{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "znzSo4wE5fes"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/IrisFDTD/DSF-UNIZAR/blob/main/dsf_propuesta-1_2d_materials.ipynb\n",
    "\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tYZjdh8TvE7-"
   },
   "source": [
    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\"><img alt=\"Licencia Creative Commons\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\" /></a><br /><span xmlns:dct=\"http://purl.org/dc/terms/\" property=\"dct:title\"></span> The following notes written by  <span xmlns:cc=\"http://creativecommons.org/ns#\" property=\"cc:attributionName\">Sergio Gutiérrez Rodrigo (<sergut@unizar.es>) </span>. Distributed under  <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\">License Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "j2H5UHGe1Uf8"
   },
   "source": [
    "```\n",
    "Departamento de Física Aplicada\n",
    "Universidad de Zaragoza\n",
    "Instituto de Nanociencia y Materiales de Aragón (INMA)\n",
    "C/ Pedro Cerbuna, 12, 50009, Zaragoza, España\n",
    "```\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D7vYGeB21ZQU"
   },
   "source": [
    "---\n",
    "# **Photonic devices and systems - 2D materials dispersion relation (hexagonal Boron Nitride)**\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "96pWrhHgDqIu"
   },
   "source": [
    "# Definitions: van der Waals polariton dispersion relation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "5ysvAQ96yLE2"
   },
   "outputs": [],
   "source": [
    "'''\n",
    "Thin Film Dispersion Relation hBN\n",
    "Eq.1 in Tunable Phonon Polaritons in Atomically Thin van der Waals Crystals of Boron Nitride\n",
    "S. Dai et al. Science 343, 1125 (2014);\n",
    "DOI: 10.1126/science.124683\n",
    "'''\n",
    "def psi(lambda_):\n",
    "    return np.sqrt(eps_z(omega(lambda_))) / (1j * np.sqrt(eps_t(omega(lambda_))))\n",
    "\n",
    "# Modes for a given qy\n",
    "qy = 0\n",
    "def qx(lambda_):\n",
    "    return -(psi(lambda_) / d) * (np.arctan(eps_a / (eps_t(omega(lambda_)) * psi(lambda_))) + np.arctan(eps_s(omega(lambda_)) / (eps_t(omega(lambda_)) * psi(lambda_))) + np.pi * l)\n",
    "\n",
    "def qz(lambda_):\n",
    "    return np.sqrt(eps_t(omega(lambda_)) / eps_z(omega(lambda_)) * ((qx(lambda_))**2 + (qy)**2) - eps_t(omega(lambda_)) * ((2.0 * np.pi) / lambda_)**2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CSLHzJ77fRCn"
   },
   "source": [
    "# Optical properties of hBN, substrate and cover"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "gsW7j1AAx_uH"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.optimize as opt\n",
    "\n",
    "# Constants\n",
    "h = 6.626e-34  # J*s\n",
    "c = 3e8  # m/s\n",
    "e = 1.6021773e-19  # J/eV\n",
    "flw = 1239.8283  # (h*c)/e * 10^9\n",
    "\n",
    "def omega(x):\n",
    "    return flw / x\n",
    "\n",
    "'''\n",
    "Dielectric functions for hBN\n",
    "'''\n",
    "# eps_per\n",
    "eps_r1 = 4.90\n",
    "lambda1 = flw / 0.16939\n",
    "Lambda_eps1 = 1.93872\n",
    "Omega1 = flw / lambda1\n",
    "Gamma1 = 8.67879831e-4\n",
    "def eps_t(omega):\n",
    "    return eps_r1 - (Lambda_eps1 * Omega1**2) / (omega**2 - Omega1**2 + 1j * omega * Gamma1)\n",
    "\n",
    "# eps_par\n",
    "eps_r2 = 2.95\n",
    "lambda2 = flw / 0.09423\n",
    "Lambda_eps2 = 0.52618\n",
    "Omega2 = flw / lambda2\n",
    "Gamma2 = 2.47966e-4\n",
    "def eps_z(omega):\n",
    "    return eps_r2 - (Lambda_eps2 * Omega2**2) / (omega**2 - Omega2**2 + 1j * omega * Gamma2)\n",
    "\n",
    "# Dielectric constant for superstrate\n",
    "eps_a=1.0\n",
    "\n",
    "# Dielectric constant for substrate\n",
    "def eps_s(omega):\n",
    "    return 1.88422  # CaF2 (fixed value)  # CaF2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9tMovjbIeLNQ"
   },
   "source": [
    "# Wavelength range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "2fDFBSfwyG4c"
   },
   "outputs": [],
   "source": [
    "# Wavelength range (nm)\n",
    "lambda_o = 6200.0\n",
    "lambda_f = 7400.0\n",
    "N_lambda = 6000\n",
    "lambda_range=np.linspace(lambda_o,lambda_f,N_lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_TerIhI7ykT0"
   },
   "source": [
    "# Example of van der Waals polariton dispersion relation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 894
    },
    "executionInfo": {
     "elapsed": 624,
     "status": "ok",
     "timestamp": 1739894575581,
     "user": {
      "displayName": "SERGIO GUTIERREZ RODRIGO",
      "userId": "07959720391705098820"
     },
     "user_tz": -60
    },
    "id": "DmAXBw8mvHDs",
    "outputId": "b2031c46-1ce5-41b5-bf5e-7b9a26877077"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = 256.0  # Thicknesses (nm)\n",
    "l = 0      # Mode index\n",
    "\n",
    "plt.plot(1e3*np.real(qx(lambda_range)),1e7/lambda_range,label=r'$Re(q_x)$')\n",
    "plt.plot(1e3*np.imag(qx(lambda_range)),1e7/lambda_range,label=r'$Im(q_x)$')\n",
    "plt.xlabel(r'$q (10^5 cm^{-1})$')\n",
    "plt.ylabel(r'$\\omega (cm^{-1})$')\n",
    "plt.xlim(0,50)\n",
    "plt.ylim(1350.0,1600.0)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(lambda_range,np.real(qz(lambda_range)),label=r'$Re(q_z)$')\n",
    "plt.plot(lambda_range,np.imag(qz(lambda_range)),label=r'$Im(q_z)$')\n",
    "plt.xlabel(r'wavelength (nm)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": [
    {
     "file_id": "1RDc21TnIt3vsc3LgKJJAOhOpDiYI0Kck",
     "timestamp": 1732534344874
    },
    {
     "file_id": "1HLJCzTifQ-QrzMvcYn1A7rTWjqy6zuE4",
     "timestamp": 1732188059193
    },
    {
     "file_id": "1OJbr7bAKIz871W8MfSe7aTYNFJTy5VYF",
     "timestamp": 1712046943589
    },
    {
     "file_id": "1YcN9LUdnqy_QaoKy50Ze6v9a-t0r7Fu4",
     "timestamp": 1705306995793
    }
   ],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
