{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Waveguide Bend Optimization\n",
    "\n",
    "In this tutorial, we'll examine how we can use Meep's adjoint solver to optimize for a particular design criteria. Specifcally, we'll maximize the transmission around a silicon waveguide bend. This tutorial will illustrate the adjoint solver's ability to quickly calculate gradients for objective functions with multiple objective quantities.\n",
    "\n",
    "To begin, we'll import meep, our adjoint module, `autograd` (as before) and we will also import `nlopt`, a nonlinear optimization package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using MPI version 3.1, 1 processes\n"
     ]
    }
   ],
   "source": [
    "import meep as mp\n",
    "import meep.adjoint as mpa\n",
    "import numpy as np\n",
    "from autograd import numpy as npa\n",
    "import nlopt\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "mp.verbosity(0)\n",
    "Si = mp.Medium(index=3.4)\n",
    "SiO2 = mp.Medium(index=1.44)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we'll build a 90 degree bend waveguide with a design region that is 1 micron by 1 micron. We'll discretize our region into a 10 x 10 grid (100 total parameters). We'll send in a narrowband gaussian pulse centered at 1550 nm. We'll also use the same objective function and optimizer object as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "resolution = 20\n",
    "\n",
    "Sx = 6\n",
    "Sy = 5\n",
    "cell_size = mp.Vector3(Sx, Sy)\n",
    "\n",
    "pml_layers = [mp.PML(1.0)]\n",
    "\n",
    "fcen = 1 / 1.55\n",
    "width = 0.2\n",
    "fwidth = width * fcen\n",
    "source_center = [-1.5, 0, 0]\n",
    "source_size = mp.Vector3(0, 2, 0)\n",
    "kpoint = mp.Vector3(1, 0, 0)\n",
    "src = mp.GaussianSource(frequency=fcen, fwidth=fwidth)\n",
    "source = [\n",
    "    mp.EigenModeSource(\n",
    "        src,\n",
    "        eig_band=1,\n",
    "        direction=mp.NO_DIRECTION,\n",
    "        eig_kpoint=kpoint,\n",
    "        size=source_size,\n",
    "        center=source_center,\n",
    "    )\n",
    "]\n",
    "\n",
    "design_region_resolution = 10\n",
    "Nx = design_region_resolution + 1\n",
    "Ny = design_region_resolution + 1\n",
    "\n",
    "design_variables = mp.MaterialGrid(mp.Vector3(Nx, Ny), SiO2, Si, grid_type=\"U_MEAN\")\n",
    "design_region = mpa.DesignRegion(\n",
    "    design_variables, volume=mp.Volume(center=mp.Vector3(), size=mp.Vector3(1, 1, 0))\n",
    ")\n",
    "\n",
    "\n",
    "geometry = [\n",
    "    mp.Block(\n",
    "        center=mp.Vector3(x=-Sx / 4), material=Si, size=mp.Vector3(Sx / 2, 0.5, 0)\n",
    "    ),  # horizontal waveguide\n",
    "    mp.Block(\n",
    "        center=mp.Vector3(y=Sy / 4), material=Si, size=mp.Vector3(0.5, Sy / 2, 0)\n",
    "    ),  # vertical waveguide\n",
    "    mp.Block(\n",
    "        center=design_region.center, size=design_region.size, material=design_variables\n",
    "    ),  # design region\n",
    "    # mp.Block(center=design_region.center, size=design_region.size, material=design_variables,\n",
    "    #         e1=mp.Vector3(x=-1).rotate(mp.Vector3(z=1), np.pi/2), e2=mp.Vector3(y=1).rotate(mp.Vector3(z=1), np.pi/2))\n",
    "    #\n",
    "    # The commented lines above impose symmetry by overlapping design region with the same design variable. However,\n",
    "    # currently there is an issue of doing that; We give an alternative approach to impose symmetry in later tutorials.\n",
    "    # See https://github.com/NanoComp/meep/issues/1984 and https://github.com/NanoComp/meep/issues/2093\n",
    "]\n",
    "\n",
    "sim = mp.Simulation(\n",
    "    cell_size=cell_size,\n",
    "    boundary_layers=pml_layers,\n",
    "    geometry=geometry,\n",
    "    sources=source,\n",
    "    eps_averaging=False,\n",
    "    resolution=resolution,\n",
    ")\n",
    "\n",
    "TE_top = mpa.EigenmodeCoefficient(\n",
    "    sim, mp.Volume(center=mp.Vector3(0, 1, 0), size=mp.Vector3(x=2)), mode=1\n",
    ")\n",
    "ob_list = [TE_top]\n",
    "\n",
    "\n",
    "def J(alpha):\n",
    "    return npa.abs(alpha) ** 2\n",
    "\n",
    "\n",
    "opt = mpa.OptimizationProblem(\n",
    "    simulation=sim,\n",
    "    objective_functions=J,\n",
    "    objective_arguments=ob_list,\n",
    "    design_regions=[design_region],\n",
    "    fcen=fcen,\n",
    "    df=0,\n",
    "    nf=1,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, we'll visualize everything to ensure our monitors, boundary layers, and geometry are drawn correctly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VSQAbAKzuWXUUNLmIyXomx4sRrfFockCLc3SqulFEvg/g7wBsF5H/BN69J0NV7+rxd58C4KWq1y8DuLh+IRG5CcBNAIBFbRRHQZOLGB6u5otXkwPaX4yYBHAIwFwAI0Dom8/ao6r3ALgHAORkUfxfkwVHQZOLmH6ZHA9dG+PZ5IAWRiciqwDcBWAzgAtUdXabpt54BcBpVa9PLb/XOaOgyUVM1ib3+OMfCa4ZE95NDmg9o7sNwFpV3ZPJbwaeAnCGiLwXJYNbB+DPOlYZBU0uYrI2ufHx1diz59LgurEQg8kBLS5GqOrlGZocVHUawM0AHgHwHIDvdPz7RkGTi5h+mNyOHZfi7LMfq7zHixHvEovJATnfR6eqD6vqH6nq6ap6e0cfHgVNLmL68d3YHTtKLQ+vuOI7wfW9E5PJAV6/AjYKmlzE9OsBAOed9xNce+1DwfW9E5vJAQ6/AlY4vdC3Ry31oj+N6YF5TJOIoFAooFgsVh7T1G0HtH4+5STp60pqic3kAIdGV1xT7NujlnrVH6THNBUKhZrHNHVzmwb7utogNpMDPB668nDVJMViscbo3njjjZqft+vQxufV2SE2kwM8Gt2BDDRHQZMLTCeHrpZMjjcMhydvkwMczt2vv/76oHqvLXwN29+7Hcv3L8eSZUuAZWF0N2Nz8FixeTOA8OsgJFNTUygUCjjmmGNw//2l95IWiI2wZHIkPBZMDnBodLff3tldKK146vdP4TNPfgbfvOSbuPCEC4PpAsDmBzYHjbUkWjK64LoBmT9/PmZmZrBv376K0b3zzjuYO3cugNpHrFs0Od5HFw72de2Bc845J4jO1gNbcev3b8WmGzdls6d5IFys9WSlG5L58+dX/j89PY158+bV/NyiyZFwsK+rASztaWJlcnKy6c9ocnFjsa+ruxldr7dWPParx7Bu0zpsWLMBK05dEfxWjUQfCH8bSJIsi7eXFItFFAqFyj1+b775ZuVnyeGgqpo3OV6M6A2rNxu7M7pmJ7XTsPXA1orJZZWERH/lf63sKdZWZKUbkkYxjo+vxq5dl5k1OdIbVk0OcGh03d5xn5hQlkmo1+821nZkpdsLybcjEupP6o+Pr8bOnZfi3HN/jGuu+W8AYc26ZHKXdaXfKm6SDssmBzg0um6wnoTYefzxj2D37ktx/vnbsHLlZgBhjTox0dJ3V9PrFwqFWQZNOsdDfUVvdB6SEDu7d19enmk9hOnpmfYf6IDSTO5SLFv2BK6++kF0cvoymRlXn/PkObrO8FJfURudlyTESLV5nHHGOC65ZBMOHgxrJE88sQ7PPbcCZ545gYsv3oC33urs88lM7tChQ5X3qu/za/e1tUHHVX2pqpuBpdC0TOyf0CVfXaIT+ydSf6YT2uljLH2sqQFKwyAzMzM1r3ft2lUJ19PYvXt3y78rdtJut3nXVwKA7ZrCO6I8OeFqTxMJ9VdZlyxZklMkvbF48eKa1x6ucPcbj/UV3aGrxyTEQL0hnHjiiTh8+O3KoaBlw9DyIerQ0BCOOurEmp9ZjjsPvNZXVEbnNQkxoaoQEQwNDeHoo4/OO5yuSf4O8i6e6yuaQ1fPSYiJWMwhlr8jFN7rK4oZnfckxEryME4PppHEyXvqZhNDfbk3uhiSECsi4sLkAM7gmhFLfbk2uliSECs0D9/EVF9u5+kxJYEQa8RWXy6NLrYkEGKJGOvLndHFmARCLBFjfbkzuhiTQIglYqwvd0YXYxIIsUSM9eXO6GJMAiExY6G+3BldaCwkgZBYsVJfA210VpJASIxY6rY3sEZHkyMkO9jX1QCW9jSExIbFvq4DZ3TW9jSExITV+1xzMToRWSsie0SkKCLL+/V7Le5pCIkFqyYH5DejexbAGgCP9+sXWk4CId6xXl+5PL1EVZ8D+vd0C+tJIMQzHuor+nN0HpJAiFe81FdmMzoR+SGAkxr86DZVfagDnZsA3AQAWNRZDF6SQIhHXNVXmp6IWQ0AWwEsT738oPd1JSRj2NfVEa72NIQ4w2V9pXHD0APADQBeBnAEwG8BPJLqcylmdGb2NJzREYe0226t1FcCUs7ocj107XS0MzpLSaDREY+02m4t1VdCWqOL5tDV5XSaECd4r68ojM57EgixTAz15d7oYkgCIVaJpb5cG10sSSDEIjHVl1ujiykJhFgjtvpyaXSxJYEQS8RYX+6MLsYkEGKJGOvLndHFmARCLBFjfbkzuhiTQIglYqwvd0YXYxIIiRkL9eXO6EJjIQmExIqV+hpoo7OSBEJixFK3vYE1OpocIdlhrdveQBqdpT0NIbFhsdvewBmdtT0NITFh9T7XgTI6i3saQmLBqskBgJSeXecDOVkUn8w7CkKIGcbwtKoub7tcmqdzWhmdNMepZv229Spjouu3re/q893oh3zCsMUnu1I/Tv1utts86isBg/go9U5XUgia6YcyOktFQP349TvdbvM0OVUaXaqV1Cst9zQBjM5aEVA/fv1Ottu8TU6VRpd7Eno1OotFQP349dNut3nXV8JAG52FJPRidFaLgPrx66fZbi3UV8LAGp2VJHRrdJaLgPrx67fbbq3UV8JAGp2lJHRjdNaLgPrx67fabi3VV8LAGZ21JHRqdB6KgPrx6zfbbq3VV8JAGZ3FJHRidF6KgPrx6zfabi3WV8LAGJ3VJKQ1Ok9FQP349eu3W6v1lTAQRmc5CWmMzlsRUD9+/ert1nJ9JURvdNaT0M7oPBYB9ePXT7Zb6/WVELXReUhCK6PzWgTUj18fY3BRXwnRGp2XJDQzOs9FQP349TEGF/WVEK3ReUlCI6PzXgTUj18/mdFlQRaTlGiNzksS6o0uhiKgfvz6IR8vVk1WR2LRGl0WZLKnqdpgYikC6sevn4XRZXm6iUaXksz2NOUNJqYioH78+qGNLutz6qaNDsDXAPwcwC4ADwI4NtXnAhtdpnuaMURXBNSPXz+k0fXjwqF1o/sAgOHy/+8AcEeqzwU0usz3NGOIrgioH79+KKPr190Rpo2uJgDgBgD3pVo2kNH1ZU9TntFlQaxFRv389UMYXT9vAfNkdN8F8NEWP78JwHYA27HITxKyunoVc5FRP3/9Xrfbft/nmrvRAfghgGcbjNVVy9xWPkcnqTR7nNH1dU+TgdHlXQTUj1+/l+02j5v5cze6tr8Y+DiAbQDmp/5MD0bX9z1NYKOzUATUj1+/2+02r28smTY6AKsA7AVwQkefY1/XYJrUp34j2Nc1rNHtA/ASgB3l8c1Un2Nf1+BQn/rVsK+rgcG+rmGhPvXrYV9XA4N9XcNBfeo3gn1dDQz2dQ0D9anfDPZ1NTDY17V3qE/9VrCvq4HBvq69QX3qt4N9XQ0M9nXtHupTPw3s62pgsK9rd1Cf+mlhX1cDg31dO4f61O8E9nU1MNjXtTOoT/1OYV9XA4N9XdNDfep3A/u6Ghjs65oO6lO/W9jX1cBgX9f2UJ/6vcC+rgYG+7q2hvrU71WffV0NDPZ1bQ71qR9Cn31dDQz2dW0M9akfSp99XQ0M9nWdDfWpH1KffV0NDPZ1rYX61A+tH2tfV1FVeEFEDgJ4Pu84UrIEwGt5B9EBnuL1FCvgK15PsQLA+1R1pN1Cw/2IJCDPq+ryvINIg4hs9xIr4CteT7ECvuL1FCtQijfNcoWsAyGEkLyh0RFCoseb0d2TdwAd4ClWwFe8nmIFfMXrKVYgZbyuLkYQQkg3eJvREUJIx9DoCCHR487oROQfRWSXiOwQkR+IyMl5x9QMEfmaiPy8HO+DInJs3jG1QkTWisgeESmKiMlbDERklYg8LyL7ROQLecfTChG5V0R+JyLP5h1LO0TkNBGZEJG95W3g03nH1AwRmSciPxORneVYv9z2M97O0YnIMar6Zvn/twA4S1U/lXNYDRGRDwDYoqrTInIHAKjq53MOqykiciaAIoB/BfBZVU11j1K/EJEhAL8AcC2AlwE8BeBGVd2ba2BNEJErALwF4Nuqek7e8bRCRJYCWKqqz4jICICnAfyJxXUrIgJggaq+JSJzADwB4NOq+mSzz7ib0SUmV2YBALNOrao/UNXp8ssnAZyaZzztUNXnVNXyN08uArBPVV9U1UkAGwCszjmmpqjq4wD+kHccaVDVV1X1mfL/DwJ4DsAp+UbVmPI3wN4qv5xTHi19wJ3RAYCI3C4iLwH4cwB/n3c8KfkLAN/POwjnnALgparXL8NoMXpGREYBnA/gpzmH0hQRGRKRHQB+B2BcVVvGatLoROSHIvJsg7EaAFT1NlU9DcB9AG62HGt5mdsATKMUb66kiZcMLiKyEMADAP6q7ujJFKo6o6rnoXSUdJGItDw1YPK7rqq6MuWi9wF4GMCXMgynJe1iFZGPA/gwgGvUwAnRDtatRV4BcFrV61PL75EAlM93PQDgPlXdlHc8aVDVN0RkAsAqAE0v+pic0bVCRM6oerkawM/ziqUdIrIKwK0ArlfVw3nHEwFPAThDRN4rIkcBWAdgc84xRUH5BP+3ADynqnflHU8rROSE5A4GETkapYtTLX3A41XXBwC8D6Wrg78C8ClVNblXF5F9AOYCeL381pNWrxADgIjcAOBuACcAeAPADlX9YK5B1SEi1wH4OoAhAPeq6u35RtQcEbkfwFUoPfrotwC+pKrfyjWoJojICgA/ArAbpdoCgL9V1Yfzi6oxIrIMwH+gtA0UAHxHVf+h5We8GR0hhHSKu0NXQgjpFBodISR6aHSEkOih0RFCoodGRwiJHhodcUH56Rr7ReT48uvjyq9Hcw6NOIBGR1ygqi8B+BcAXym/9RUA96jqgdyCIm7gfXTEDeWvKD0N4F4AnwBwnqpO5RsV8YDJ77oS0ghVnRKRzwH4XwAfoMmRtPDQlXjjQwBeBWD6QZbEFjQ64gYROQ+lL3BfAuCvy0/FJaQtNDrigvLTNf4Fpeek/RrA1wDcmW9UxAs0OuKFTwD4taqOl1//M4AzReTKHGMiTuBVV0JI9HBGRwiJHhodISR6aHSEkOih0RFCoodGRwiJHhodISR6aHSEkOj5fw15u4JU6cp2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0 = 0.5 * np.ones((Nx * Ny,))\n",
    "opt.update_design([x0])\n",
    "\n",
    "opt.plot2D(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now define a cost function wrapper that we can feed into our `nlopt` optimizer. `nlopt` expects a python function where the gradient is passed in place. In addition, we'll update a list with every objective function call so we can track the cost function evolution each iteration.\n",
    "\n",
    "Notice the `opt` adjoint solver object requires we pass our numpy array of design parameters within an additional list. This is because the adjoint solver can solve for multiple design regions simultaneously. It's useful to break up each region's parameters into indvidual numpy arrays. In this simple example, we only have one design region."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "evaluation_history = []\n",
    "sensitivity = [0]\n",
    "\n",
    "\n",
    "def f(x, grad):\n",
    "    f0, dJ_du = opt([x])\n",
    "    f0 = f0[0]  # f0 is an array of length 1\n",
    "    if grad.size > 0:\n",
    "        grad[:] = np.squeeze(dJ_du)\n",
    "    evaluation_history.append(np.real(f0))\n",
    "    sensitivity[0] = dJ_du\n",
    "    return np.real(f0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can set up the actual optimizer engine. We'll select the Method of Moving Asymptotes because it's a gradient based method that allows us to specify linear and nonlinear constraints. For now, we'll simply bound our parameters between 0 and 1.\n",
    "\n",
    "We'll tell our solver to maximize (rather than minimize) our cost function, since we are trying to maximize the power transmission around the bend.\n",
    "\n",
    "We'll also tell the optimizer to stop after 10 function calls. This will keep the wait time short and demonstrate how powerful the adjoint solver is."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "algorithm = nlopt.LD_MMA\n",
    "n = Nx * Ny\n",
    "maxeval = 10\n",
    "\n",
    "solver = nlopt.opt(algorithm, n)\n",
    "solver.set_lower_bounds(0)\n",
    "solver.set_upper_bounds(1)\n",
    "solver.set_max_objective(f)\n",
    "solver.set_maxeval(maxeval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n"
     ]
    }
   ],
   "source": [
    "x = solver.optimize(x0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that the solver is done running, we can evaluate our progress."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.figure()\n",
    "plt.plot(evaluation_history, \"o-\")\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.ylabel(\"FOM\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can update our optimization object and visualize the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "opt.update_design([x])\n",
    "opt.plot2D(\n",
    "    True,\n",
    "    plot_monitors_flag=False,\n",
    "    output_plane=mp.Volume(center=(0, 0, 0), size=(2, 2, 0)),\n",
    ")\n",
    "plt.axis(\"off\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We quickly see that the solver improves the design, but because of the way we chose to formulate our cost function, it's difficult to quantify our results. After all, how good is a figure of merit (FOM) of 70?\n",
    "\n",
    "To overcome this, we'll slightly modify our objective function to include an extra monitor just after the source. This monitor will track however much power is transmitted into the waveguide. We can then normalize the upper monitor's response by this parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "TE0 = mpa.EigenmodeCoefficient(\n",
    "    sim, mp.Volume(center=mp.Vector3(-1, 0, 0), size=mp.Vector3(y=2)), mode=1\n",
    ")\n",
    "ob_list = [TE0, TE_top]\n",
    "\n",
    "\n",
    "def J(source, top):\n",
    "    return npa.abs(top / source) ** 2\n",
    "\n",
    "\n",
    "opt.objective_functions = [J]\n",
    "opt.objective_arguments = ob_list\n",
    "opt.update_design([x0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll refresh our solver and try optimizing again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n",
      "Starting forward run...\n",
      "Starting adjoint run...\n",
      "Calculating gradient...\n"
     ]
    }
   ],
   "source": [
    "evaluation_history = []\n",
    "solver = nlopt.opt(algorithm, n)\n",
    "solver.set_lower_bounds(0)\n",
    "solver.set_upper_bounds(1)\n",
    "solver.set_max_objective(f)\n",
    "solver.set_maxeval(maxeval)\n",
    "x = solver.optimize(x0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can view our results and normalize the FOM as the percent power transmission."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.figure()\n",
    "plt.plot(np.array(evaluation_history) * 100, \"o-\")\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.ylabel(\"Transmission (%)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We once again clearly see great improvement, from about 5% transmission to about 85%, after just 10 iterations!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Achieved an improvement of 28.0x\n"
     ]
    }
   ],
   "source": [
    "improvement = max(evaluation_history) / min(evaluation_history)\n",
    "print(\"Achieved an improvement of {0:1.1f}x\".format(improvement))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can visualize our new geometry. We see that the design region naturally connected the two waveguide segements in a bend fashion and has placed several other distinctive features around the curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "opt.update_design([x])\n",
    "opt.plot2D(\n",
    "    True,\n",
    "    plot_monitors_flag=False,\n",
    "    output_plane=mp.Volume(center=(0, 0, 0), size=(2, 2, 0)),\n",
    ")\n",
    "plt.axis(\"off\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also visualize the sensitivity to see which geometric areas are most sensitive to perturbations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.rot90(np.squeeze(np.abs(sensitivity[0].reshape(Nx, Ny)))));"
   ]
  }
 ],
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