Designing a metasurface polarization grating.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook I will demonstrate how to design a metasurface polarization grating and write it out as a CAD file (.gds) based on a pre-compiled library of metasurface unit elements. First, we import the relevant code which has to be in the same directory as your code or added to your Python path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import Core.polarization_gratings as pg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Declaring the number of structures and instantiating the grating object."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step in designing the grating is to decide how many \"pillar\" elements will comprise the unit cell of the metasurface diffraction grating along the $x$ and $y$ directions, denoted $N_x$ and $N_y$. This decision is informed by what should be the angular separation of the diffraction orders along the $x$ and $y$ directions. In particular, we will have\n",
    "\n",
    "\n",
    "$$\n",
    "\\theta_x = \\arcsin\\frac{\\lambda_0}{N_x d_x}\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "\\theta_y = \\arcsin\\frac{\\lambda_0}{N_y d_y}\n",
    "$$\n",
    "\n",
    "where $\\lambda_0$ is the free-space operating wavelength and $d_x$ and $d_y$ are the spacings between pillars along the $x$ and $y$ directions. These choices will be informed by design.\n",
    "\n",
    "In what follows, we will just assume that $N_x=N_y=11$. Based on this choice, we instantiate a <code>grating</code> object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nx, Ny = 11, 11\n",
    "\n",
    "grating = pg.MetasurfaceGratingUnitCell(Nx, Ny)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the set of desired orders and for which polarization states they should analyze"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we declare the set of diffraction orders we are interested in; we declare these as a list of grating orders denoted by their indices $(m,n)$ numbered from the zero order of the diffraction grating.\n",
    "\n",
    "Next, we define the polarization states for which these diffraction orders should act as analyzers. We declare these polarization states as Jones vectors and correspond in order to the diffraction orders declared in <code>orders</code>. For instance, the order (0, -1) here will be optimized in what follows to serve as a polarizer that prefers the state with a Jones vector given by <code>[1/np.sqrt(2),1j*1/np.sqrt(2)]</code> (circular polarization)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "orders = [(1, 0), (-1, 0), (0, 1), (0, -1)] # set of diffraction orders of interest; innermost four orders in this case\n",
    "# Jones vectors of states these should analyze\n",
    "# These match the tetrahedron set from the paper, with the last one circular\n",
    "polarizations =  np.array([ [0.514099,0.794104 -0.324192*1j],\\\n",
    "                           [0.985599, -0.169102*1j],\\\n",
    "                           [0.514099, -0.794104 -0.324192*1j] ,\\\n",
    "                           [1/np.sqrt(2),1j*1/np.sqrt(2)]] , dtype=complex)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute the weight matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rather than using an FFT, the code computes the Jones matrix-valued Fourier transforms analytically; this is sped up internally by computing what I call the \"weight matrices\" for the diffraction orders of interest ahead-of-time. You don't need to worry about this very much but it has to be done once."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "weight_matrices = grating.compute_weight_matrices(orders)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the merit function and constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code as-written is completely general - we could optimize almost anything about the grating under any constraints, so long as we can define these as simple functions of the <code>state_vec</code> which contains all of the phase shifts $\\phi_x$, $\\phi_y$ and orientations $\\theta$ for each pillar in the $N_x\\times N_y$ grid.\n",
    "\n",
    "The merit function <code>power_merit_function</code> defined below matches what was done in the paper - specifically, it optimizes the power in the orders of interest (averaged over all possible incident polarization states, i.e., the power in the desired orders for unpolarized incident light). The constraints defined here are also the same used in the paper. The constraint defined by <code>no_variability_constraint</code> attempts to enforce our desire that the average power of the orders should be identical (their standard deviation should be 0). The second constraint <code>contrast_constraint</code> is the workhorse that makes the grating do what we want - in it, we are coaxing the contrast or diattenuation of the diffraction orders to be as close to 1 as possible for the polarizations we specified.\n",
    "\n",
    "This is how it was done in the *Science* paper but the code is general; many different combinations of merit functions and constraints could be tried."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# negative sign because optimizer minimizes\n",
    "def power_merit_function(state_vec):\n",
    "    return -np.sum(grating.power_in_orders_fast(orders, weight_matrices, state_vec))\n",
    "\n",
    "# compute the standard deviation of the expected power in the orders of interest\n",
    "def no_variability_constraint(state_vec):\n",
    "    return np.std(grating.power_in_orders_fast(orders, weight_matrices, state_vec))\n",
    "\n",
    "# compute the mean of the contrast in each order, minus 1\n",
    "def contrast_constraint(state_vec):\n",
    "    return (np.mean(grating.order_contrasts_fast(orders, polarizations, weight_matrices, state_vec)) - 1)\n",
    "\n",
    "merit_func = power_merit_function # we use minimize, not maximize\n",
    "cons = [no_variability_constraint, contrast_constraint] # list of constraints\n",
    "\n",
    "# internally, my code is using scipy.minimize\n",
    "# we have to declare constraints as equality or inequality constraints\n",
    "# these are equality constraints, they should equal 0\n",
    "cons_type = ['eq', 'eq']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run the optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we are ready to optimize the parameters of the grating to design our polarization grating. We call the grating object's internal <code>optimize</code> command and pass in the constraints. The <code>tolerance</code> argument gives the residual of the merit function at which the optimization stops. Start with large tolerances and decrease and re-optimize. You can run the code many times with different tolerance values without overwriting anything - the grating object is storing the entire history of all optimization done on it, so if you optimize it again it starts where it left off from the previous optimization. When called initially, the <code>grating</code> object stores a random initial condition from which the optimization begins.\n",
    "\n",
    "The merit function being displayed in this case is the power in the orders of interest divided by the power in all transmitted orders."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:  1  - Merit = 0.05565965457865001\n",
      "Iteration:  2  - Merit = 0.09383886810511806\n",
      "Iteration:  3  - Merit = 0.11093629722232456\n",
      "Iteration:  4  - Merit = 0.12107452403100064\n",
      "Iteration:  5  - Merit = 0.13145491799477343\n",
      "Iteration:  6  - Merit = 0.143768340740982\n",
      "Iteration:  7  - Merit = 0.14766223904719938\n",
      "Iteration:  8  - Merit = 0.14870826234223064\n",
      "Iteration:  9  - Merit = 0.1498004317161855\n",
      "Iteration:  10  - Merit = 0.15184803755838028\n",
      "Iteration:  11  - Merit = 0.15455594773449083\n",
      "Iteration:  12  - Merit = 0.157816717613765\n",
      "Iteration:  13  - Merit = 0.15948631928757004\n",
      "Iteration:  14  - Merit = 0.16100578058582918\n",
      "Iteration:  15  - Merit = 0.16428067489126794\n",
      "Iteration:  16  - Merit = 0.16742010110969835\n",
      "Iteration:  17  - Merit = 0.17589414700599862\n",
      "Iteration:  18  - Merit = 0.19664092143509743\n",
      "Iteration:  19  - Merit = 0.2294366100382858\n",
      "Iteration:  20  - Merit = 0.29555179577680324\n",
      "Iteration:  21  - Merit = 0.26966969064512814\n",
      "Iteration:  22  - Merit = 0.32694574094481255\n",
      "Iteration:  23  - Merit = 0.31658849290304025\n",
      "Iteration:  24  - Merit = 0.3264289079150629\n",
      "Iteration:  25  - Merit = 0.34826360517136057\n",
      "Iteration:  26  - Merit = 0.3513297087228745\n",
      "Iteration:  27  - Merit = 0.3668044234088458\n",
      "Iteration:  28  - Merit = 0.3778882149596975\n",
      "Iteration:  29  - Merit = 0.37981482334291733\n",
      "Iteration:  30  - Merit = 0.39555320470680827\n",
      "Iteration:  31  - Merit = 0.4133120851271611\n",
      "Iteration:  32  - Merit = 0.4297417477157598\n",
      "Iteration:  33  - Merit = 0.43745876091818126\n",
      "Iteration:  34  - Merit = 0.4495648750897405\n",
      "Iteration:  35  - Merit = 0.4634544568669161\n",
      "Iteration:  36  - Merit = 0.470975497585739\n",
      "Iteration:  37  - Merit = 0.49630882048586616\n",
      "Iteration:  38  - Merit = 0.5102603946598452\n",
      "Iteration:  39  - Merit = 0.5195365074545806\n",
      "Iteration:  40  - Merit = 0.5218577351666003\n",
      "Iteration:  41  - Merit = 0.5292672285889848\n",
      "Iteration:  42  - Merit = 0.5381689720699745\n",
      "Iteration:  43  - Merit = 0.542127534581597\n",
      "Iteration:  44  - Merit = 0.5506342417625898\n",
      "Iteration:  45  - Merit = 0.5651182864927824\n",
      "Iteration:  46  - Merit = 0.5810244796779827\n",
      "Iteration:  47  - Merit = 0.5942665363263664\n",
      "Iteration:  48  - Merit = 0.6100609295647298\n",
      "Iteration:  49  - Merit = 0.6113671588647185\n",
      "Iteration:  50  - Merit = 0.6163197406974585\n",
      "Iteration:  51  - Merit = 0.6197948989609836\n",
      "Iteration:  52  - Merit = 0.6232094740581005\n",
      "Iteration:  53  - Merit = 0.6279642100631135\n",
      "Iteration:  54  - Merit = 0.6348634883877543\n",
      "Iteration:  55  - Merit = 0.6409061777426903\n",
      "Iteration:  56  - Merit = 0.6473158507242772\n",
      "Iteration:  57  - Merit = 0.6557927137809967\n",
      "Iteration:  58  - Merit = 0.6625771540243143\n",
      "Iteration:  59  - Merit = 0.666112423522188\n",
      "Iteration:  60  - Merit = 0.6677339031852245\n",
      "Iteration:  61  - Merit = 0.6700931208489032\n",
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      "Iteration:  63  - Merit = 0.6811122457250183\n",
      "Iteration:  64  - Merit = 0.6852131821367219\n",
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      "Iteration:  69  - Merit = 0.7183977823845498\n",
      "Iteration:  70  - Merit = 0.7228332725949529\n",
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      "Iteration:  72  - Merit = 0.7311233523362846\n",
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      "Iteration:  74  - Merit = 0.7409022108160519\n",
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      "Iteration:  93  - Merit = 0.7887611930743923\n",
      "Iteration:  94  - Merit = 0.790448731808403\n",
      "Iteration:  95  - Merit = 0.7920844430120199\n",
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      "Iteration:  97  - Merit = 0.7942994409369023\n",
      "Iteration:  98  - Merit = 0.7949179946823792\n",
      "Iteration:  99  - Merit = 0.7963328886767221\n",
      "Iteration:  100  - Merit = 0.7975416782547137\n",
      "Iteration:  101  - Merit = 0.7991668059385006\n",
      "Iteration:  102  - Merit = 0.8005023249829999\n",
      "Iteration:  103  - Merit = 0.8014299093398087\n",
      "Iteration:  104  - Merit = 0.8026076498691099\n",
      "Iteration:  105  - Merit = 0.8040674536646997\n",
      "Iteration:  106  - Merit = 0.8060909843822142\n",
      "Iteration:  107  - Merit = 0.8070663941649905\n",
      "Iteration:  108  - Merit = 0.8079447949316331\n",
      "Iteration:  109  - Merit = 0.8087835832664048\n",
      "Iteration:  110  - Merit = 0.8094989198304321\n",
      "Iteration:  111  - Merit = 0.8100471023310158\n",
      "Iteration:  112  - Merit = 0.8107929367850814\n",
      "Iteration:  113  - Merit = 0.8123274032546322\n",
      "Iteration:  114  - Merit = 0.8129044953392486\n",
      "Iteration:  115  - Merit = 0.8144392756657375\n",
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      "Iteration:  117  - Merit = 0.8160508173508569\n",
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      "Iteration:  120  - Merit = 0.8178335143374618\n",
      "Iteration:  121  - Merit = 0.8189141095002216\n",
      "Iteration:  122  - Merit = 0.8190182005932046\n",
      "Iteration:  123  - Merit = 0.8195930388277475\n",
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      "Iteration:  128  - Merit = 0.8221847632284203\n",
      "Iteration:  129  - Merit = 0.8231421090042079\n",
      "Iteration:  130  - Merit = 0.8237623393784319\n",
      "Iteration:  131  - Merit = 0.8242044914209494\n",
      "Iteration:  132  - Merit = 0.8243440959811156\n",
      "Iteration:  133  - Merit = 0.8245925861894134\n",
      "Iteration:  134  - Merit = 0.8247984939202282\n",
      "Iteration:  135  - Merit = 0.8249685200133399\n",
      "Iteration:  136  - Merit = 0.8253174412391182\n",
      "Iteration:  137  - Merit = 0.8254975934987663\n",
      "Iteration:  138  - Merit = 0.8257752286234737\n",
      "Iteration:  139  - Merit = 0.8262830330284696\n",
      "Iteration:  140  - Merit = 0.8264275668967036\n",
      "Iteration:  141  - Merit = 0.8266099054448481\n",
      "Iteration:  142  - Merit = 0.8269749213459594\n",
      "Iteration:  143  - Merit = 0.8271421538573553\n",
      "Iteration:  144  - Merit = 0.8272556477384249\n",
      "Iteration:  145  - Merit = 0.8274011381969755\n",
      "Iteration:  146  - Merit = 0.827456402152571\n",
      "Iteration:  147  - Merit = 0.8275524387909469\n",
      "Iteration:  148  - Merit = 0.8276583234533473\n",
      "Iteration:  149  - Merit = 0.8277930796616502\n",
      "Iteration:  150  - Merit = 0.8279205561524207\n",
      "Iteration:  151  - Merit = 0.8280979244616085\n",
      "Iteration:  152  - Merit = 0.8282968292134827\n",
      "Iteration:  153  - Merit = 0.8283986763617256\n",
      "Iteration:  154  - Merit = 0.8285244827584382\n",
      "Iteration:  155  - Merit = 0.8286380101748241\n",
      "Iteration:  156  - Merit = 0.8287253732265137\n",
      "Iteration:  157  - Merit = 0.8288114808605352\n",
      "Iteration:  158  - Merit = 0.8288719307603478\n",
      "Iteration:  159  - Merit = 0.8289262295151479\n",
      "Iteration:  160  - Merit = 0.8290015524697754\n",
      "Iteration:  161  - Merit = 0.8290466273084847\n",
      "Iteration:  162  - Merit = 0.8290982360405228\n",
      "Iteration:  163  - Merit = 0.8292161251456434\n",
      "Iteration:  164  - Merit = 0.8293998387317566\n",
      "Iteration:  165  - Merit = 0.8296170742240411\n",
      "Iteration:  166  - Merit = 0.8297711676891459\n",
      "Iteration:  167  - Merit = 0.8298412482171148\n",
      "Iteration:  168  - Merit = 0.829884932939909\n",
      "Iteration:  169  - Merit = 0.8299333481873277\n",
      "Iteration:  170  - Merit = 0.82998042511948\n",
      "Iteration:  171  - Merit = 0.8300165389770986\n",
      "Iteration:  172  - Merit = 0.8300604873913775\n",
      "Iteration:  173  - Merit = 0.8301186432662873\n",
      "Iteration:  174  - Merit = 0.830212959972317\n",
      "Iteration:  175  - Merit = 0.8303259849622366\n",
      "Iteration:  176  - Merit = 0.8304023224880193\n",
      "Iteration:  177  - Merit = 0.8305014748066649\n",
      "Iteration:  178  - Merit = 0.830501201878012\n",
      "Iteration:  179  - Merit = 0.8305370909364017\n",
      "Iteration:  180  - Merit = 0.8305584733936795\n",
      "Iteration:  181  - Merit = 0.8305642693967297\n",
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: -0.8305642693967297\n",
      "            Iterations: 181\n",
      "            Function evaluations: 65900\n",
      "            Gradient evaluations: 181\n"
     ]
    }
   ],
   "source": [
    "output_power = grating.optimize(merit_func, cons, cons_type, tolerance=0.0001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Saving the grating"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a built-in save method; it saves two files: a file containing the grating object and a second for its history. There is also a built-in <code>load</code> command to load that same two files later into a <code>grating</code> object later to continue working with it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "grating.save('Grating Designs/eleven_element_grating_test.npz')\n",
    "\n",
    "# this would be the command to load a previously saved grating into the grating object\n",
    "# grating.load('Grating Designs/eleven_element_grating_test.npz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analyzing our optimized result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can analyze the optimized result to see the power numerically predicted by the Fourier optics model in all of the diffraction orders."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'n')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extract the final parameters\n",
    "phi_x, phi_y, theta = grating.phi_x, grating.phi_y, grating.theta\n",
    "\n",
    "# pack these into a final 'state vector'\n",
    "final_state = grating.pack(phi_x, phi_y, theta)\n",
    "\n",
    "# decide how many orders to plot\n",
    "Nx_plotting, Ny_plotting = 4, 4\n",
    "\n",
    "# instantiate empty arrays of complex numbers\n",
    "Js = np.zeros([2*Nx_plotting+1, 2*Ny_plotting+1, 2, 2], dtype=complex)\n",
    "pwr = np.zeros([2*Nx_plotting+1, 2*Ny_plotting+1], dtype=complex)\n",
    "\n",
    "# get list of orders\n",
    "orders_x = np.arange(-Nx_plotting, +Nx_plotting+1)\n",
    "orders_y = np.arange(-Ny_plotting, +Ny_plotting+1)\n",
    "\n",
    "# iterate over orders and compute power\n",
    "for i in range(len(orders_x)):\n",
    "    for j in range(len(orders_y)):\n",
    "        m, n = orders_x[i], orders_y[j]\n",
    "        weight_matrix = grating.calculate_weight_matrix(m,n)\n",
    "        J = grating.calculate_Jmn_fast(m,n,weight_matrix,final_state) # find Jones matrix of diffraction order\n",
    "        Js[i,j,:,:] = J\n",
    "        pwr[i,j] = 0.5 * np.trace(np.conj(J).T @ J) # average power is 0.5 * (J^dagger J)\n",
    "\n",
    "# plot the result\n",
    "M, N = np.meshgrid(orders_x, orders_y)    \n",
    "plt.pcolormesh(M, N, np.abs(pwr), shading='auto')\n",
    "plt.colorbar()\n",
    "plt.title('Relative (unpolarized) power of orders')\n",
    "plt.xlabel('m')\n",
    "plt.ylabel('n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use this same information to view the map of order powers when the different preferred polarization states are incident, demonstrating the designed polarization selectivity of the diffraction orders as in Fig. 11 of the supplemental information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = Js.shape\n",
    "output_powers = np.zeros([size[0], size[1], len(polarizations)]) # array to store output powers\n",
    "\n",
    "# for each designed polarization state\n",
    "for polarization, i in zip(polarizations, range(len(polarizations))):\n",
    "    output_pol = Js@polarization # find the output Jones vector on each order using Jones matrices computed above\n",
    "    output_powers[:, :, i] = np.linalg.norm(output_pol, axis=2)**2 # compute the intensity on each order\n",
    "\n",
    "# plot the results\n",
    "fig, axs = plt.subplots(1, len(polarizations))\n",
    "for i in range(len(polarizations)):\n",
    "    ax = axs[i]\n",
    "    ax.pcolormesh(M, N, output_powers[:, :, i], shading='auto')\n",
    "    ax.set_title('State ' + str(i+1))\n",
    "    ax.set_xlabel('m')\n",
    "    ax.set_ylabel('n')\n",
    "    ax.set_aspect('equal')\n",
    "    ax.set_xticklabels([])\n",
    "    ax.set_yticklabels([])\n",
    "    \n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also compare the polarization ellipses realized numerically in the optimization to those desired at the outset. The top row are the desired ellipses and the bottom row are the ones that are predicted by the Jones matrix Fourier optics formalism.\n",
    "\n",
    "To do this we use some helpful polarization functions provided."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Desired (top) vs. realized (bottom) polarization analyzer states')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gCIKgLGEkgiAIgrKEkQiCIAjKEkYiCIIgKEsYiSAIgqAsYSSCIAiCsoSRCIIgCMoSRiIIgiAoSxiJIAiCoCxhJIIgCIKyhJEIgiAIyhJGIgiCIChLGIkgCIKgLGEkgiAIgrKEkSgAiUklDpJ4UuJVicOkOBfNjsQIieclXpE4Q2LWonUKgq6IG1MNkZDECOBV4BDgK+B14ABg+wJVC6qMxILABcC3wHPACOB5iaMlxitUuSDohDASNUJifOB8/EbxPDCPGUsDKwOPA5sVplxQC/4AfA8sa8Y6wGD8etgbuE9i2gJ1C4KyyMyK1qHpkZgUuAFYFDgUOMyMn0ve/wCYygwVpGJQZSRuAAaZMazd62vjA4evgVXMeKYA9YKgLDGTqDISUwP3APMB65txSKmBSExVe82CGjMu8EP7F824BlgMMOAeiUVqrVgQdEYYiSoiMRVwJzA9sLIZV5X56IXAyFrpFRTCKGCSjt4w4zncUHwC/Fti0RrqFQSdEkaiSiQX03+AQbiBuKuTj08PvFMLvYLCGAlMJ9G7ozfNeAcYDnwI3CoxXy2VC4JyhJGoAhITAjcDMwOrm3FfJ58VMBe+mB00Ly8C4wEzlfuAGe8Dy+KzjlslhtRGtSAoTxiJnJEYB7gCWADYqIsZBMCMuBviqWrrFhTK4+l5wc4+ZMZIYEVAwG0SU1RbsSDojDASOZJmBScDqwI7m3FtNzZbIj0/UC29grrgeTwvZsmuPmjGy/g1NBVwvUTfKusWBGUJI5EvOwM7AseZcXo3t1kOX7AMd1MTkyLa7sXdSd35/KPAJsBCwLlpABIENSeMRE5ILA+cCFwP7NPNbXrhroU7zPiliuoF9cHtwBCJmbvz4RQeuy+wEbBfNRULuoHUC6lfeoyP1BKGO5LpckBiBtzn/AGwqBlfd3O7hYGHgU3NuKSKKgZ1gMRMwGvAbmac3M1tBFyEZ2yvbsZNVVQx8Bv/TMDiwNzAUGA6YBpgonaf/hH4FHgPL7XzAvAo8AhmX9ZK5WoTRiIjyV/8IB7GuoAZr/dg26OBPYApzPi8OhoG9YTEf4HPU0mW7m4zAXA/HuSwgBmvVUm91kQaF5/RrwWsAgxM73yP3/jfAt4FvgC+AX7BkyMHAJPjRmQIfg8gvf8IcBNwBWYNfb7CSGRE4jxgC2C1nozy0gjxNeA1M1aqknpBnSFxCHAgMI0ZH/Zgu+mBJ/B8i0XN+K4qCrYS0gzATnixxcnx0ii3AncA9wEvY9a+OkJn8iYG5sfzXVbC15PAvQV/B67E7DdZ9/VOrElkQGJL3EAcVoEbYH58ZHhl3noFdc0V+O9ug55sZMZbwKbAPMBp+avVQkizIV2GD9J2xQ3CGsDkmG2A2ZmYvdAjAwFgNgqzOzA7CLOF8RnGnniI+4XAm0i7ITVUtFrMJCpEYk7c//gQsGIH9Zi62v5kvDz4lGaMyl/DoF6ReAr4nxkLV7DtYXhp+RFmXJS7cs2MNBlwBLANXrL9dOBkzN6r8n4FLI8HHyyNzwb3xGcWdX8DDiNRAclH/DjwO2BYT9wGaftx8cWue81YrwoqBnWMxJ+B44HZzXiph9uOg7tD5gfmTzkVQWf4TXpTPPpwAO76ORyzTwrQZWngBGBevGzPNpi9XXM9ekC4myrjJGB2YLOeGojEqrgP9PwcdQoah0uAn4Ete7qhGT8xtjfFZdGwqAt8neBy3N3zMjAfZrsWYiAAzO7Gs+53BBYBnkPauBBdukkYiR4isQ6wLXCMGf+uUMzWeLjsrbkpFjQMZnwE3AhsnmaVPd3+PWArfDR6RM7qNQ/SHMBjwDq4q2cpzJ4tVinA7GfMTsdrtj0DXIp0KtI4BWvWIWEkeoDENMDZuKvpwAplDMLD7M5Po8KgNTkbmBJYvZKNzbged5vsnhI5g1KkZfCooomAZTA7qscL0dXG7C1gGdz1uBNwI1L7XIzCiTWJbpKyo2/D6/7Pa8YrFcr5C77wOGOKWAlakFQy/E3gJTNWrFBGX+BJoD8wlxlf5Khi4yKtAfwTT3BbGbP679UibQOcgQ9Af4/ZqGIVGkvMJLrPjniEwp8zGIg+uKvq1jAQrU2KhjsTWEFilgplfIcvyE6JzyoC6ffAVcDTuHup/g0EgNk/gHXxDpa3I/UvWKMxhJHoBulHfCxwC3BWBlHr4pU9T8lDr6Dh+Qde2mGnSgWY8QRwCLCR1LPci6ZDWgi4BngOWAmzxqpiYHYdYw3FVUh9CtYICHdTlyS3wH3AbMCcqTFMpbIeBCYDZouCfgGAxEXAmsC0ZnxVoYxx8NIwMwJD08J4ayENwvOWvgMWLix6KQ+kLYFzgdMx27FodWIm0TV/AhbF+0NkMRCLJDmnhoEISjgJX1PYulIBKQBiBDAhcEbLlRX32ktX4N9/tYY2EABm5wF/BXZAGlG0OjGT6ASJ2XDf5i3AOmZUfLAkrsDruUxrxuh8NAyaAYn78F7oM2eJeJPYE3eLbmzG5XnpV/dIhwP7AxthdkXR6uSCh8P+G+9wOQ9mbxSmShiJjknRTPfhSXNzVJg01yZrBjzS4gQz9spJxaBJkFgTuBZvd1vxTS65Rh/ES13PYcbH+WhYx0jz4W6mCzHbqmh1csVdaM8C/wWGF1XCI9xN5dkJD3fdLYuBSPwZLx/crR4CQctxA/AKsGcWV1GKmNoSd181/7Um9cIDST4Bdi9Ym/zxyKzd8Za3mxWlRhiJDpCYDjgKz4vIVERNYjLc33xRypQNgl+R1qj+itdjWi6jrBfwLOyNJFbLQb16ZlP8mO2BWbPmiJyH96Y4FmnCIhQId1M70kjuBjwTcmjWfIZUtXP/JOvF7BoGzUiqwfQm8KJZNkOR8nGeACbG3U7d6pTYUHh46GvAR3g0U/MGg0iL4m7EfTA7pta7j5nEb1kfL8B3QA4GYgCwC/CvMBBBZ5jxA14ddNkUCZdF1v/wpM1pgMNyUK8e2QRf7D+wqQ0EgNlDePDMnkgT1Hr3MZMoQWJi4EW8jPfCPe0R0YG8fYEj8ZaTT2TXMGhmJPrjrTIfNKusplM7eafhPUsWNuPxrPLqBi/9/RzwP7yqa/PfxKSlgHuA7TDLktDb8123wvHtLiU/qgXNeDKjrH74D/4xM1bOQb2gBZA4AB/9z2fGUxllDcAHPR/i13R9FbirFGkJPPJwa8zOLVqdmuCG8QmgN2bz1HLX4W5KSCwI7ACcktVAJHYAJgUOzUFW0DqcCnxJhVWGSzHjSzwZdF78emwWtsT7UTdHTkR38NH8ucDcSHPXctcxk2BMfPkjwEC8ZEZF5RFK5PUD3gCeMmOlHFQMWgiJg/F6TPOa8XRGWcKj9BbGr+0PMitYJJ5d/SFwC2abFq1OTfH2qx8Cx2K2X612GzMJ5//wULo/ZzUQiZ3wznMH5yAraD1OBkbhhiITqUrATsD4eDZ2o7M43jb46qIVqTlmnwL344E1NaPljYTE5Hhc+Z3kMH2VmAjYC7jZjIezygtaDzNG4ZFOa0oskIO8V/E8jE0llswqr2CWw1u/3lG0IgVxM+5ymqpWO2x5I4EbiP7ALllqM5WwGz7SiVlEkIWTgc+Aw3OSdxQwEjg1VY1tVIYDT2CWx4y/Ebk3PS9Wqx22tJFIo7Rt8MXqF3KQNymwB3BNU4UcBjUnuT2PBlbKY/Rvxjd4eZi5cfdq4+FlOObF+1a3Kk/hob8L12qHLbtwnRb07gdmBmZJkSBZZR6LG4m5zHg+q7yiSXH7swKz4EXjpgemw5O0BgIDuhDxM17f/4f0+DG99guMmbX1To9x02N8oC90Odr9FvgAz2l5B3gbDxZ4BXjZjMYuFw1ITIAXhnwLWCLrTDdd83cA8wBDzGispjzSjMDrwLapk1trIj0LvIVZ5lya7tDI086sbIRP2bbJyUAMAv6I12hqOAMhMT4+OlkcWBAYhhuFUj7Eb8gv4ms4H+JlET5Lj1F4+ObXwGjgf5Xe2CTGxfsD9MeN0cS4G28yPChgSmBq3GAtCWyMG5u27T/By7w/DjwE3N9oPaDN+FbiULzN6Wp4uZgs8kxiV/y4/AXYObOStWWm9PxqoVoUz0u4oa8JLTmTSCO0l4BPySnJSOIcvODYLGa8nVVeLZCYEFgP2ABYFh/Fg4/Gn8ZLFL+Q/n8j9VSuS5JRGYTPemYH5sRdE3Phg6FfgIeBfwGX5FDZtyak7/U87mKYJ6dr9TRgO2DuPNysNUPaBjgbmB6zhviNVQXpRHw21a8m+zOzlnuAHQBmYEvlJG8o2M9gJxT93bqp77hge4N9kY7Dm2Ang60O9rui9cv5u/YFGw52KNiT6fv+D+x0sEmK1q+b32G9pPdWOcmbDGwU2M1Ff7cePWAv8wMxYeG6FHsc9k7HoV8t9tdyMwmJqfHp6m1mrJuTzBuBJfDOYp/mIbNaJL/0NXhf5Rvw2PkH/NprfiRmxd2C/4evZwwzDzmtW9I5ewifKQ0x49scZO4OHAf83ozbssqrCdKReHj5uLTajasUaUfgNGBKzKreWKoVo5sOA/oAe+chTGJZPLnlyHo3EIk5cQNxqBlrmHF/qxgIADNeNmMnYG1gMJ5pX9ek87MnHizw55zEnoov9P81VRxoBHoDP7a0gXDWT89z1GJnLWUkJObE676casZrOcjrhScpvQP8Lau8GvEhHnG0WhpVtxypEVRbSYdLitSlu5hxHz4D3EcicyKVeWnyffA1m82zyqshFXfuayJeTs81iU5rKSOBx51/jSfQ5cEIYD5gXzO+z0lmVTEPDd0QD/19QeIaiXXSInbTIjGOxNISZ+Ihpevh5+0vxWrWI/YGxoPcdL4KX8w/PAVz1DvfAuMhtXJUJjAm2OD9WuysZYyExNKMdQt9loO8fngW68PAZVnl1RIzbsCjgP6Kh7xeDXwucZfEXyRWkxiYpd9y0UhMIrGMxF4S1+F9kO/CewVfhUf2HF2okj3EvLzGacDWUvYQyOTG2gsPJf5jVnk1YFR67io/p9mZFM8zGlWLnbXEwnW62T2M+3RnsRxCOSUOx9uSLmoNXKMplWhYClgFD4Odh7GDh8/wnIhX8CSmN/GktfeAD8w7oBVC0nsKPE9iEJ7TMRNjQ2CnKfn4a8DdwK3ArebZxw2JxCR44MWzwLJ5rCdJXI9fAzPlMYCqGtKGwOXA3Jg9W7Q6hSGdBayJ2ZQ12V2LGIm18fj4bcw4Jwd5M+JTvqvMaKpyxWmGNC9uLObCF8eG4Mlr7fkC+BjPN/mcscl0XwHfpMd3wPd4nH9HGde98AXJcfCAgraM6754Il1bMt0APJluUtw4TMZvZ8JfkjKu8c5lTwNPWhNkX5ci0Rbdsq4Z/8pB3lA8J+YEM/bMKq9qSAvhgQZrYnZ90eoUhnQH0A+zmpTmaHojkSI3nsUXvOYy46ccZF4N/B6flbyXVV4jkNYsBuNlOabFXRRTMTYDepL0mCg98oiYMdzQfIkboM/x2c3H6fE+PqsZCbxlDZZRXSlpFvUU0A+YI6eZ8QV4UuXMdXtNSxPjA5N9MWsoV2GuSO8Dt2O2RS121woLQH/A3Q/r52QglgfWAQ6o2x9TFUgumheggTJ0mxQzfpLYBV9j2ZN8FrIPwUubHIi38K0/zEYhvYkHi7Qm0tT4AK1m7ramnkmkkgYv4SPRBcz4JaO8PsAzeCG6ORsloiloTiSuANYAZjfjrRzknYYnGc5ixptZ5VUF6XK8Vte0LZkvIa2DB5osillN1kKbPbppc2BG4MCsBiKxKzAb8McwEEEdsAe+vnNSTvKOxNeMDshJXjW4Ew9AackcH2B53AX7VK122LRGIo36DwAexbs5ZZU3CG8kdL1ZdnlBkBUzRuKupjWl7C0tk/v0dGBziZmzyqsSt6fnmpTJrisk4WH8/8Hsh1rttmmNBD6LGAwcnFPZiZPw47VrDrKCIC9OxF2qp+SUEHcMHoW2fw6y8sfsLeAJxpamaCUWxgNHrqvlTpvSSKS1iP3xcLnMxcskVsEXqw/Lw/cbBHmRclV2BGYghxu7eQn1M4DNUqh3PXIZsCBSTWoX1RGb4eHkV9dyp025cC2xJXAusGpW11AK/XweLwkwrMgEsiAoh8SFeCOtYZaxR4TEQLz438VmbJOHfrkiTQ7JNWbWGjN7aSLgXeB6zGqam9V0M4kUQ74fvrBzSw4iD8bdVtuFgQjqmN3xboBnpsKTFWPG+8A/gBFpLa6+MPsEuBLYCul3RatTI7bGE0tPqvWOm85I4IXbZgaOyLoWITEML838j1SFMwjqkpRVvgfe1ySP0f9f8QTUPXKQVQ2OwZMJm38mIU2A19i6B7PHa777ZnI3pRpNT+GlHebIEvaaZiSP4NnFs1ujNY0PWo50/d+Jl1WZI80Issg7D68YPLguS5tIV+GVD2bGrCHa0VaEtBduFJfCrOaD1WabSayE1xw6Joe8iD/hmZ07h4EIGoE0c/4/vJz4aTlU8T0Wr6G1U1bdqsQ+eL2vI4tWpGpIA/Es+BuLMBDQfDOJ/+AlOGbIsn4gMQueWX0bsHYrdW4LGh+JtpHnhmZcmVHWdbgLa7q6rJ4rHY332VgOszuLVidXPC/iKjw3Yg7M3ihEjWYxEhLzAk8Ce5txbAY5vYB78DafQ7NO2YOg1iRX6cN4TP3QLK4iiSWA+4AdzTg9JxXzQ+qLV7AdB5gXs1HFKpQj0qbARcA+mB1TmBpNZCQuAtYCBmVpbJ8Kp/0N2NKM83NRLghqjMRceNLZNWZsmEFOWy+WSYDZcipvky/SIrghuw5YvylqOkmzAY/hHo3hmP1clCpNsSYhMTW+wHZuRgMxBJ+m3wJckI92QVB7zHgWOBTYQKo8Ozm5Wk/Ae4pkLv1RFbzQ3X7AusC+BWuTHS+Jfg3ei2WjIg0ENMlMQuJQfHFnFjNeq1BGb3w0Mjte4bVlyoAHzUlyOz2EZ2PPmbKpK5XzFvCCGSvmp2GOuP/+ImAT4A+YNVRL4TFI4+FroYsBK2J2d7EKNcFMIhXy2w64uVIDkdgTWBTYJQxE0Ayk/ikj8HyCsyqNdkpyTgdWkJgtRxXzw0e72+DriRchrVmwRj3HDcQ/geHAFvVgIKAJjAReU2lKvJ1jRaRF77/gkQSX5KRXEBSOGS/ioaKr41m7lXIW3oJ2hzz0qgpm3+Pf8wngKqQ/FKxR95EmxF1MqwM7YnZpwRqNoeHdTRL34AlvQypZVJPoCzyOL8zNVdeN4IOgAlLE3u34THmYGa9WKOcSfF1ioBnf5qhivnido+vxEfk+wLF1vZgtTQXciCdBbo/Z2QVr9CsaeiYhMSuwFHB2hqiL44A5gC3CQATNSPptbAH8AFySXLSVcAYwACqPlqoJZl/hmdhXAkcDlybDUX9IS+Gh+7MDa9abgYAGNxK4D/InqCxUVWINvMzy8WZjmpkEQdNhxrvAtsCCwGEVirkfeAXYKi+9qoa7njbCo502AJ5GWqJYpUqQxkM6Ai+j8jWwCGY3FqxVhzSskUgRF5sBN1UStZGqW54HPE29NlgJghwx42p8bWEvqedRSikc9lxgiVSVoL4xM8yOxntiC7gP6SykSQvVS1oOnz3sh0dkLYjZs4Xq1AkNaySAFfEF6/N7umEyMJfhdV82NKNmrQCDoGD+BLwAXJTyi3rKRXhf7c1y1aqamD0IzAUcj8+C3kDaD6l/TfWQ5kO6HvgPMAGwKmZbJvdY3dLIRmIT4HMq6199OLA4sL0Zr+SqVRDUMWnBeQM8LPayNGDqyfbvA3cAm+ZQQLB2mI3GbA+8AOjdwBHASKSjkGao2n6l3kirId2KR10tic8gZscsU0O0WtGQRiJ1i1sLuKqnhfzSOsTewJlmEe4atB5mPI+vxQ2nsvWJS4DpgYVyVKs2mD2P2Zp4v+jb8T4NbyDdhbQTUvYmS9K4SEsgnQC8A9wAzI0n/E6P2VFpzaQhaMgQWIl18ZyG5czoduXHVHbjMeB1YHEzGuZEBUHeSJyFL2avbca1PdhuYuBj4BQzdq+OdjXCjcII3H02a3r1Vbz6wlPAc8CbwPuY/dhuW+Hd4gbjjc7mwQMDlgAmAn7ES/xcDFz7m+0bhEY1EpfgvSOmStmg3dmmH95EaEpgATPeqp6GQVD/SIwP3AvMBiycEu+6u+1NeNjmTE1TSt+L6q2Kh9UvAbRvjTo6PQwYFzcEpeHEv+DrPQ/is5Q7mqEqbcMZieRD/QS4zowturlNL3zmsSawkhn/qZ6GQdA4pCi/x4EvcUPxRTe3+z/gTDwB9bkqqlgMPksYCAwFBuEJuwPwtRyAn/Fj9inwLj77eBmz0bVXtrr0aNGqTlgYmBi4qQfbHAqsDfwpDEQQjMWMkRLrAHcBV0qsYkZ33CJti64rQRMaCR89v5ceLU0jLlwvh0/37ujOhyU2Bw4AzgFOrqJeQdCQmPEA3vZ0eeCU7kQtpeS8F4EVqqxeUDCNaCSGA890p++0xPLAP/C45B2axncaBDmTGmwdhVdU3qebm90NLJbK7AdNSkMZibS2sABeI7+rzy4AXIuPdtbr5hQ6CFqZA/Dw1iOlblWMfRCP7pm9qloFhdJQRgKPzZ4IT2kvi8ScwK34Avfvzfiy+qoFQWOTCgFuhTe9OUtigy42eTo9z1NNvYJiaTQjMSQ9v1zuA8lA3IFXvFw+ZYgGQdANUnLqOvgs4VKJ9Tr5eFvJ8ZmrrlhQGI1mJKZKzx3e+JOL6W48PG1ZM16vkV5B0DSk0h2rAA8Dl0sdh5qX1DyruId2UP80mpFoS1z5TUG+VG7jHrzs7pJm5WcbQRB0jhlf4z0Z7gTOkzi4k6inobXTLKg1jWYkRqXnydtekOgjcSRwHb5IvWjMIIIgO2aMxttpXgAcAlwr/eq31xbVdH7NlQtqRqMZiUfS8zYSk0tshC+e7YvnQSxZSW+JIAg6JrmUtgR2BVYGXpLYQ2Jweh16ltgaNBiNWJbjdGD7kpdeAf5sFhdqEFQTiaHASXjSXRuP4oOzHlVjDhqHRjQSvfAiXDMBzwD3ZOhvHQRBD0kRhEsCXwFXRzXl5qbhjEQQBEFQOxptTSIIgiCoIWEkgiAIgrKEkQiCIAjKEkYiCIIgKEsYiSAIgqAsYSSCIAiCsoSRCIIgCMoSRiIIgiAoSxiJIAiCoCxhJIIgCIKyhJEIgiAIyhJGIgiCIChLGIkgCIKgLGEkgiAIgrKEkQiCIAjKEkYiCIIgKEsYiSAIgqAsYSSCIAiCsoSRCIIgCMoSRiIIgiAoSxiJIAiCoCxhJIIgCIKyhJEIgiAIyhJGIgiCIChLGIkgCIKgLOMUrUCrItEbGAb0Bx4x47tiNQqqTTrnCwN9gMfM+KZglYKgS2ImUWMkekn8H/Am8DhwF/CCxLTFahZUE4k+wB3AA/g5/0DiaImJitUsCDonjEQNkRgE3A2cCYwENgXWA6YCDixOs6AG/AEYDuwOrAzcCOwN/Fdi8SIVC4LOkJkVrUNLkG4E1wB9gZ2BC82w9N6/gDnNmKVAFYMqInEBsCIwsOS8LwpcBAwGdjbjzAJVDIIOiZlEDZBYC7gTGAUsYMYFbTeKxNrAkAJUC2rHFMC7pefdjIeABYB/A2dIHC6hohQMgo4II1FlJDYGrgaeAhY14+UOPvZ2bbUKCuAnOggUMWMUsAbwD2B/4MQwFEE9EdFNVURiQ+Bi4D5gNTNGl/noExDRTU3Ox8D8Hb1hxk8pmGE0sBtgEn9uN9sMgkIII1ElJFbFDcQDwKpdhDsOAd6oiWJBUbwOTC3R34yv279p5oYBn93vBnwFHFxbFYPgt4S7qQqkBcl/As/gM4iyBkJifGB24L81Ui8ohmfT8zzlPpBmDrsB5wIHSexYA72CoFPCSOSMxBDgBuB9YBUzvupik/nwGd0j1dYtKJTH0vPCnX0oGYrtgOuBUyTWqLZiQdAZYSRyROJ3wE2AAb834+NubLZUen6waooFhWPGh8BreK5EV5/9Cc+reAK4TGK+KqsXBGUJI5ETEuPiLqbBwNpmvNbNTVcEnummQQkamzuApVP2dackF+XqwKfAdRJTV1u5IOiIWLjOj+OAZYEtzLi/OxtIDACWAE6spmJB3XAr7kpaAs+b6RQzPkrupgeBf0ksbcYPVdYxaEMSMAiYDpgGGAD0S+/+hAcXfAq8C7yGWbnoxYYmjEQOSIwA/gicaMYFPdh0JWBcfA0jaH7+A/yA50V0aSQAzHgmXV9XAX/DjUxQDaQJgGVwl+BiwNx4Ac7ubv8Ovvb0AHA78AJNUNIiynJkRGJefKT3ELBi8id3d9sr8ItyajN+rpKKQR0hcT1e/XdwT/IgJI4C9gG2MeOcKqnXekjj4W69zXDX7/jAj/jN/ingObwY57vAF8A3+JrjuMBEwOT4TGMIHrm2EDBDkv42cAVwEWbP1eYL5U8YiQxITIwvLo4HzNeTdQWJCYBP8BpOO1RHw6DekNgcOB9YLJXl6O52vYHbgMXxzP2nq6JgqyBNCewE7ABMhkcj/guPKrsfs8qTW6XpcIOzTnruDdwPnARcg9kvWVSvNWEkKiSVTrgaH4Us1ZMffNp+I+AyYBkz7s5fw6AeSaXBPwbOMuOPPdx2CuBJ4Ht8UNJVeHXQHul3+IxsF3xwdz1wBvBvzPKfzUuTA5vjxmhG4Hm84vO1jeKKiuimytkZL8y3T08NRGIzvFz4vblqFdQ16cZ+A7BRiojrybYfAxsC0wNnRo2nHiD1QtoGD0PeA7gSmA2ztTC7tSoGAsDsE8yOA2bBw5p74zOWO5Bmr8o+cyaMRAWkdYjj8J4AJ1Sw/dT4ovUlZjTU1DPIhQtwX/bKPd3QjAfwkehGwNY569WcSIPxRk9n45UNhmG2OWav1EwHs58xuwyYC3dzDQOeQtobqXfN9KiAcDf1EIkJ8Sl/P2AeMz6tQMbewNHArGbU7kIN6oI0gxgJPGzGWhVs3wtfn1gMmN+Ml/LVsImQ1sHLnLTVxDqvLtw8viZyOu6N+A+wCWZ1mSsVM4mecyIeybBJhQZC+Ajw/jAQrYkZP+KL16tJDKxg+1+AEcC3eEb2ePlq2ARIQjoUXzd8GZ89nFsXBgLA7CNgXfxesATwBFLZul5FEkaiB0isDWwLHJthsXlZ3MhEF7LW5h+4f3qrSjY244O07TDgL/mp1QRI45CKJOLGeDhm9Vdl2cwwOxdYFBBwP9JyBWv1G8Ld1E0kpsIreb6DhyD+r0I5/8QNxTRmfJ+jikGDIfFvYDZghp7k17STcSY+cFnaLIIgkoG4FFgfOAT4S93MHjpDmga4BR9AroXZbQVrNIaYSXSD5CI6C8++3DSDgZgW90GeGwYiAP4OTIuHUVfK7nivigtTeG3rIvUCzsENxB6YHdoQBgLA7D188PgScB3SEgVrNIYwEt1jC/yHvK8ZL2aQsz1+zP+eh1JBw3MDvoC9S6UCUrfDEXiNoeNy0qtRORQ/FgdhdnzRyvQYs0+BFYC3gBvqJUQ23E1dIDEIT81/Gk98qyhkVaIvnqb/kBlr5qdh0MhI7AUcg0fKVdx4SuIYYC+8h8kteenXMEgb4CUwzgG2bZgZREdI0+P9Zb4AFsKs0KTJMBKdkNxMt+DRB3ObVd5iVGIbPE47MqyDMaQeJCOBK8wqW8ROcsbHS8QMAIaa8WVOKtY/0kx4naVngWUwq8gdXFdIw/HS8lcDGxVp9MLd1Dlb4klve2c0EL2AP+EX8j056RY0AWZ8jkfgbJKlZ0Ra49oCmJpWcjt5ItrFeOnujZvCQACY3YMnTW4AbFykKmEkypDi10/Ay2acnlHcysAcwAk9qfwZtAwn4lVFK16bADDjMdxAbCOxQh6KNQA7AYsAO2P2TtHK5MyxeIXpU5EmK0qJcDd1QHIz/Qv4Pe5mejWjvHvxjnUzp0SqIPgVElfj0S2DsxTuS26nZ3CjM1fqcNecSFPgtZjuB1Zt6HWIckhD8fXQ8zD7vyJUiJlEx6wNrAUcnIOBWBRYEp9FhIEIynEMMDGQ6UaQ3E7b4j0Nmj3J7lCgL7BbUxoIALPngVOAbZDmKEKFmEm0I/WIeAH4CFiw0iSnEnk34BmVg5t6VBdkRuIOYHZgxqx5NBJn4MZiITOeyEO/usJ7NrwOnI3ZjkWrU1WkSfHGR7dhtn6tdx8zid9yFDAl3gEsq4GYB1gNOCkMRNANjsIXnrfIQdY+pL4VUlO2Kd4jPR9dqBa1wOwzvHXtukhDar37MBIlSCyC9xD+W06jr/2Br4HTcpAVND93AA8D+/S010R7zBgF7ArMR8YF8bpD6odHHl7WhIvV5TgNj+DqUaOqPAgjkUijrTOA9/DCYFnlDQXWww3OF1nlBc1Pinw7HA9y2CwHkf/E83z+kkrCNAsb4aX6zyhakZph9gF+PjdFGr+Wuw4jMZZd8Ebmu5rxdQ7yDsCbpp+Yg6ygdbgZT4o7IIfZhOEdFMehguZYdcwf8PLflXSEbGQuxIMbVq3lTsNIMCYn4lD8B3pNDvKG4m0mTzXjs6zygtYh3dgPwaOTMs8mUhLoEcD6EitllVc4HvY6HLiyaSOayvMf4FPoeaOqLER0EyBxKbAOXs7g9Rzk/RPP1J4hjETQU1KezqPAZHj3wkxZxKkp0bPp37nM+CGjisUhbYJnWC+I2eNFq1NzpAuBVYApq9aXux0tP5OQWBpPez86JwMxD74WcVIYiKAS0mziIGB6KmxK1E7eD/iC5xC8PEwjsyxe+O6pohUpiNuBSYGhtdphS88k0mL1k8BEwOxmfJeDzBvwgoAzxoJ1UClpNnEf7naaOadr8xpgRXx28m5WeYUgvQC8htkaRatSCNKMeH7IjphlLRfULZoxfron7ADMBayb049wMTwvYt9mNBBpIXWa9BiI55NMjrtFfgdMghvcifDokwnwjNjx6d619jPwP+A7vH/zaDyE+CtgFPA58Bke//8x8D4ejfauGd/m8BXrBjNM4gDgLmBHII/+CH8GXsSzuzfJQV5tkSbEO/ldWbQqBfIm/huYt1Y7bNmZhMSkwKv4TGKFrIX30sjvLvwinqmRk+ckJscjvebCM4BnAWbEjUN7F6Xh0//P8Bv5l/iNfTQe3fUd8EN6/IjHev+StlOS1xuvNTQublD64gamH94NcAAe1TEJPtXuyOB8ArwBvIJHvrT1AHmnkYsqStwKLIjPTDOX/5Y4DI+8W8KMB7LKqynSvPjvdT3Mri5ancKQ7gMMs6VqsbtWnkkcgt98dsvpJrIyHnWxS6MZCIlpcP2XARbDfeFtfIrfeO/CO2a9A7wLfAB8CHxmRk0W0JKuwg3GVHh28jR4V7bpgZnw71AaFfSpxEN4ifZbgRcazGjsh4fE7onf3LNyNJ7RfbLEQpU20SqIGdLzm4VqUTyvQu0i1VpyJiExB/Bf4EwzdspBXm98IW0CYI6s0Si1ILmO/oDX91k8vfwhXlHzEfz7/NeMT4rRsHIk+uMLe/Pio/Al8EVb8FnGefi5H1WIgj1E4nK8fe7MZnyQg7y2CKEtzLggq7yaIe2Cl6eYErOPi1anMKQjgL2B8WoR4dSqRuJmfMQ8sxmf5iBvBHABsLEZl2eVV20khgGXA7PijdcvAq4Hnm+wUXa3SRnHq+PZukvh6xv/Z0bduy0kZsLXEs4zY7sc5PXCE9GmBWZpmJmvdCBe2bYPZq1bUVnaDU/SnRSzz6u9u5YLgU3NWFYGDsvJQPTFk5Uew3vs1jVplH07MCGwBj7zOdKM55rVQACY8a4Zp5sxHK9n9CpwlVRs16/ukEKzT8ebCWUuF51cTH/Cgw/26OLj9UQ/4IeWNhDONOl5ilrsrKWMRHILHYcvcJ6ak9jd8BHZHg1yk50Zj0j6qxk3NIjOuWLGU3ikD3it/kbgMDwY4Ng8hJnxIF4LaM8sbVMLoOWu1w5YMD0PrMXOWspI4Auac+MhqpmzTiWmBPYFrjfj3qzyasSzeITI8RLHNNgNIjMS/SR2Bm5ILy3Y2efrhTTrPQJYVWK5nMTuC/ShcZoT/YJHwrU6t6TnTA3RukvLGInkFjoMdwv9Myexh+HhmnvmJK/qpB4ZywOX4HqPlLhFYgeJmVP0UFMhMaXExhKX4FFZp+DGcjazhoqU+RseYXZCmhVnIrmx/g5sJTF7Vnk14Ctg3FpXQa1D2harK25z2xNaxkjgVV6nBfbMw8UiMTewNV7E75Ws8mqJGV+YsQWe/3Bcev47PjJ5X+I6iUMk1pWYXaJPgep2G4neEtNLrCyxp8SlEq/iUVuX4mGDVwCLm7G0GS8XqnAPSd3q9oYx114eHI7nsxyZk7xq0pagOmmhWhTPlHjeUU2MREtEN0lMgq9DPGiWvcxuGm3fif9YZ2707Or0fWbBcwwWBxbAI5/aZhW/4PkRbwFv41nO7+M334/xXIrPgVHVKB6XyqcMwG8Ok+ILdlPgPtlpgOnwPInpgfFKNh2J5xg8BNwNPFHLnI5qkM7VPXjS5pCcEuz2x43F4mmtoj6RVgFuAhbHrH71rDbSpcCimM3Q5Wfz2F2LGIkj8XaOw8z4bw7y1gWuAnY0oyb1U2qN5DkfeMb1EHzBe3B6TEV533DbCOcbxmZcf4+X2/gRnyq3ZVyDz2bHSY8+jM247svYjOsJOlH1Y9wYvMWvM66fN6Pq4YFFIDEf8Dhwohm75yBvQrwe0MvA0nUbzCDNhocCj8DsoqLVKQzpCeBTzGqSUNf0RkJiKvzmcY1Z9no1aW3jRfxGOF/WPtiNSPKHT87Y2k2T4yUzSms3TZge46dHn/TozdhyHJYeP6XHD/y2dtNovNTHKH5bu+mjRkhcrAYSZ+OZ03Ob8WIO8nbG12pWMuP2rPKqgjQuXvLlVMwaKXQ3P6Te+L3nbMx2q8kuW8BInAzshC9SvpaDvEOAg4FlzLg7q7wgqIRUX+tVPBBjxRxqj42HzyQ+BRas49nEo8C3mC1dtCqFIM2D1yTbFLNLarHLpl64lhgEbI9nquZhIGbE3VaXh4EIiiSVSzkIj1RbJwd5P+ChsPPjmen1yv3AIkh9i1akINpK6NRsTaapZxISZ+BNW4aY8XYO8q7HF3dnM+O9rPKCIAtpQf8JvEz7bFnLayR5L+JrSfPVZfE/aVXgRmBFzP5dtDo1R7oBXyucuVbtW5t2JiExGDcQ/8jJQKyBj7AODQMR1ANpPWxHPLT7wJzkHYqXiV87q7wqcRe+XlWv+lUP76exHHBTLft7N+1MIs0itsRDVEdmlDUh8AJjF6tbvXZMUEdInAdsikfvPZ9RVm/8Wv+O+p1NXImX5Z+2peo4SZvixTiXwuy+Wu22KWcSaS1iK+CcrAYicSAei79DGIigDtkTH8CckSq8VkzKIzkcn03U69rEhXieTL3qVy22xEO9a9osqimNBLAXHmZ5TFZBEnMBuwPnmnF/VnlBkDeprtOeeN+MLXMQeRnwGnBgnZZpuQVvfJW5F0zDIM0FLAuciVlNZ3dNZyRSXsS2wAVZ1yLSqOwsvBxAw9RnClqS84H7gL+mwpMVk9YmjsYjnVbIrlrOeKOdvwHLIi1UtDo1Yg/cBXh2rXfcdEYC2BXvlZx5FoEvCi4C7N6s2btBc5DWDrbDExhPykHkRfhoff8cZFWDM/DB2yEF61F9PNN8U+DvmH1W6903lZGQGIDf2K8yy1ZGV2I64Ci8Qc/FOagXBFUlZV4fCWwkZatRljLZjweWklg0D/1yxexr/LuujLR80epUmaPxiK48Br49pqmimyT2wg/k/GY8mUGO8EJiSwFzmvFWPhoGQXVJmdNP4AURh5pVXilUoh9e2PEeszoMOfWS4S/g5VyGYZZ7ccnCGVvUcG/Mcmk41VOaZiaRylnvCtyRxUAkNsNbnO4fBiJoJFLm9FZ4hdxMNxUzRgOnAWtKzJqDevli9j2wA14R94CCtckfaWLgTLwP/UlFqdE0RgJvcD8Q749QMalT28l4mFmjtLYMgjGY8ShwIrBdDl3sTsGLLu6WVa+qYHYbcAGwH9KSRauTG5LwFstTA5tjVlghy6ZwNyX30JP4gvVclRYnS3KuBVYE5mm0ZkJB0EaqVvw03l9jLjO+ziDrHGBjYJAZNV847RKpP/777wssgNmHBWuUHWkHvBHYwZgV2l62WWYSSwLDgJMzVq8cAayBu5nCQAQNixnf4aXEB5Fxdo3PSvoC/5dRTnXwRez18VL11zZ88T9pOdybcTOe2FgozTKTuBpYGh/pfFuhjEHAc8AzeOOV+itHEAQ9ROJYPMdnFTNuySDnDrz51Ix120NFWhv4F3ADsG5DluyQ5sU7D74NLInZqGIVaoKZhMS0wJp4Ib9KDUQvPBmpN7BlGIigiTgIH/ycI2XqDX0KPitZIxetqoHZNXgI/OrApUgN0Zt9DNJ8wH/wBlsr14OBgCYwEvgUuBeeXFMpu+Ip77uZ8XouWgVBHWDG93i03mTAmRnKbNyAt4ndPi/dqoLZ6cCfgfWA65H6FaxR95CWAe7EO+8Nx+zdgjUaQ0MbiVT/fmvgVjPerFDG3HjS3PXAOTmqFwR1gRlP40Uq18XXKSqR8TNeEmIFiSG5KVcNzE4EtsFLijyANEPBGnWOtDVwG/AebiAqupdVi4Y2EsAqeNjrmZVsnCJALsPT+7ep25aNQZCd44C7gVMy3OTPAX7GB2b1jdk5+P1hOuDxtF5RX0j9kM4D/oGfm8Uxy9z7Jm8a3UhsDXyIZyRWwgl4l6cRqR1kEDQlaSawGZ6dfHnKzO6pjPfxCqybp1l8feM5FAsCbwL/QjoPKcu6TH64e+m/wOZ429i6WYNoT8MaCYkp8JHChZVEW0isj/tXjzOj9dogBi2HGe/i2djz4fWAKuEcYCpgpbz0qipmrwGL4XWeNgVeRtoeadxC9JGmQ7oMX3/4GXcvHZwq29YlDWsk8OSecfBsyx4hMSM+xXuE+q1yGQS5Y8Z1eCbvbhJrViDiZuAz/IbbGJj9D7P9gXmB54HTgeeRtkLq8YyqIqTpkf4OvAqshc8e5qllh7lKadg8CYlHgD5mzNvD7cYHHgRmAOaN2kxBq5FcTQ8AM+EtSnu0UCpxGj4jmSJLJncheLmLVfAktWG4u/pc4HzMMlWO7mBfffDqDdsCq+Ezh3OBIzF7J9d9VZGGnEmkmcBC+KJzT/kbPqLYLAxE0IqkIoAb4N0br04BHD3hcmB8yFaOvBDMDLObcJfbCnjF3H2AV5CeRjoUaXiqMNtzpGmQ/oB0AfABHjq8KF6deibMtm8kAwENOpOQ2AP4K5792e1RkMS2eKe5o8zYr1r6BUEjILEafhM7D9i6u9F9Kfl0JPCwGetWUcXaIA3E3ddrAYvjxvNH4EU8EfEtvAHTF8BowPA6cQPw/JPBeDb6PHhBPnCX3K24Qb29yAJ9WWlUI3E/MGFPXE0Si+Dp7ncBq6ZojyBoaSQOxbOydzHj1B5s93e81tlkKWGvOZAmwQ3F4sDcwFBgWrwaQzlG42sNLwCP4u7sp+p5MbonNJyRSKUFPgYON+Pgbm4zCHgM+AZYMFqRBoGTZgXX4K6jFc24s5vb/R4Ph81UE6ohkHoDUwITAf3Tqz8DXwKfAl/RaDfSHlD/sc6/ZXl8LaVbF2bqrnUdMAGwbBiIIBiLGb9IbIaPfq+WWMSMl7ux6T14zsWKdPO32LD4jOD99Gg5GnHhehm8vsnjXX0wJfxcjvsKNzLjhSrrFgQNR2pxujruh78p5SB1tc13wP14zbOgiWlEI7E48EBXCXSpkNlp+DR6JzNuroVyQdCIpACQNfAyNzdKTNiNze4D5pIYUFXlgkJpKCMhMQFeRuPRbnz8cLxC7FFmmSrEBkFLYMbDeBvg+YFrulG64xE8EmhYlVULCqShjAQwK67zfzv7kMR+wH541crIqA6CbmLG9XhNtBWAKyQ668nwbHqes+qKBYXRaEaireTvGx29KSGJA4EjgIuBHaKyaxD0DDPOB3bGm3ldmaoUdMT7+OL19LXRLCiCRjMSv0vPv2nGnkL5jsdrolwIbBG5EEFQGWacxlhDcVNH6w5pADYesEeN1QtqSKMZibZZwa/0lpgIuBr4E152Y8swEEGQjWQoRgBLAQ/VfbOhoCo0mpFoq3kyW9sLEssAT+EhfLviLUijR3UQ5IAZF+G5EFMCT0psJ3n2cUnP7IOK0i+oPg2VcZ2im94BPgIuxWO0l8XXKEaY8UCB6gVB05KqFlyA5ym9hM/cF8IXuOcx6zyYJGhcGspIAEisCJyPF9J6HW9dempK7gmCoEqk3KP1cLfuIniZm317UvMpaDwazkjAmEXqvmZ8U7QuQdCKpNDYn2Ptr/lpSCMRBEEQ1IZGW7gOgiAIakgYiSAIgqAsYSSCIAiCsoSRCIIgCMoSRiIIgiAoSxiJIAiCoCxhJIIgCIKyhJEIgiAIyhJGIgiCICjL/wMkgQ8yboCS8wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import Core.helpful_polarization_functions as pol\n",
    "\n",
    "desired_polarizations = [pol.jones_to_stokes(jones) for jones in polarizations]\n",
    "\n",
    "jones_matrices = np.zeros([len(orders), 2, 2], dtype=complex)\n",
    "\n",
    "for i, order in zip(range(len(orders)), orders):\n",
    "    m, n = order\n",
    "    weight_matrix = grating.calculate_weight_matrix(m,n)\n",
    "    J = grating.calculate_Jmn_fast(m,n,weight_matrix,final_state) # find Jones matrix of diffraction order\n",
    "    jones_matrices[i, :, :] = J\n",
    "    \n",
    "mueller_matrices = [pol.jones_mueller(jones_matrix) for jones_matrix in jones_matrices]\n",
    "realized_analyzer_states = [pol.stokes_to_jones(mueller_matrix[0, 1:]) for mueller_matrix in mueller_matrices]\n",
    "\n",
    "fig, axs = plt.subplots(2, 4)\n",
    "\n",
    "for i in range(len(polarizations)):\n",
    "    pol.plot_polarization_ellipse(axs[0,i], polarizations[i])\n",
    "    pol.plot_polarization_ellipse(axs[1,i], realized_analyzer_states[i])\n",
    "    \n",
    "fig.suptitle('Desired (top) vs. realized (bottom) polarization analyzer states')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also extract the diattenuation from the Mueller matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.9999999993233868,\n",
       " 0.9999999953599483,\n",
       " 0.9999999990622025,\n",
       " 0.9999999971248837]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diattenuation = [np.sqrt(mueller[0,1]**2+mueller[0,2]**2+mueller[0,3]**2)/mueller[0,0] for mueller in mueller_matrices]\n",
    "diattenuation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating a CAD version of the grating"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far, the metasurface polarization grating has been described as a purely mathematical object. We haven't even made any reference in the design process to the wavelength of light being used.\n",
    "\n",
    "Next, as described in the paper, we find a best-fit physical implementation corresponding to the design by referring to a library of structures. I have included several such libraries of pillars simulated at different wavelengths as a part of this code library. If you need to generate a new one at a different wavelength using, e.g., Lumerical, feel free to ask me."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# location of pillar library to load\n",
    "# the example here is a library of TiO2 rectangles for use at 550 nm\n",
    "library_file = 'Pillar libraries\\\\550 nm TiO2\\\\library_550_lumerical_denser_2020_06.mat'\n",
    "library_dict = pg.load_simulation_library(library_file)\n",
    "\n",
    "# find the design by lookup table for the given library\n",
    "# you can specify a minimum size to use, so that your features are not too small for fabrication\n",
    "# N_offset acknowledges that the phase shifts found in optimization can be shifted up or down arbitrarily\n",
    "# N_offset different shifts are tried to find the best fit to the library\n",
    "# this step can take a little while if the grating is large\n",
    "# min_size is the minimum acceptable feature size in nm\n",
    "design = grating.get_unitcell_design_offset(library_dict,min_size=50,N_offset=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we can actually write out the CAD to a <code>.gds</code> file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x288 with 1 Axes>,\n",
       " <Axes: title={'center': 'Grating design'}, xlabel='x (μm)', ylabel='y (μm)'>)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "size_x = 3100 # in microns\n",
    "size_y = 3100\n",
    "\n",
    "filename = 'test_gds.gds'\n",
    "\n",
    "# separation in microns between pillar elements\n",
    "# this is chosen in accordance with whatever the desired grating angle will be, as discussed above\n",
    "separation = 0.420\n",
    "\n",
    "# generate and save the CAD file as a .gds file\n",
    "# size_offset is a size subtracted from all dimensions, if desired, in nm\n",
    "# open the gds with, e.g., KLayout\n",
    "grating.get_cad(size_x, size_y, filename, design, separation, size_offset=0)\n",
    "\n",
    "grating.plot_design(design, separation)"
   ]
  }
 ],
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   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
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 },
 "nbformat": 4,
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}