{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# This file is part of nannos\n# License: GPLv3\n%matplotlib notebook"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Permittivity approximation\n\nGet the Fourier representation of the permittivity as a function of number of harmonics.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\nimport numpy as np\n\nimport nannos as nn\n\nlattice = nn.Lattice([[1.5, 0], [0.4, 1]], discretization=(2**10, 2**10))\nsup = lattice.Layer(\"Superstrate\", epsilon=1)\nsub = lattice.Layer(\"Substrate\", epsilon=1)\nhole = lattice.ellipse(center=(1.1, 0.6), radii=(0.2, 0.4), rotate=60)\nincl = lattice.rectangle(center=(0.5, 0.3), widths=(0.2, 0.4), rotate=-45)\nepsilon = lattice.ones() * 4\nepsilon[hole] = 1\nepsilon[incl] = 6\nms = lattice.Layer(\"Metasurface\", thickness=0.5, epsilon=epsilon)\npw = nn.PlaneWave(wavelength=1.5, angles=(0, 0, 0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Lets first plot the permmitivity we want to approximate\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "plt.figure()\nims = ms.plot(cmap=\"viridis\")\nplt.xlabel(\"$x$\")\nplt.ylabel(\"$y$\")\nplt.colorbar(ims[0], orientation=\"horizontal\")\nplt.tight_layout()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Loop through number of harmonics\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "for n in [3, 5, 7, 11, 21, 41]:\n    sim = nn.Simulation([sup, ms, sub], pw, nh=n**2)\n    eps = sim.get_epsilon(ms)\n    plt.figure(figsize=(2, 2))\n    approx = plt.pcolormesh(*lattice.grid, eps.real)\n    ims = ms.plot(alpha=0.1, cmap=\"Greys\")\n    plt.xlabel(\"$x$\")\n    plt.ylabel(\"$y$\")\n    plt.colorbar(approx, orientation=\"horizontal\")\n    plt.title(rf\"$n_h = {sim.nh}$\")\n    plt.tight_layout()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import nannos.utils.jupyter\n%nannos_version_table"
      ]
    }
  ],
  "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": "3.10.13"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}