{
 "metadata": {
  "name": "Optics"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Interactive Introduction to Optics"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The objective is to review some principles in optics and how light interacts with matter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Classical Propagation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A simple model to understand the propagation of light in matter is to consider matter as a collection of dipoles.\n",
      "\n",
      "$$ m_0\\frac{d^2x}{dt^2} + m_0\\gamma\\frac{dx}{dt} + m_0\\omega_0^2x = -e \\varepsilon $$ where $m_0$ is the electron mass, $\\gamma$ the damping rate, $e$ the electric charge and $\\varepsilon$ the electric field of the light wave driving the dipole.\n",
      "\n",
      "All the effect of the interaction with matter, can be encoded in what is known as the complex dielectric function \n",
      "\n",
      "$$\\epsilon(\\omega)= \\frac{Ne^2}{\\epsilon_0 m_0}\\frac{\\gamma\\omega}{(\\omega_0^2-\\omega^2)+ (\\gamma\\omega)^2}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import *\n",
      "import sympy.plotting as p\n",
      "init_printing()\n",
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = symbols('x')\n",
      "omega, gamma, omega_0 = symbols('omega, gamma, omega_0', positive = True, real = True)\n",
      "p.plot(x, x**2, x**3, (x,-5,5))\n",
      "epsilon = symbols('epsilon', cls=Function)\n",
      "epsilon = gamma*omega/((omega_0**2-omega**2)+ (gamma*omega)**2)\n",
      "epsilon"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ITU3VUB1R7WLHXAPz5gH//KdMiWvaVHc1nmnevHl499130aNHD7z66qto0qQJ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\nrkJggg==\n"
      },
      {
       "latex": [
        "$$\\frac{\\gamma \\omega}{\\gamma^{2} \\omega^{2} - \\omega^{2} + \\omega_{0}^{2}}$$"
       ],
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "      \u03b3\u22c5\u03c9       \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        " 2  2    2     2\n",
        "\u03b3 \u22c5\u03c9  - \u03c9  + \u03c9\u2080 "
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}