{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7c995adf-84ef-41d6-ab49-4345b761e8e7",
   "metadata": {},
   "source": [
    "# First lecture : Oscillators and 2-3-4 level systems\n",
    "\n",
    "\n",
    "Aim is to revisit the concept of laser physics solving numerically equation instead of analytically. \n",
    "\n",
    "If you were to find a mystake in the notebook, please send me some feedback !\n",
    "\n",
    "## The two level system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b30cdc0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy as sc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfa3a8cf-0609-418c-86d6-122ce004e263",
   "metadata": {},
   "source": [
    "## Solving for a 2-level system\n",
    "\n",
    "For a 2 level system, solving the differential equation is not so interesting, we merely plot the result.\n",
    "\n",
    "For 3-level and 4-level system, the situation is much more intersting. We will developp the formalism for a 4-level-system first without a photon flux and then with a photon flux ($f_{32,se} \\neq 0$). This allows to study the dynamics of population inversion independently from the laser dynamic.\n",
    "\n",
    "Exercice : \n",
    "- Starting with all parameters equal to 1, change the different values to obtain population inversion.\n",
    "- Add a spontaneous emission term $f_{32,se} \\neq 0$ to obtain a gain in the laser flux\n",
    "- Playing with this different terms, can you demonstrate spiking  ?\n",
    "- Explain why the decay time measured when we switch the pump off is not the decay time of the transition.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8563dc12-69a8-402c-8c70-f2880d03d98e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = np.linspace(0.01, 10, 1000)\n",
    "\n",
    "A, B = 1, 2\n",
    "\n",
    "def N2(u,A, B):\n",
    "    return B*u / (2*B*u +A)\n",
    "twolevel = plt.figure(figsize = (5,4))\n",
    "plt.plot(u, N2(u,A,B), label = r'$N_2$')\n",
    "plt.plot(u, 1 - N2(u,A,B), label = r'$N_2$')\n",
    "plt.xlabel('Normalized incoming photon flux')\n",
    "plt.ylabel('Normalized population')\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d90bc856",
   "metadata": {},
   "source": [
    "## The three level case\n",
    "\n",
    "As we have seen, a laser requires at least 3 levels to reach population inversion.\n",
    "Here is a basic illustration, starting with dumb numbers. Your mission, should you accept it, is to run it with the actual values of the Ruby laser. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "49634c3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --- Parameters (dummy values) ---\n",
    "f_31 = 1.0   # fast pump into N3\n",
    "f_32 = 0.5   # fast non-radiative decay into N2\n",
    "f_21 = 0.1   # radiative transition\n",
    "Rp = 10      # pump rate\n",
    "\n",
    "# Initial conditions: all atoms in ground state\n",
    "N0 = [1, 0, 0]\n",
    "\n",
    "# ODEs\n",
    "def three_level(N, t):\n",
    "    N1, N2, N3 = N\n",
    "    dN1 = -Rp*N1 + f_21*N2\n",
    "    dN2 = -f_21*N2 + f_32*N3\n",
    "    dN3 = Rp*N1 - (f_32+f_31)*N3\n",
    "    return [dN1, dN2, dN3]\n",
    "\n",
    "# Time integration\n",
    "t = np.linspace(0, 5, 500)\n",
    "N_t = sc.integrate.odeint(three_level, N0, t)\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(6,4))\n",
    "for i, label in enumerate([r'$N_1$', r'$N_2$', r'$N_3$']):\n",
    "    plt.plot(t, N_t[:,i], label=label)\n",
    "plt.xlabel(\"Time [a.u.]\")\n",
    "plt.ylabel(\"Population\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8794ab96",
   "metadata": {},
   "source": [
    "## Four level system\n",
    "\n",
    "The more levels involved, the merrier ! Same logic with a  4 level system, such as Nd:YAG."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7518891a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$N_{1}$\n",
      "$N_{2}$\n",
      "$N_{3}$\n",
      "$N_{4}$\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --- Nd:YAG-like parameters ---\n",
    "Rp = 20       # pump\n",
    "f_43 = 100.   # fast nonradiative decay to N3\n",
    "f_42 = 1\n",
    "f_41 = 1\n",
    "f_32sp = 0.1  # spontaneous emission\n",
    "f_32se = 20   # stimulated emission\n",
    "f_31 = 1\n",
    "f_21 = 50\n",
    "alpha = 5000  # losses\n",
    "\n",
    "# Initial condition: ground state + small photon seed\n",
    "N_i_0 = np.array([1, 0, 0, 0, 0.1])\n",
    "t_tot = 1\n",
    "t_list = np.linspace(0.001, t_tot, 1000)\n",
    "\n",
    "def four_level_system(N_i, t):\n",
    "    d_N_1 = -Rp * N_i[0] + f_21 * N_i[1] + f_31 * N_i[2] + (Rp + f_41) * N_i[3]\n",
    "    d_N_2 = -f_21*N_i[1] + f_32sp *N_i[2] + f_32se *N_i[2]*N_i[4] + f_42 *N_i[3]\n",
    "    d_N_3 = -(f_31 + f_32sp) * N_i[2] + f_43 * N_i[3] - f_32se *N_i[2]*N_i[4]\n",
    "    d_N_4 = Rp * N_i[0] - (f_41 + f_42 + f_43 + Rp) * N_i[3]\n",
    "    d_phi = 100*f_32se*(N_i[2] - N_i[1])*N_i[4] - alpha*N_i[4]\n",
    "    if N_i[4]<0.01 and d_phi < 0:\n",
    "        d_phi = 0\n",
    "    return np.array([d_N_1, d_N_2, d_N_3, d_N_4, d_phi])\n",
    "\n",
    "# Integrate\n",
    "N_i_t = sc.integrate.odeint(four_level_system, N_i_0, t_list)\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(6,4))\n",
    "for k in range(4):\n",
    "    print(r'$N_{'+str(k+1)+'}$')\n",
    "    plt.plot(t_list, N_i_t[:,k], label=r'$N_{'+str(k+1)+'}$')\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.twinx()\n",
    "plt.plot(t_list, N_i_t[:,4], 'purple', label=r'$\\phi$')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Population')\n",
    "plt.legend(loc='center right')\n",
    "plt.grid()\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv-1 (3.11.9)",
   "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": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
