{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Nkv7GoeTOK66"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/IrisFDTD/OPTICS-UNIZAR/blob/main/Topic_2/chapter2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "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",
    "# **Optics - Chapter 2 - Basic phenomena of light-matter interaction. Light sources**\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "cstwFWb35zRx"
   },
   "source": [
    "# Main libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "8wjwSqRq4SdL"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QwQCqCwo-hdU"
   },
   "source": [
    "# Physical constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "AM9SRaX6WEav"
   },
   "outputs": [],
   "source": [
    "# Constants\n",
    "kB = 1.380649e-23  # Boltzmann constant in J/K\n",
    "T_room = 298.15    # Room temperature in Kelvin\n",
    "h = 6.62607015e-34  # Planck constant in J·s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qhYY9BuUWHUu"
   },
   "source": [
    "# Function definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "HEz2Fgp7xYOR"
   },
   "outputs": [],
   "source": [
    "# Function to calculate kB*T\n",
    "def calculate_kBT(temperature):\n",
    "    return kB * temperature\n",
    "\n",
    "# Function to calculate h*nu\n",
    "def calculate_hnu(frequency):\n",
    "    return h * frequency\n",
    "\n",
    "# Function to calculate N1/N2\n",
    "def N1overN2(frequency,g1,g2,T):\n",
    "    beta=1.0/(kB*T)\n",
    "    return (g1/g2)*np.exp(beta*h*frequency)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3QB4LAyHWWN3"
   },
   "source": [
    "# Compare $h\\nu$ vs $k_B T$ at visible and microwave regimes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 546
    },
    "executionInfo": {
     "elapsed": 1372,
     "status": "ok",
     "timestamp": 1695847072326,
     "user": {
      "displayName": "SERGIO GUTIERREZ RODRIGO",
      "userId": "07959720391705098820"
     },
     "user_tz": -120
    },
    "id": "9WciYJXpWVk_",
    "outputId": "196d1d6f-8ad2-4d91-b82a-8494c4a5d667"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Frequency range from microwave to visible\n",
    "microwave_freq = np.linspace(1e9, 1e13, 100)  # 1 GHz to 1 THz\n",
    "visible_freq = np.linspace(4e14, 7.5e14, 100)  # 400 THz to 750 THz\n",
    "\n",
    "# Calculate energies\n",
    "microwave_energy = calculate_hnu(microwave_freq)\n",
    "visible_energy = calculate_hnu(visible_freq)\n",
    "\n",
    "# Create the plot Energy vs Frequency\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.semilogx(microwave_freq, microwave_energy, label='Microwave Range', color='blue')\n",
    "plt.semilogx(visible_freq, visible_energy, label='Visible Range', color='red')\n",
    "plt.axhline(calculate_kBT(T_room),color='green',label=r'$k_BT$ (T=room temperature)')\n",
    "plt.axvline(2.4*1e9,label='2.4 GHz microwave oven/phone',linestyle='--',color='grey')\n",
    "plt.xlabel('Frequency (Hz)')\n",
    "plt.ylabel('Energy (Joules)')\n",
    "#plt.title('Energy vs. Frequency')\n",
    "plt.yscale('log')  # Use a logarithmic scale for y-axis\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "#plt.xlim(1.0e9,1.0e12)\n",
    "# Show the visible and microwave range labels\n",
    "plt.annotate('Microwave Range', xy=(1.5e11, 1e-27), color='blue')\n",
    "plt.annotate('Visible Range', xy=(5e14, 1e-27), color='red')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HuW-06CIWmLQ"
   },
   "source": [
    "# Calculate $N_1/N_2$ from Boltzmann distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 568
    },
    "executionInfo": {
     "elapsed": 1751,
     "status": "ok",
     "timestamp": 1695847077674,
     "user": {
      "displayName": "SERGIO GUTIERREZ RODRIGO",
      "userId": "07959720391705098820"
     },
     "user_tz": -120
    },
    "id": "AeT5x3mUWmTX",
    "outputId": "074c5503-5f3e-4570-a778-52c76e8e3a5a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Calculate N1/N2\n",
    "N1oN2=N1overN2(visible_freq,1,1,T_room)\n",
    "\n",
    "# Create the plot N1/N2\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.semilogx(visible_freq, N1oN2, label='N1/N2', color='red')\n",
    "plt.xlabel('Frequency (Hz)')\n",
    "plt.ylabel('N1/N2')\n",
    "plt.title('N1/N2 as a function of the transition frequency '+ r'$\\nu$ ($\\Delta E=h\\nu$)')\n",
    "plt.yscale('log')  # Use a logarithmic scale for y-axis\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "#plt.xlim(1.0e9,1.0e12)\n",
    "# Show the visible and microwave range labels\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": [
    {
     "file_id": "11r2xfnB-NZWuxYdZ2nV8sqh6XwCua4Sq",
     "timestamp": 1695846667454
    },
    {
     "file_id": "1yf9Faj4pp9NSKJbCDm4GsOXxIWhUk7sF",
     "timestamp": 1693481770581
    },
    {
     "file_id": "1tKsdck-ZuuzCsWEJ1i7XGcXrrLCQgcLQ",
     "timestamp": 1693389677769
    }
   ],
   "toc_visible": true
  },
  "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
