{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Notebook 03: Inverse design parameterization\n", "\n", "This notebook will introduce a few basic parameterization concepts for inverse design. The same mode converter device concept as in the previous notebook will be used here as an example.\n", "\n", "*Parameterization* refers to how we are representing our device. In the previous notebook, we simply used a 2D array of permittivity values, $\\epsilon_r[x,y]$.\n", "However, we observed that this led to continuously varying features, which is not ideal for fabricating devices generated by our optimization. \n", "In this notebook, we will use a modified parameterization of the device to encourage more *binarized* features in the optimized device.\n", "However, as we will see, we will still need to tune various hyperparameters in order to get desirable results.\n", "\n", "We begin by importing the necessary python packages:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import autograd.numpy as npa\n", "\n", "import copy\n", "\n", "import matplotlib as mpl\n", "mpl.rcParams['figure.dpi']=100\n", "\n", "import matplotlib.pylab as plt\n", "\n", "from autograd.scipy.signal import convolve as conv\n", "from skimage.draw import circle\n", "\n", "import ceviche\n", "from ceviche import fdfd_ez, jacobian\n", "from ceviche.optimizers import adam_optimize\n", "from ceviche.modes import insert_mode\n", "\n", "import collections\n", "# Create a container for our slice coords to be used for sources and probes\n", "Slice = collections.namedtuple('Slice', 'x y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction: device parameterization\n", "\n", "Here, our device will be parameterized by a 2D array of density values (a density distribution, referred to as $\\rho[x,y]$).\n", "This part of the parameterization actually looks very similar to the 2D array of permitivitty values we used in the previous notebook. \n", "However, the difference is that we then definite two relatively simple operators that will be applied to this density. They are:\n", "\n", " - **Blur operator**: A 2D convolution blur filter with a configurable radius; can be applied a configurable number of times\n", " - **Projection operator**: A sigmoid-like nonlinear function for *binarizing* the output materials; has tunable slope and transition region\n", "\n", "After these two operations are applied, the resulting density distribution, $\\tilde{\\rho}[x,y]$, will be a 2D array with values varying between `0.0` and `1.0`. A value of `0.0` represents a *background* material, while a value of `1.0` represents a *foreground* material.\n", "The permitivitty distribution, which represents the optical description of our device, is then constructed as:\n", "\\begin{equation}\n", " \\epsilon_r[x,y] = \\epsilon_{\\text{min}} + \\left(\\epsilon_{\\text{max}} - \\epsilon_{\\text{min}} \\right) \\tilde{\\rho}{[x,y]}\n", "\\end{equation}\n", "\n", "We start by defining our parameterization operators:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Projection that drives rho towards a \"binarized\" design with values either 0 or 1 \n", "def operator_proj(rho, eta=0.5, beta=100, N=1):\n", " \"\"\"Density projection\n", " eta : Center of the projection between 0 and 1\n", " beta : Strength of the projection\n", " N : Number of times to apply the projection\n", " \"\"\"\n", " for i in range(N):\n", " rho = npa.divide(npa.tanh(beta * eta) + npa.tanh(beta * (rho - eta)), \n", " npa.tanh(beta * eta) + npa.tanh(beta * (1 - eta)))\n", " \n", " return rho\n", "\n", "# Blurring filter that results in smooth features of the structure\n", "# First we define a function to create the kernel\n", "def _create_blur_kernel(radius):\n", " \"\"\"Helper function used below for creating the conv kernel\"\"\"\n", " rr, cc = circle(radius, radius, radius+1)\n", " kernel = np.zeros((2*radius+1, 2*radius+1), dtype=np.float)\n", " kernel[rr, cc] = 1\n", " return kernel/kernel.sum()\n", "\n", "# Then we define the function to apply the operation\n", "def operator_blur(rho, radius=2, N=1):\n", " \"\"\"Blur operator implemented via two-dimensional convolution\n", " radius : Radius of the circle for the conv kernel filter\n", " N : Number of times to apply the filter\n", " \n", " Note that depending on the radius, the kernel is not always a\n", " perfect circle due to \"pixelation\" / stair casing\n", " \"\"\"\n", " \n", " kernel = _create_blur_kernel(radius)\n", " \n", " for i in range(N):\n", " # For whatever reason HIPS autograd doesn't support 'same' mode, so we need to manually crop the output\n", " rho = conv(rho, kernel, mode='full')[radius:-radius,radius:-radius]\n", " \n", " return rho" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualization of the blur\n", "\n", "Below we visualize the blur operator applied to a random 2D array:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Specify a range of values for the blur radius\n", "blur_radii = [2, 3, 4, 5, 6]\n", "\n", "# Number of times to apply the blur filter\n", "N_blur = 1\n", "\n", "# Define a random 2D array to test our blur filter on\n", "rho = np.random.rand(50, 50)\n", "\n", "# Create a figure with panels to plot into\n", "fig, axs = plt.subplots(2, len(blur_radii)+1,figsize=(12,4), constrained_layout=True)\n", "\n", "# First, plot a dummy conv filter\n", "axs[0,0].set_title('Initial random image')\n", "axs[0,0].imshow(np.zeros((1,1)), vmin=0, cmap='Greys')\n", "# And also plot the initial random image\n", "axs[1,0].imshow(rho)\n", "\n", "# Now, loop over the blur radii and visualize each result\n", "for i, radius in enumerate(blur_radii):\n", " kernel = _create_blur_kernel(radius)\n", " \n", " kernel_pad = np.pad(kernel, (2+np.max(blur_radii)-radius, 2+np.max(blur_radii)-radius),\n", " 'constant', constant_values=(0, 0))\n", " axs[0,i+1].imshow(kernel_pad, vmin=0)\n", " \n", " axs[0,i+1].set_title('radius = %d' % radius)\n", "\n", " rho_p = operator_blur(rho, radius=radius, N=N_blur)\n", " axs[1,i+1].imshow(rho_p)\n", "\n", "axs[0,0].set_yticks([])\n", "axs[0,0].set_xticks([])\n", "axs[0,0].set_ylabel('Conv filter')\n", "axs[1,0].set_ylabel('Image')\n", "\n", "fig.align_labels()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualization of the projection\n", "\n", "Below we visualize the projection operator:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho = np.linspace(-0.5, +1.5, 999)\n", "\n", "# Visualize different values of the projection strength\n", "plt.figure()\n", "for beta in [5, 10, 50, 100]:\n", " plt.plot(rho, operator_proj(rho, beta=beta), label=r\"$\\beta$ = %d\" % beta)\n", "\n", "plt.xlabel(r\"Input $\\rho$\")\n", "plt.ylabel(r\"Projected $\\hat{\\rho}$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualization of blur + projection\n", "\n", "Finally, we visualize the combined projection and blur operation. Notice how the larger blur radius leads to larger and smoother features." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Specify a range of values for the blur radius\n", "blur_radii = [2, 3, 4, 5, 6, 10]\n", "\n", "# Number of times to apply the blur filter\n", "N_blur = 1\n", "\n", "# Number of times to apply the projection operator\n", "N_proj = 1\n", "\n", "# Specify beta value to use for projection\n", "beta = 200\n", "\n", "# Specify eta value to use for projection\n", "eta = 0.5\n", "\n", "# Define a random 2D array to test our blur filter on\n", "rho = np.random.rand(100, 100)\n", "\n", "# Create a figure with panels to plot into\n", "fig, axs = plt.subplots(2, len(blur_radii)+1,figsize=(12,4), constrained_layout=True)\n", "\n", "# First, plot a dummy conv filter\n", "axs[0,0].set_title('Initial random image')\n", "axs[0,0].imshow(np.zeros((1,1)), vmin=0, cmap='Greys')\n", "# And also plot the initial random image\n", "axs[1,0].imshow(rho)\n", "\n", "# Now, loop over the blur radii and visualize each result\n", "for i, radius in enumerate(blur_radii):\n", " kernel = _create_blur_kernel(radius)\n", " \n", " kernel_pad = np.pad(kernel, (2+np.max(blur_radii)-radius, 2+np.max(blur_radii)-radius),\n", " 'constant', constant_values=(0, 0))\n", " axs[0,i+1].imshow(kernel_pad, vmin=0)\n", " \n", " axs[0,i+1].set_title('radius = %d' % radius)\n", "\n", " rho_p = operator_blur(rho, radius=radius, N=N_blur)\n", " rho_p = operator_proj(rho_p, beta=beta, eta=eta, N=N_proj)\n", " axs[1,i+1].imshow(rho_p)\n", "\n", "axs[0,0].set_yticks([])\n", "axs[0,0].set_xticks([])\n", "axs[0,0].set_ylabel('Conv filter')\n", "axs[1,0].set_ylabel('Image')\n", "\n", "fig.align_labels()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulation and optimization parameters" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Angular frequency of the source in 1/s\n", "omega=2*np.pi*200e12\n", "# Spatial resolution in meters\n", "dl=40e-9\n", "# Number of pixels in x-direction\n", "Nx=120\n", "# Number of pixels in y-direction\n", "Ny=120\n", "# Number of pixels in the PMLs in each direction\n", "Npml=20\n", "# Minimum value of the relative permittivity\n", "epsr_min=1.0\n", "# Maximum value of the relative permittivity\n", "epsr_max=12.0\n", "# Radius of the smoothening features\n", "blur_radius=5\n", "# Number of times to apply the blur\n", "N_blur=1\n", "# Strength of the binarizing projection\n", "beta=500.0\n", "# Middle point of the binarizing projection\n", "eta=0.5\n", "# Number of times to apply the blur\n", "N_proj=1\n", "# Space between the PMLs and the design region (in pixels)\n", "space=10\n", "# Width of the waveguide (in pixels)\n", "wg_width=12\n", "# Length in pixels of the source/probe slices on each side of the center point\n", "space_slice=8\n", "\n", "# Number of epochs in the optimization \n", "Nsteps=50\n", "# Step size for the Adam optimizer\n", "step_size=5e-3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Utility functions\n", "\n", "As in **Notebook 02**, here we define several utility functions for constructing the simulation domain, feed waveguides, design region, input source, and output probe," ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def init_domain(Nx, Ny, Npml, space=10, wg_width=10, space_slice=5):\n", " \"\"\"Initializes the domain and design region\n", "\n", " space : The space between the PML and the structure\n", " wg_width : The feed and probe waveguide width\n", " space_slice : The added space for the probe and source slices\n", " \"\"\"\n", " rho = np.zeros((Nx, Ny)) \n", " bg_rho = np.zeros((Nx, Ny)) \n", " design_region = np.zeros((Nx, Ny))\n", " \n", " # Input waveguide\n", " bg_rho[0:int(Npml+space),int(Ny/2-wg_width/2):int(Ny/2+wg_width/2)] = 1\n", "\n", " # Input probe slice\n", " input_slice = Slice(x=np.array(Npml+1), \n", " y=np.arange(int(Ny/2-wg_width/2-space_slice), int(Ny/2+wg_width/2+space_slice)))\n", " \n", " # Output waveguide \n", " bg_rho[int(Nx-Npml-space)::,int(Ny/2-wg_width/2):int(Ny/2+wg_width/2)] = 1\n", " \n", " # Output probe slice\n", " output_slice = Slice(x=np.array(Nx-Npml-1), \n", " y=np.arange(int(Ny/2-wg_width/2-space_slice), int(Ny/2+wg_width/2+space_slice)))\n", " \n", " design_region[Npml+space:Nx-Npml-space, Npml+space:Ny-Npml-space] = 1\n", " \n", " # Const init\n", " rho[Npml+space:Nx-Npml-space, Npml+space:Ny-Npml-space] = 0.5\n", " # Random init\n", " # rho = design_region * np.random.rand(Nx, Ny)\n", "\n", " return rho, bg_rho, design_region, input_slice, output_slice\n", "\n", "def viz_sim(epsr, source, slices=[]):\n", " \"\"\"Solve and visualize a simulation with permittivity 'epsr'\n", " \"\"\"\n", " simulation = fdfd_ez(omega, dl, epsr, [Npml, Npml])\n", " Hx, Hy, Ez = simulation.solve(source)\n", " \n", " fig, ax = plt.subplots(1, 2, constrained_layout=True, figsize=(6,3))\n", " ceviche.viz.real(Ez, outline=epsr, ax=ax[0], cbar=False)\n", " for sl in slices:\n", " ax[0].plot(sl.x*np.ones(len(sl.y)), sl.y, 'b-')\n", " ceviche.viz.abs(epsr, ax=ax[1], cmap='Greys');\n", " plt.show()\n", " \n", " return (simulation, ax)\n", "\n", "def mask_combine_rho(rho, bg_rho, design_region):\n", " \"\"\"Utility function for combining the design region rho and the background rho\n", " \"\"\"\n", " return rho*design_region + bg_rho*(design_region==0).astype(np.float)\n", "\n", "def epsr_parameterization(rho, bg_rho, design_region, radius=2, N_blur=1, beta=100, eta=0.5, N_proj=1):\n", " \"\"\"Defines the parameterization steps for constructing rho\n", " \"\"\"\n", " # Combine rho and bg_rho; Note: this is so the subsequent blur sees the waveguides\n", " rho = mask_combine_rho(rho, bg_rho, design_region)\n", " \n", " rho = operator_blur(rho, radius=radius, N=N_blur)\n", " rho = operator_proj(rho, beta=beta, eta=eta, N=N_proj)\n", " \n", " # Final masking undoes the blurring of the waveguides\n", " rho = mask_combine_rho(rho, bg_rho, design_region)\n", " \n", " return epsr_min + (epsr_max-epsr_min) * rho\n", "\n", "def mode_overlap(E1, E2):\n", " \"\"\"Defines an overlap integral between the sim field and desired field\n", " \"\"\"\n", " return npa.abs(npa.sum(npa.conj(E1)*E2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulate the initial structure\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Initialize the parametrization rho and the design region\n", "rho, bg_rho, design_region, input_slice, output_slice = \\\n", " init_domain(Nx, Ny, Npml, space=space, wg_width=wg_width, space_slice=space_slice)\n", "\n", "# Compute the permittivity from rho_init, including blurring and projection\n", "epsr_init = epsr_parameterization(rho, bg_rho, design_region, \\\n", " radius=blur_radius, N_blur=N_blur, beta=beta, eta=eta, N_proj=N_proj)\n", "\n", "# Setup source\n", "source = insert_mode(omega, dl, input_slice.x, input_slice.y, epsr_init, m=1)\n", "\n", "# Setup probe\n", "probe = insert_mode(omega, dl, output_slice.x, output_slice.y, epsr_init, m=2)\n", "\n", "# Simulate initial device\n", "simulation, ax = viz_sim(epsr_init, source, slices=[input_slice, output_slice])\n", "\n", "# get normalization factor (field overlap before optimizing)\n", "_, _, Ez = simulation.solve(source)\n", "E0 = mode_overlap(Ez, probe)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Run the mode converter optimization" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch: 1/ 50 | Duration: 0.15 secs | Value: 1.000000e+00\n", "Epoch: 2/ 50 | Duration: 0.14 secs | Value: 4.456358e+06\n", "Epoch: 3/ 50 | Duration: 0.15 secs | Value: 1.271317e+07\n", "Epoch: 4/ 50 | Duration: 0.16 secs | Value: 1.435436e+07\n", "Epoch: 5/ 50 | Duration: 0.16 secs | Value: 1.480551e+07\n", "Epoch: 6/ 50 | Duration: 0.14 secs | Value: 1.572114e+07\n", "Epoch: 7/ 50 | Duration: 0.14 secs | Value: 1.699668e+07\n", "Epoch: 8/ 50 | Duration: 0.13 secs | Value: 1.788798e+07\n", "Epoch: 9/ 50 | Duration: 0.14 secs | Value: 1.845224e+07\n", "Epoch: 10/ 50 | Duration: 0.13 secs | Value: 1.876436e+07\n", "Epoch: 11/ 50 | Duration: 0.14 secs | Value: 1.902127e+07\n", "Epoch: 12/ 50 | Duration: 0.13 secs | Value: 1.931158e+07\n", "Epoch: 13/ 50 | Duration: 0.13 secs | Value: 1.949692e+07\n", "Epoch: 14/ 50 | Duration: 0.13 secs | Value: 1.960007e+07\n", "Epoch: 15/ 50 | Duration: 0.14 secs | Value: 1.971148e+07\n", "Epoch: 16/ 50 | Duration: 0.13 secs | Value: 1.981570e+07\n", "Epoch: 17/ 50 | Duration: 0.14 secs | Value: 1.987639e+07\n", "Epoch: 18/ 50 | Duration: 0.13 secs | Value: 1.994972e+07\n", "Epoch: 19/ 50 | Duration: 0.13 secs | Value: 2.004990e+07\n", "Epoch: 20/ 50 | Duration: 0.13 secs | Value: 2.012583e+07\n", "Epoch: 21/ 50 | Duration: 0.13 secs | Value: 2.016142e+07\n", "Epoch: 22/ 50 | Duration: 0.13 secs | Value: 2.022432e+07\n", "Epoch: 23/ 50 | Duration: 0.14 secs | Value: 2.033500e+07\n", "Epoch: 24/ 50 | Duration: 0.13 secs | Value: 2.043152e+07\n", "Epoch: 25/ 50 | Duration: 0.13 secs | Value: 2.048668e+07\n", "Epoch: 26/ 50 | Duration: 0.15 secs | Value: 2.052932e+07\n", "Epoch: 27/ 50 | Duration: 0.15 secs | Value: 2.057662e+07\n", "Epoch: 28/ 50 | Duration: 0.15 secs | Value: 2.061488e+07\n", "Epoch: 29/ 50 | Duration: 0.15 secs | Value: 2.063028e+07\n", "Epoch: 30/ 50 | Duration: 0.14 secs | Value: 2.063803e+07\n", "Epoch: 31/ 50 | Duration: 0.15 secs | Value: 2.066751e+07\n", "Epoch: 32/ 50 | Duration: 0.13 secs | Value: 2.071816e+07\n", "Epoch: 33/ 50 | Duration: 0.14 secs | Value: 2.076390e+07\n", "Epoch: 34/ 50 | Duration: 0.13 secs | Value: 2.079915e+07\n", "Epoch: 35/ 50 | Duration: 0.14 secs | Value: 2.084087e+07\n", "Epoch: 36/ 50 | Duration: 0.13 secs | Value: 2.089344e+07\n", "Epoch: 37/ 50 | Duration: 0.14 secs | Value: 2.094184e+07\n", "Epoch: 38/ 50 | Duration: 0.13 secs | Value: 2.098001e+07\n", "Epoch: 39/ 50 | Duration: 0.14 secs | Value: 2.102069e+07\n", "Epoch: 40/ 50 | Duration: 0.14 secs | Value: 2.106964e+07\n", "Epoch: 41/ 50 | Duration: 0.15 secs | Value: 2.111672e+07\n", "Epoch: 42/ 50 | Duration: 0.18 secs | Value: 2.115774e+07\n", "Epoch: 43/ 50 | Duration: 0.17 secs | Value: 2.120122e+07\n", "Epoch: 44/ 50 | Duration: 0.17 secs | Value: 2.125224e+07\n", "Epoch: 45/ 50 | Duration: 0.16 secs | Value: 2.130581e+07\n", "Epoch: 46/ 50 | Duration: 0.16 secs | Value: 2.135658e+07\n", "Epoch: 47/ 50 | Duration: 0.16 secs | Value: 2.140655e+07\n", "Epoch: 48/ 50 | Duration: 0.16 secs | Value: 2.145944e+07\n", "Epoch: 49/ 50 | Duration: 0.16 secs | Value: 2.151167e+07\n", "Epoch: 50/ 50 | Duration: 0.17 secs | Value: 2.155647e+07\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def objective(rho):\n", " \"\"\"Objective function called by optimizer\n", " \n", " 1) Takes the density distribution as input\n", " 2) Constructs epsr\n", " 2) Runs the simulation\n", " 3) Returns the overlap integral between the output wg field \n", " and the desired mode field\n", " \"\"\"\n", " rho = rho.reshape((Nx, Ny))\n", " epsr = epsr_parameterization(rho, bg_rho, design_region, \\\n", " radius=blur_radius, N_blur=N_blur, beta=beta, eta=eta, N_proj=N_proj)\n", " simulation.eps_r = epsr\n", " _, _, Ez = simulation.solve(source)\n", " return mode_overlap(Ez, probe) / E0\n", "\n", "# Compute the gradient of the objective function using revere-mode differentiation\n", "objective_jac = jacobian(objective, mode='reverse')\n", "\n", "# Maximize the objective function using an ADAM optimizer\n", "(rho_optimum, loss) = adam_optimize(objective, rho.flatten(), objective_jac,\n", " Nsteps=Nsteps, direction='max', step_size=step_size)\n", "\n", "# Simulate optimal device\n", "rho_optimum = rho_optimum.reshape((Nx, Ny))\n", "epsr = epsr_parameterization(rho_optimum, bg_rho, design_region, \\\n", " radius=blur_radius, N_blur=N_blur, beta=beta, eta=eta, N_proj=N_proj)\n", "\n", "viz_sim(epsr, source, slices=[input_slice, output_slice]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualizing the parameterization steps\n", "\n", "We can take a look what each step of our parameterization actually looks like. Below we visualize the raw density distribution, the blurred density distribution, and finally, the projected device density." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1,3,constrained_layout=True,sharex=True,sharey=True, figsize=(8.5,3))\n", "Z = mask_combine_rho(rho_optimum, bg_rho, design_region)\n", "ceviche.viz.abs(Z, cmap='Greys', ax=axs[0])\n", "axs[0].set_xlabel('')\n", "axs[0].set_xticks([])\n", "axs[0].set_ylabel('')\n", "axs[0].set_yticks([])\n", "axs[0].set_title('Raw input density')\n", "\n", "Z = mask_combine_rho(rho_optimum, bg_rho, design_region)\n", "Z = operator_blur(Z, radius=blur_radius, N=N_blur)\n", "# Z = operator_proj(Z, beta=beta, eta=eta)\n", "Z = mask_combine_rho(Z, bg_rho, design_region)\n", "ceviche.viz.abs(Z, cmap='Greys', ax=axs[1])\n", "axs[1].set_xlabel('')\n", "axs[1].set_ylabel('')\n", "axs[1].set_title('Blurred density')\n", "\n", "Z = rho_optimum\n", "Z = mask_combine_rho(Z, bg_rho, design_region)\n", "Z = operator_blur(Z, radius=blur_radius, N=N_blur)\n", "Z = operator_proj(Z, beta=beta, eta=eta, N=N_proj)\n", "Z = mask_combine_rho(Z, bg_rho, design_region)\n", "ceviche.viz.abs(Z, cmap='Greys', ax=axs[2])\n", "axs[2].set_xlabel('')\n", "axs[2].set_ylabel('')\n", "axs[2].set_title('Projected density (final structure)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Penalizing the amount of material\n", "\n", "We notice that in the optimized device shown above that there seems to be a lot of unnecessary material in the device. Here, we will try to eliminate some of this extra material by adding a penalty term to the objective function.\n", "\n", "To add the penalty term, we only need to modify the objective function:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def objective(rho, penalty_weight=1e8): \n", " rho = rho.reshape((Nx, Ny))\n", " epsr = epsr_parameterization(rho, bg_rho, design_region, \\\n", " radius=blur_radius, N_blur=N_blur, beta=beta, eta=eta, N_proj=N_proj)\n", " simulation.eps_r = epsr\n", " _, _, Ez = simulation.solve(source)\n", " \n", " # This penalty term is directly proportional to the material area\n", " # penalty = penalty_weight * (design_region*(epsr-1)).sum() # penalty_weight = 1e-10\n", " \n", " # This penalty term is the L2-norm of the raw density\n", " penalty = penalty_weight * npa.linalg.norm(rho)\n", " \n", " return mode_overlap(Ez, probe) / E0 - penalty" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch: 1/ 50 | Duration: 0.19 secs | Value: -3.000000e+09\n", "Epoch: 2/ 50 | Duration: 0.20 secs | Value: -2.994089e+09\n", "Epoch: 3/ 50 | Duration: 0.18 secs | Value: -2.985150e+09\n", "Epoch: 4/ 50 | Duration: 0.18 secs | Value: -2.976833e+09\n", "Epoch: 5/ 50 | Duration: 0.22 secs | Value: -2.970420e+09\n", "Epoch: 6/ 50 | Duration: 0.21 secs | Value: -2.963942e+09\n", "Epoch: 7/ 50 | Duration: 0.20 secs | Value: -2.956911e+09\n", "Epoch: 8/ 50 | Duration: 0.18 secs | Value: -2.949055e+09\n", "Epoch: 9/ 50 | Duration: 0.19 secs | Value: -2.941095e+09\n", "Epoch: 10/ 50 | Duration: 0.18 secs | Value: -2.933183e+09\n", "Epoch: 11/ 50 | Duration: 0.19 secs | Value: -2.924825e+09\n", "Epoch: 12/ 50 | Duration: 0.18 secs | Value: -2.916705e+09\n", "Epoch: 13/ 50 | Duration: 0.21 secs | Value: -2.907614e+09\n", "Epoch: 14/ 50 | Duration: 0.22 secs | Value: -2.897752e+09\n", "Epoch: 15/ 50 | Duration: 0.21 secs | Value: -2.888235e+09\n", "Epoch: 16/ 50 | Duration: 0.20 secs | Value: -2.879241e+09\n", "Epoch: 17/ 50 | Duration: 0.22 secs | Value: -2.869495e+09\n", "Epoch: 18/ 50 | Duration: 0.22 secs | Value: -2.862507e+09\n", "Epoch: 19/ 50 | Duration: 0.20 secs | Value: -2.852476e+09\n", "Epoch: 20/ 50 | Duration: 0.20 secs | Value: -2.842571e+09\n", "Epoch: 21/ 50 | Duration: 0.19 secs | Value: -2.832474e+09\n", "Epoch: 22/ 50 | Duration: 0.21 secs | Value: -2.822361e+09\n", "Epoch: 23/ 50 | Duration: 0.22 secs | Value: -2.812278e+09\n", "Epoch: 24/ 50 | Duration: 0.23 secs | Value: -2.803447e+09\n", "Epoch: 25/ 50 | Duration: 0.22 secs | Value: -2.794993e+09\n", "Epoch: 26/ 50 | Duration: 0.20 secs | Value: -2.785540e+09\n", "Epoch: 27/ 50 | Duration: 0.20 secs | Value: -2.777071e+09\n", "Epoch: 28/ 50 | Duration: 0.19 secs | Value: -2.768470e+09\n", "Epoch: 29/ 50 | Duration: 0.19 secs | Value: -2.758579e+09\n", "Epoch: 30/ 50 | Duration: 0.18 secs | Value: -2.748415e+09\n", "Epoch: 31/ 50 | Duration: 0.19 secs | Value: -2.738816e+09\n", "Epoch: 32/ 50 | Duration: 0.18 secs | Value: -2.729582e+09\n", "Epoch: 33/ 50 | Duration: 0.18 secs | Value: -2.718876e+09\n", "Epoch: 34/ 50 | Duration: 0.18 secs | Value: -2.709153e+09\n", "Epoch: 35/ 50 | Duration: 0.18 secs | Value: -2.698591e+09\n", "Epoch: 36/ 50 | Duration: 0.18 secs | Value: -2.688507e+09\n", "Epoch: 37/ 50 | Duration: 0.18 secs | Value: -2.679019e+09\n", "Epoch: 38/ 50 | Duration: 0.18 secs | Value: -2.668650e+09\n", "Epoch: 39/ 50 | Duration: 0.17 secs | Value: -2.659922e+09\n", "Epoch: 40/ 50 | Duration: 0.17 secs | Value: -2.649376e+09\n", "Epoch: 41/ 50 | Duration: 0.17 secs | Value: -2.639219e+09\n", "Epoch: 42/ 50 | Duration: 0.17 secs | Value: -2.629614e+09\n", "Epoch: 43/ 50 | Duration: 0.20 secs | Value: -2.620170e+09\n", "Epoch: 44/ 50 | Duration: 0.22 secs | Value: -2.610861e+09\n", "Epoch: 45/ 50 | Duration: 0.19 secs | Value: -2.601588e+09\n", "Epoch: 46/ 50 | Duration: 0.20 secs | Value: -2.592253e+09\n", "Epoch: 47/ 50 | Duration: 0.20 secs | Value: -2.582968e+09\n", "Epoch: 48/ 50 | Duration: 0.20 secs | Value: -2.573436e+09\n", "Epoch: 49/ 50 | Duration: 0.20 secs | Value: -2.563783e+09\n", "Epoch: 50/ 50 | Duration: 0.19 secs | Value: -2.554230e+09\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Initialize the parametrization rho and the design region\n", "rho, bg_rho, design_region, input_slice, output_slice = \\\n", " init_domain(Nx, Ny, Npml, space=space, wg_width=wg_width, space_slice=space_slice)\n", "\n", "# Compute the permittivity from rho_init, including blurring and projection\n", "epsr_init = epsr_parameterization(rho, bg_rho, design_region, \\\n", " radius=blur_radius, N_blur=N_blur, beta=beta, eta=eta, N_proj=N_proj)\n", "\n", "# Setup source\n", "source = insert_mode(omega, dl, input_slice.x, input_slice.y, epsr_init, m=1)\n", "\n", "# Setup probe\n", "probe = insert_mode(omega, dl, output_slice.x, output_slice.y, epsr_init, m=2)\n", "\n", "# Simulate initial device\n", "viz_sim(epsr_init, source, slices=[input_slice, output_slice])\n", "\n", "# Run optimization\n", "objective_jac = jacobian(objective, mode='reverse')\n", "(rho_optimum, loss) = adam_optimize(objective, rho.flatten(), objective_jac,\n", " Nsteps=Nsteps, direction='max', step_size=step_size)\n", "\n", "# Simulate optimal device\n", "rho_optimum = rho_optimum.reshape((Nx, Ny))\n", "epsr_pen = epsr_parameterization(rho_optimum, bg_rho, design_region, \\\n", " radius=blur_radius, N_blur=N_blur, beta=beta, eta=eta, N_proj=N_proj)\n", "viz_sim(epsr_pen, source, slices=[input_slice, output_slice]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then quantify how much our penalization impacted the amount of material used in the final design. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Design region area: 5.76 um^2\n", "Unpenalized design area: 1.96 um^2\n", "Penalized design area: 1.03 um^2\n", "---\n", "Improvement: 47.32%\n" ] } ], "source": [ "# Calculate areas\n", "def calc_design_area(design_region, epsr_max, epsr_min, epsr, dl):\n", " \"\"\"Computes the area of material used in the design region\n", " \"\"\"\n", " A = ((epsr-epsr_min)/epsr_max * design_region).sum() * dl**2 * 1e12\n", " A_design_region = design_region.sum() * (dl)**2 * 1e12\n", " return A, A_design_region\n", "\n", "_, A_design_region = calc_design_area(design_region, epsr_max, epsr_min, epsr, dl)\n", "A_original, _ = calc_design_area(design_region, epsr_max, epsr_min, epsr, dl)\n", "A_pen, _ = calc_design_area(design_region, epsr_max, epsr_min, epsr_pen, dl)\n", "\n", "# Print summary\n", "print('Design region area: %.2f um^2' % A_design_region)\n", "print('Unpenalized design area: %.2f um^2' % A_original)\n", "print('Penalized design area: %.2f um^2' % A_pen)\n", "print('---')\n", "print('Improvement: %.2f%%' % (100*(1-A_pen/A_original)))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }