{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "\n",
    "from IPython.display import display, Markdown, Math\n",
    "from matplotlib.pyplot import *\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Paramètres de la gaussienne\n",
    "A = 1.0  # Amplitude\n",
    "  # Moyenne, le maximum est à x = 0\n",
    "sigma = 20*10**(-6) # Écart-type, contrôle la largeur de la cloche\n",
    "i=complex(0,1)\n",
    "\n",
    "# Créer un ensemble de valeurs x\n",
    "x = linspace(-0.015, 0.015, 10001)  # Vous pouvez ajuster la plage en fonction de vos besoins\n",
    "z = linspace(0,0.001,1000)\n",
    "\n",
    "k=2*pi/(600*10**(-9))\n",
    "nx=len(x)\n",
    "nz=len(z)\n",
    "dx=0.03/nx\n",
    "dz=1/nz\n",
    "# Calculer les valeurs de la gaussienne pour chaque x\n",
    "E0 = A * exp(-(x )**2 / (2 * sigma**2))\n",
    "\n",
    "# Tracer la gaussienne\n",
    "plt.plot(x, E0)\n",
    "plt.title('Gaussienne avec un maximum à x=0')\n",
    "plt.xlim(-0.001,0.001)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('E(x,z=0)')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10471975.511965975"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "fourier_transform = np.fft.fftshift(np.fft.fft(E0))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "nux=np.fft.fftshift(np.fft.fftfreq(nx,dx))\n",
    "kx=2*pi*nux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "kz=np.sqrt(k**2-kx**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ez=fourier_transform*exp(i*kz*0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.04403150e-14-3.00439272e-14j, -5.02186263e-14+3.00862303e-14j,\n",
       "        4.97677360e-14-3.01329564e-14j, ...,\n",
       "       -4.98190361e-14+3.00564478e-14j,  5.02454587e-14-3.00361688e-14j,\n",
       "       -5.04469045e-14+3.00266971e-14j])"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inverse_transform = np.fft.ifft(Ez)\n",
    "inverse_transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,inverse_transform)\n",
    "plt.plot(x, E0)\n",
    "plt.title('Gaussienne avec un maximum à x=0')\n",
    "plt.xlim(-0.001,0.001)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('E(x,z=zmax)')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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