examples.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples of plots and calculations using the tmm package"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division, print_function, absolute_import\n",
    "\n",
    "from tmm import (coh_tmm, unpolarized_RT, ellips,\n",
    "                       position_resolved, find_in_structure_with_inf)\n",
    "\n",
    "from numpy import pi, linspace, inf, array\n",
    "from scipy.interpolate import interp1d\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__name__ and __package__ in site-packages version: tmm.color , None\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    import colorpy.illuminants\n",
    "    import colorpy.colormodels\n",
    "    from tmm import color\n",
    "    colors_were_imported = True\n",
    "except ImportError:\n",
    "    # without colorpy, you can't run sample5(), but everything else is fine.\n",
    "    colors_were_imported = False\n",
    "\n",
    "\n",
    "# \"5 * degree\" is 5 degrees expressed in radians\n",
    "# \"1.2 / degree\" is 1.2 radians expressed in degrees\n",
    "degree = pi/180"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a thin non-absorbing layer, on top of a thick absorbing layer, with\n",
    "air on both sides. Plotting reflected intensity versus wavenumber, at two\n",
    "different incident angles.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "jq35GIZhGDnHjI9hGIaRc8z4GIZhGDnHjI9hGIaRc8z4GIZhGDnHjI9hGIaRc8z4GIZhGDnHjI9h\n",
       "GIaRc8z4GIZhGDnn/wHFluMXKGO24wAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1038c8210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# list of layer thicknesses in nm\n",
    "d_list = [inf,100,300,inf]\n",
    "# list of refractive indices\n",
    "n_list = [1,2.2,3.3+0.3j,1]\n",
    "# list of wavenumbers to plot in nm^-1\n",
    "ks=linspace(0.0001,.01,num=400)\n",
    "# initialize lists of y-values to plot\n",
    "Rnorm=[] \n",
    "R45=[]\n",
    "for k in ks:\n",
    "    # For normal incidence, s and p polarizations are identical.\n",
    "    # I arbitrarily decided to use 's'.\n",
    "    Rnorm.append(coh_tmm('s',n_list, d_list, 0, 1/k)['R'])\n",
    "    R45.append(unpolarized_RT(n_list, d_list, 45*degree, 1/k)['R'])\n",
    "kcm = ks * 1e7 #ks in cm^-1 rather than nm^-1\n",
    "plt.figure()\n",
    "plt.plot(kcm,Rnorm,'blue',kcm,R45,'purple')\n",
    "plt.xlabel('k (cm$^{-1}$)')\n",
    "plt.ylabel('Fraction reflected')\n",
    "plt.title('Reflection of unpolarized light at 0$^\\circ$ incidence (blue), '\n",
    "            '45$^\\circ$ (purple)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the transmitted intensity versus wavelength through a single-layer\n",
    "film which has some complicated wavelength-dependent index of refraction.\n",
    "(I made these numbers up, but in real life they could be read out of a\n",
    "graph / table published in the literature.) Air is on both sides of the\n",
    "film, and the light is normally incident."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "DS2u4zArz0jgL7lFloCvDjRpQKqQyQ877kZq1TVYXwF+0oDj2BDjOw4zM6uL6zjMzKwuThxmZlYX\n",
       "Jw4zM6uLE4eZmdXFicPMzOrixGFmZnX5f94udShmmAHDAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113cf490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#index of refraction of my material: wavelength in nm versus index.\n",
    "material_nk_data = array([[200, 2.1+0.1j],\n",
    "                          [300, 2.4+0.3j],\n",
    "                          [400, 2.3+0.4j],\n",
    "                          [500, 2.2+0.4j],\n",
    "                          [750, 2.2+0.5j]])\n",
    "material_nk_fn = interp1d(material_nk_data[:,0].real,\n",
    "                          material_nk_data[:,1], kind='quadratic')\n",
    "d_list = [inf,300,inf] #in nm\n",
    "lambda_list = linspace(200,750,400) #in nm\n",
    "T_list = []\n",
    "for lambda_vac in lambda_list:\n",
    "    n_list = [1, material_nk_fn(lambda_vac), 1]\n",
    "    T_list.append(coh_tmm('s',n_list,d_list,0,lambda_vac)['T'])\n",
    "plt.figure()\n",
    "plt.plot(lambda_list,T_list)\n",
    "plt.xlabel('Wavelength (nm)')\n",
    "plt.ylabel('Fraction of power transmitted')\n",
    "plt.title('Transmission at normal incidence');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a calculation of the psi and Delta parameters measured in\n",
    "ellipsometry. This reproduces Fig. 1.14 in Handbook of Ellipsometry by\n",
    "Tompkins, 2005."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "muM4jlMLXKE5juM4tcAVmuM4jlML/h9noysXyVoFjAAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f2aced0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_list=[1,1.46,3.87+0.02j]\n",
    "ds=linspace(0,1000,num=100) #in nm\n",
    "psis=[]\n",
    "Deltas=[]\n",
    "for d in ds:\n",
    "    e_data=ellips(n_list, [inf,d,inf], 70*degree, 633) #in nm\n",
    "    psis.append(e_data['psi']/degree) # angle in degrees\n",
    "    Deltas.append(e_data['Delta']/degree) # angle in degrees\n",
    "plt.figure()\n",
    "plt.plot(ds,psis,ds,Deltas)\n",
    "plt.xlabel('SiO2 thickness (nm)')\n",
    "plt.ylabel('Ellipsometric angles (degrees)')\n",
    "plt.title('Ellipsometric parameters for air/SiO2/Si, varying '\n",
    "        'SiO2 thickness.\\n' \n",
    "        '@ 70$^\\circ$, 633nm. '\n",
    "        'Should agree with Handbook of Ellipsometry Fig. 1.14');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sample 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is an example where we plot absorption and Poynting vector\n",
    "as a function of depth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
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       "51xvvOTgXAHMbDxxJcO6DIIjLujTLCsLukHASw7OOee68JKDc865Ljw5OOec68KTg3POuS48OTjn\n",
       "nOvCk4NzzrkuPDk455zr4v8DGsWHWi7Yla4AAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1111aa1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d_list = [inf, 100, 300, inf] #in nm\n",
    "n_list = [1, 2.2+0.2j, 3.3+0.3j, 1]\n",
    "th_0=pi/4\n",
    "lam_vac=400\n",
    "pol='p'\n",
    "coh_tmm_data = coh_tmm(pol,n_list,d_list,th_0,lam_vac)\n",
    "\n",
    "ds = linspace(0,400,num=1000) #position in structure\n",
    "poyn=[]\n",
    "absor=[]\n",
    "for d in ds:\n",
    "    layer, d_in_layer = find_in_structure_with_inf(d_list,d)\n",
    "    data=position_resolved(layer,d_in_layer,coh_tmm_data)\n",
    "    poyn.append(data['poyn'])\n",
    "    absor.append(data['absor'])\n",
    "# convert data to numpy arrays for easy scaling in the plot\n",
    "poyn = array(poyn)\n",
    "absor = array(absor)\n",
    "plt.figure()\n",
    "plt.plot(ds,poyn,'blue',ds,200*absor,'purple')\n",
    "plt.xlabel('depth (nm)')\n",
    "plt.ylabel('AU')\n",
    "plt.title('Local absorption (purple), Poynting vector (blue)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sample 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Color calculations: What color is a air / thin SiO2 / Si wafer?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "air / 300nm SiO2 / Si --- rgb = [ 0.07281632  0.15136527  0.43237682] , xyY = [0.21695453785914581, 0.20726889780765714, 0.1549495698024714]\n",
      "Saving plot temp_plot.png\n",
      "Saving plot temp_plot.png\n",
      "Making color vs SiO2 thickness graph. Compare to (for example)\n",
      "http://www.htelabs.com/appnotes/sio2_color_chart_thermal_silicon_dioxide.htm\n"
     ]
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1111f2fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11129cd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c811d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if not colors_were_imported:\n",
    "    print('Colorpy was not detected (or perhaps an error occurred when',\n",
    "          'loading it). You cannot do color calculations, sorry!',\n",
    "          'http://pypi.python.org/pypi/colorpy')\n",
    "else:\n",
    "\n",
    "    # Crystalline silicon refractive index. Data from Palik via\n",
    "    # http://refractiveindex.info, I haven't checked it, but this is just for\n",
    "    # demonstration purposes anyway.\n",
    "    Si_n_data = [[400, 5.57 + 0.387j],\n",
    "                 [450, 4.67 + 0.145j],\n",
    "                 [500, 4.30 + 7.28e-2j],\n",
    "                 [550, 4.08 + 4.06e-2j],\n",
    "                 [600, 3.95 + 2.57e-2j],\n",
    "                 [650, 3.85 + 1.64e-2j],\n",
    "                 [700, 3.78 + 1.26e-2j]]\n",
    "    Si_n_data = array(Si_n_data)\n",
    "    Si_n_fn = interp1d(Si_n_data[:,0], Si_n_data[:,1], kind='linear')\n",
    "    # SiO2 refractive index (approximate): 1.46 regardless of wavelength\n",
    "    SiO2_n_fn = lambda wavelength : 1.46\n",
    "    # air refractive index\n",
    "    air_n_fn = lambda wavelength : 1\n",
    "\n",
    "    n_fn_list = [air_n_fn, SiO2_n_fn, Si_n_fn]\n",
    "    th_0 = 0\n",
    "\n",
    "    # Print the colors, and show plots, for the special case of 300nm-thick SiO2\n",
    "    d_list = [inf, 300, inf]\n",
    "    reflectances = color.calc_reflectances(n_fn_list, d_list, th_0)\n",
    "    illuminant = colorpy.illuminants.get_illuminant_D65()\n",
    "    spectrum = color.calc_spectrum(reflectances, illuminant)\n",
    "    color_dict = color.calc_color(spectrum)\n",
    "    print('air / 300nm SiO2 / Si --- rgb =', color_dict['rgb'], ', xyY =', color_dict['xyY'])\n",
    "    plt.figure()\n",
    "    color.plot_reflectances(reflectances,\n",
    "                        title='air / 300nm SiO2 / Si -- '\n",
    "                              'Fraction reflected at each wavelength')\n",
    "    plt.figure()\n",
    "    color.plot_spectrum(spectrum,\n",
    "                        title='air / 300nm SiO2 / Si -- '\n",
    "                              'Reflected spectrum under D65 illumination')\n",
    "\n",
    "    # Calculate irgb color (i.e. gamma-corrected sRGB display color rounded to\n",
    "    # integers 0-255) versus thickness of SiO2\n",
    "    max_SiO2_thickness = 600\n",
    "    SiO2_thickness_list = linspace(0,max_SiO2_thickness,num=80)\n",
    "    irgb_list = []\n",
    "    for SiO2_d in SiO2_thickness_list:\n",
    "        d_list = [inf, SiO2_d, inf]\n",
    "        reflectances = color.calc_reflectances(n_fn_list, d_list, th_0)\n",
    "        illuminant = colorpy.illuminants.get_illuminant_D65()\n",
    "        spectrum = color.calc_spectrum(reflectances, illuminant)\n",
    "        color_dict = color.calc_color(spectrum)\n",
    "        irgb_list.append(color_dict['irgb'])\n",
    "\n",
    "    # Plot those colors\n",
    "    print('Making color vs SiO2 thickness graph. Compare to (for example)')\n",
    "    print('http://www.htelabs.com/appnotes/sio2_color_chart_thermal_silicon_dioxide.htm')\n",
    "    plt.figure()\n",
    "    plt.plot([0,max_SiO2_thickness],[1,1])\n",
    "    plt.xlim(0,max_SiO2_thickness)\n",
    "    plt.ylim(0,1)\n",
    "    plt.xlabel('SiO2 thickness (nm)')\n",
    "    plt.yticks([])\n",
    "    plt.title('Air / SiO2 / Si color vs SiO2 thickness')\n",
    "    for i in range(len(SiO2_thickness_list)):\n",
    "        # One strip of each color, centered at x=SiO2_thickness_list[i]\n",
    "        if i==0:\n",
    "            x0 = 0\n",
    "        else:\n",
    "            x0 = (SiO2_thickness_list[i] + SiO2_thickness_list[i-1]) / 2\n",
    "        if i == len(SiO2_thickness_list) - 1:\n",
    "            x1 = max_SiO2_thickness\n",
    "        else:\n",
    "            x1 = (SiO2_thickness_list[i] + SiO2_thickness_list[i+1]) / 2\n",
    "        y0 = 0\n",
    "        y1 = 1\n",
    "        poly_x = [x0,  x1,  x1, x0]\n",
    "        poly_y = [y0, y0, y1, y1]\n",
    "        color_string = colorpy.colormodels.irgb_string_from_irgb(irgb_list[i])\n",
    "        plt.fill(poly_x, poly_y, color_string, edgecolor=color_string)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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