:Group and phase velocities'''\n",
    "\n",
    "import math\n",
    "\n",
    "#declaring variables\n",
    "Lambda=1*10**-6         #wavelength of light\n",
    "n=1.450                 #refractive index\n",
    "c=3*10**8               #velocity of light in free space\n",
    "group_index=1.46        #Group index(available from graph)\n",
    "\n",
    "#calculations\n",
    "phase_velocity=c/n      #calculation of phase velocity\n",
    "group_velocity=c/group_index    #calculation of group velocity\n",
    "\n",
    "#results\n",
    "\n",
    "print \"The phase velocity is \",phase_velocity\n",
    "print \"The group velocity is \",group_velocity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1.6.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Phase change and Penetration Depth,Page Number-24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A\n",
      "the crirical angle is equal to   0.986206896552 \n",
      "\n",
      "B\n",
      "The phase change in medium 1 at incident angle=85 degrees with electrical component perpendicular to the plane of incidence is 116.45255621 degrees\n",
      "The phase change in medium 1 at incident angle=85 degrees with electrical component parallel to the plane of incidence is -62.1314255434 degrees\n",
      "The phase change in medium 1 at incident angle=90 degrees with electrical component perpendicular to the plane of incidence is 180.0 degrees\n",
      "The phase change in medium 1 at incident angle=90 degrees with electrical component parallel to the plane of incidence is -2.84217094304e-14 degrees \n",
      "\n",
      "C\n",
      "The penetration depth of medium 2 at incident angle of 85 degrees is  7.80048054638e-07 meters\n",
      "The penetration depth of medium 2 at incident angle of 90 degrees is  6.63145596216e-07 meters\n"
     ]
    }
   ],
   "source": [
    "'''Example 1.6.2'''\n",
    "import math\n",
    "\n",
    "#declaration of variables\n",
    "\n",
    "n1=1.450            #refractive index of first medium\n",
    "n2=1.430            #refractive index of second medium\n",
    "Lambda=1*10**-6     #wavelength of light at standard units\n",
    "theta_i1=85         #declaration of incidence angle 1\n",
    "theta_i2=90         #declaration of incidence angle 2\n",
    "\n",
    "#Calculation of minimum incidence angle\n",
    "theta_c=n2/n1       #calculation of critical angle\n",
    "\n",
    "#Calculation of phase change in medium 1 at incident angle 85 with perpendicular electrical component\n",
    "tanphi_pp_85m1=math.sqrt(math.pow(math.sin(math.radians(theta_i1)),2)-math.pow((n2/n1),2))/math.cos(math.radians(theta_i1))\n",
    "phi_pp_85im1=2*math.degrees(math.atan(tanphi_pp_85m1))\n",
    "\n",
    "#Calculation of phase change in medium 1 at incident angle 85 with parallel electrical component\n",
    "tanphi_prll_85m1=math.pow((n1/n2),2)*tanphi_pp_85m1\n",
    "phi_prll_85m1=2*(math.degrees(math.atan(tanphi_prll_85m1)))-math.degrees(math.pi)\n",
    "phi_prll_inv_85m1=180+phi_prll_85m1\n",
    "\n",
    "#Calculation of phase change in medium 1 at incident angle 90 with perpendicular electrical component\n",
    "tanphi_pp_90m1=math.sqrt(math.pow(math.sin(math.radians(theta_i2)),2)-math.pow((n2/n1),2))/math.cos(math.radians(theta_i2))\n",
    "phi_pp_90m1=2*math.degrees(math.atan(tanphi_pp_90m1))\n",
    "\n",
    "#Calculation of phase change in medium 1 at incident angle 85 with parallel electrical component\n",
    "tanphi_prll_90m1=math.pow((n1/n2),2)*tanphi_pp_90m1\n",
    "phi_prll_90m1=2*(math.degrees(math.atan(tanphi_prll_90m1)))-math.degrees(math.pi)\n",
    "phi_prll_inv_90m1=180+phi_prll_90m1\n",
    "\n",
    "#Calculation of penetration depth in medium 2 at incident angle 85\n",
    "alpha_85=(2*math.pi*n2/Lambda)*(math.sqrt((math.pow((n1/n2),2)*math.pow(math.sin(math.radians(theta_i1)),2))-1))\n",
    "delta_85=1/alpha_85\n",
    "\n",
    "#calculation of penetration depth in medium 2 at incident angle 90\n",
    "alpha_90=(2*math.pi*n2/Lambda)*(math.sqrt((math.pow((n1/n2),2)*math.pow(math.sin(math.radians(theta_i2)),2))-1))\n",
    "delta_90=1/alpha_90\n",
    "\n",
    "#Results\n",
    "print \"A\"\n",
    "print \"the crirical angle is equal to  \",theta_c,\"\\n\"\n",
    "print \"B\"\n",
    "print \"The phase change in medium 1 at incident angle=85 degrees with electrical component perpendicular to the plane of incidence is\",phi_pp_85im1,\"degrees\"\n",
    "print \"The phase change in medium 1 at incident angle=85 degrees with electrical component parallel to the plane of incidence is\",phi_prll_85m1,\"degrees\"\n",
    "print \"The phase change in medium 1 at incident angle=90 degrees with electrical component perpendicular to the plane of incidence is\",phi_pp_90m1,\"degrees\"\n",
    "print \"The phase change in medium 1 at incident angle=90 degrees with electrical component parallel to the plane of incidence is\",phi_prll_90m1,\"degrees \\n\"\n",
    "print \"C\"\n",
    "print \"The penetration depth of medium 2 at incident angle of 85 degrees is \",delta_85,\"meters\"\n",
    "print \"The penetration depth of medium 2 at incident angle of 90 degrees is \",delta_90,\"meters\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1.6.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reflection at normal Incidence,Page number-25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A\n",
      "the reflection coefficient when light travels from air to glass is  -0.2\n",
      "the reflectance when light passes from air to glass is  0.04\n",
      "The phase change of the reflected light is \n",
      "180\n",
      "B\n",
      "the reflection coefficient when light travels from glass  to air is  0.2\n",
      "the reflectance when light passes from glass to air is  0.04\n",
      "The phase change of the reflected light is \n",
      "180\n",
      "C\n",
      "The polarisation angle is  56.309932474\n"
     ]
    }
   ],
   "source": [
    "# '''Example 1.6.3: Reflection at normal Incidence.Internal and external reflection'''\n",
    "import math\n",
    "\n",
    "#declaration of variables\n",
    "nglass=1.5\n",
    "nair=1\n",
    "\n",
    "#declaration of phase change\n",
    "def phasechange(r):\n",
    "    if r<0:\n",
    "        return 180\n",
    "    else:\n",
    "        return 0 \n",
    "#Calculation of reflection coefficient and intensity from air to glass\n",
    "r_coeffag=(nair-nglass)/(nair+nglass)         #reflection coefficient\n",
    "Rag=math.pow(r_coeffag,2)                       #Reflectance\n",
    "pag=phasechange(r_coeffag)\n",
    "\n",
    "\n",
    "#Calculation of relection and intensity from glass to aie\n",
    "r_coeffga=(nglass-nair)/(nglass+nair)\n",
    "Rga=math.pow(r_coeffga,2)\n",
    "pga=phasechange(r_coeffga)\n",
    "\n",
    "#calculation of polarisation angle\n",
    "theta_p=math.degrees(math.atan(nglass/nair))\n",
    "\n",
    "#Results\n",
    "print \"A\"\n",
    "print\"the reflection coefficient when light travels from air to glass is \",r_coeffag\n",
    "print \"the reflectance when light passes from air to glass is \",Rag\n",
    "print \"The phase change of the reflected light is \\n\",pag\n",
    "print \"B\"\n",
    "print\"the reflection coefficient when light travels from glass  to air is \",r_coeffga\n",
    "print \"the reflectance when light passes from glass to air is \",Rga\n",
    "print \"The phase change of the reflected light is \\n\",pag\n",
    "\n",
    "print \"C\"\n",
    "print \"The polarisation angle is \",theta_p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1.6.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Antireflection coatings on solar cells,Page number-25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the reflectance of the Silicon is  0.308641975309\n",
      "the refractive index of coating must be  1.87082869339\n",
      "the thickness of the coating is  9.21052631579e-08  meters\n"
     ]
    }
   ],
   "source": [
    "# '''Example 1.6.4: Antireflection coatings on solarcells'''\n",
    "import math\n",
    "\n",
    "#Declaration of variables\n",
    "nair=1\n",
    "nsi=3.5\n",
    "ncoating=1.9\n",
    "Lambda=700*10**-9\n",
    "\n",
    "#declaration of phase change\n",
    "def phasechange(r):\n",
    "    if r<0:\n",
    "        return 180\n",
    "    else:\n",
    "        return 0 \n",
    "\n",
    "#Calculation of reflectance at Silicon\n",
    "rsi=((nair-nsi)/(nair+nsi))\n",
    "Rsi=math.pow(rsi,2)\n",
    "psi=phasechange(rsi)\n",
    "\n",
    "#calculation of refractive index of coating\n",
    "ncoating_theoritical=math.sqrt(nair*nsi)\n",
    "\n",
    "#calculation of thickness\n",
    "d=Lambda/(4*ncoating)\n",
    "\n",
    "#results\n",
    "print \"the reflectance of the Silicon is \",Rsi\n",
    "print \"the refractive index of coating must be \",ncoating_theoritical\n",
    "print \"the thickness of the coating is \",d,\" meters\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1.7.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resonator modes and Spectral width,Page number-31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The seperation of modes is  1.5e+12  Hertz\n",
      "The spectral width is 1.35888872682e-10  meters\n"
     ]
    }
   ],
   "source": [
    "# '''Example 1.7.1: Resonator modes and spectral width'''\n",
    "import math\n",
    "\n",
    "#declaration of variables\n",
    "L=100*10**-6\n",
    "R=0.9\n",
    "Lambda=900*10**-9\n",
    "c=3*10**8\n",
    "\n",
    "#Calculation of seperation of modes\n",
    "delta_vm=c/(2*L)\n",
    "\n",
    "#calculation of finesse\n",
    "F=((math.pi)*math.sqrt(R))/(1-R)\n",
    "\n",
    "#calculation of modewidth\n",
    "del_vm=delta_vm/F\n",
    "\n",
    "#calculation of mode frequency\n",
    "vm=c/Lambda\n",
    "\n",
    "#calculation of spectral width\n",
    "del_lambda=(c/math.pow(vm,2))*del_vm\n",
    "\n",
    "#Results\n",
    "print \"The seperation of modes is \",delta_vm,\" Hertz\"\n",
    "print \"The spectral width is\", del_lambda,\" meters\""
   ]
  }
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