{
  "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# Dielectric patch array\n\nTransmission spectrum.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\nimport numpy as np\nfrom matplotlib.colors import ListedColormap\nfrom scipy.constants import c, e, h\n\nimport nannos as nn"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Results are compared to the reference :cite:p:`Tikhodeev2002`.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "eps_quartz = 2.132\neps_active = 3.97\n\nN = 2**7\nperiod = 0.68\nl_patch = 0.8 * period"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Define the lattice\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "lattice = nn.Lattice(([period, 0], [0, period]), discretization=(N, N))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Define the slab layer with a square patch\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "epsilon = lattice.ones() * eps_quartz\nsquare = lattice.square(center=(0.5 * period, 0.5 * period), width=l_patch)\nepsilon[square] = eps_active\n\nslab = lattice.Layer(\"Slab\", thickness=0.12)\nslab.epsilon = epsilon\n\ncmap = ListedColormap([\"#dddddd\", \"#73a0e8\"])\n\n\nplt.figure(figsize=(3, 2.5))\nim = slab.plot(cmap=cmap)\ncbar = plt.colorbar(im[0], ticks=[eps_quartz, eps_active])\nplt.xlabel(r\"$x$ ($\\mu$m)\")\nplt.ylabel(r\"$y$ ($\\mu$m)\")\nplt.title(r\"$\\varepsilon$\")\nplt.axis(\"scaled\")\nplt.tight_layout()\nplt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Define the simulation\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "sup = lattice.Layer(\"Superstrate\", epsilon=1)\nsub = lattice.Layer(\"Substrate\", epsilon=eps_quartz)\nstack = [sup, slab, sub]\n\n\ndef compute_transmission(fev):\n    w = h * c / e / (fev * 1e-6)\n    pw = nn.PlaneWave(wavelength=w, angles=(0, 0, 90))\n    sim = nn.Simulation(stack, pw, 100, formulation=\"tangent\")\n    R, T = sim.diffraction_efficiencies()\n    print(f\"f = {fev}eV\")\n    print(\"T = \", T)\n    return T\n\n\nfreqsev = np.linspace(1, 2.6, 101)\nfev_adapted, transmission = nn.adaptive_sampler(\n    compute_transmission, freqsev, max_bend=10, max_x_rel=0.001, max_df=0.005\n)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Figure 4 from :cite:p:`Tikhodeev2002`.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "plt.figure()\nplt.plot(fev_adapted * 1000, transmission, c=\"#be4c83\")\nplt.ylim(0.4, 1)\nplt.xlabel(\"frequency (meV)\")\nplt.ylabel(\"Transmissivity\")\nplt.tight_layout()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Plot the fields at the resonant frequency of 2456meV\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "fev = 2.456\nw = h * c / e / (fev * 1e-6)  # /1000\n\npw = nn.PlaneWave(wavelength=w, angles=(0, 0, 90))\nsim = nn.Simulation(stack, pw, 151, formulation=\"tangent\")\nE, H = sim.get_field_grid(\"Superstrate\", shape=(N, N))\n\nEx, Ey, Ez = E[:, :, :, 0]\nHx, Hy, Hz = H[:, :, :, 0]\nnE2 = np.abs(Ex) ** 2 + np.abs(Ey) ** 2  # + np.abs(Ez)**2\nnH2 = np.abs(Hx) ** 2 + np.abs(Hy) ** 2  # + np.abs(Hz)**2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Electric field\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "extent = [0, period, 0, period]\nx, y = np.linspace(0, period, N), np.linspace(0, period, N)\n\nplt.figure()\nplt.imshow(epsilon.real, cmap=\"Greys\", origin=\"lower\", extent=extent)\nplt.imshow(nE2, alpha=0.9, origin=\"lower\", extent=extent)\nplt.colorbar()\ns = 3\nplt.quiver(x[::s], y[::s], Ex[::s, ::s].real, Ey[::s, ::s].real, color=\"w\")\nplt.xlabel(r\"$x$ ($\\mu$m)\")\nplt.ylabel(r\"$y$ ($\\mu$m)\")\nplt.title(\"$E$\")\nplt.tight_layout()\nplt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Magnetic field\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "plt.figure()\nplt.imshow(epsilon.real, cmap=\"Greys\", origin=\"lower\", extent=extent)\nplt.imshow(nH2, alpha=0.9, origin=\"lower\", extent=extent)\nplt.colorbar()\nplt.quiver(x[::s], y[::s], Hx[::s, ::s].real, Hy[::s, ::s].real, color=\"w\")\nplt.xlabel(r\"$x$ ($\\mu$m)\")\nplt.ylabel(r\"$y$ ($\\mu$m)\")\nplt.title(\"$H$\")\nplt.tight_layout()\nplt.show()"
      ]
    },
    {
      "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"
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  "nbformat": 4,
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}