{
  "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# One dimensional grating\n\nConvergence.\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"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We will study the 1D metallic grating as in :cite:p:`Li1993`.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "def convergence_study(form, psi, Nh):\n    ts0 = []\n    tsm1 = []\n    ns = []\n    for nh in Nh:\n        lattice = nn.Lattice(1, 2**9)\n        eps_metal = (0.22 + 6.71j) ** 2\n        epsgrid = lattice.ones() * 1\n        hole = lattice.stripe(0.5, 0.5)\n        epsgrid[hole] = eps_metal\n        sup = lattice.Layer(\"Superstrate\")\n        sub = lattice.Layer(\"Substrate\", epsilon=eps_metal)\n        grating = lattice.Layer(\"Grating\", thickness=1)\n        grating.epsilon = epsgrid\n        stack = [sup, grating, sub]\n        pw = nn.PlaneWave(wavelength=1, angles=(30, 0, psi))\n        sim = nn.Simulation(stack, pw, nh, formulation=form)\n        R, T = sim.diffraction_efficiencies()\n        Ri, Ti = sim.diffraction_efficiencies(orders=True)\n        R0 = sim.get_order(Ri, 0)\n        Rm1 = sim.get_order(Ri, -1)\n        ts0.append(R0)\n        tsm1.append(Rm1)\n        ns.append(sim.nh)\n    return np.array(ns), 100 * np.array(ts0), 100 * np.array(tsm1)\n\n\ndef run(psi):\n    Nh = range(5, 125, 2)\n    fig, ax = plt.subplots(2, 1, figsize=(2.0, 3.0))\n    title = \"TM\" if psi == 0 else \"TE\"\n    ns, ts0, tsm1 = convergence_study(\"original\", psi, Nh)\n    ax[0].plot(ns, ts0, \"-o\", label=\"original\", c=\"#dd803d\", ms=1)\n    ax[1].plot(ns, tsm1, \"-o\", label=\"original\", c=\"#dd803d\", ms=1)\n    ns_tan, ts0_tan, tsm1_tan = convergence_study(\"tangent\", psi, Nh)\n    ax[0].plot(\n        ns_tan, ts0_tan, \"--s\", label=\"tangent\", c=\"#4a4082\", ms=2, mew=0.4, mfc=\"None\"\n    )\n    ax[1].plot(\n        ns_tan, tsm1_tan, \"--s\", label=\"tangent\", c=\"#4a4082\", ms=2, mew=0.4, mfc=\"None\"\n    )\n    ax[0].set_title(\"order 0\")\n    ax[1].set_title(\"order -1\")\n    ax[0].legend()\n    ax[1].legend()\n    ax[0].set_xlabel(\"number of harmonics\")\n    ax[0].set_ylabel(\"diffraction efficiency (%)\")\n    ax[1].set_ylabel(\"diffraction efficiency (%)\")\n    plt.suptitle(title, weight=\"bold\", size=8)\n    plt.tight_layout()\n    plt.pause(0.1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "For TE polarization the two formulations are equivalent:\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "run(psi=90)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can see that in TM polarization, the convergence is greatly\nimproved by using proper Fourier factorization rules implemented by the\n``tangent`` formulation.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "run(psi=0)"
      ]
    },
    {
      "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
}