LennartNaeve_code/spilling_code/harmonic_approximation/test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31mThe Kernel crashed while executing code in the current cell or a previous cell. \n",
      "\u001b[1;31mPlease review the code in the cell(s) to identify a possible cause of the failure. \n",
      "\u001b[1;31mClick <a href='https://aka.ms/vscodeJupyterKernelCrash'>here</a> for more info. \n",
      "\u001b[1;31mView Jupyter <a href='command:jupyter.viewOutput'>log</a> for further details."
     ]
    }
   ],
   "source": [
    "from ODT import *\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "options = {\n",
    "    \"prop_dir\" : \"v\", #direction of beam propagation, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"wavelength\" : 532*u.nm,\n",
    "    \"alpha\" : 184.4, # Dy polarizability in terms of a_0\n",
    "    \"dy_mass\" : 164*u.u,\n",
    "    \"dy_mag_moment\" : 9.93 * ac.muB,\n",
    "    \"power\" : 0.2*u.mW,\n",
    "    \"w_0\" : 1*u.um, #beam waist in transverse-plane\n",
    "    \"gravity\" : True, #bool for gravity in z direction\n",
    "    \"mag_dir\" : \"v\", #direction of magnetic field and gradient, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"mag_grad\" : 4*u.G/u.cm, #magnetic gradient\n",
    "    \"mag_offset\" : 0*u.G, #magnetic offset\n",
    "    \"mJ\" : 0, #magnetic quantum number\n",
    "    \"ref_ind\" : 1  #refractive index\n",
    "}\n",
    "trap = ODP_1D(options)\n",
    "\n",
    "z = np.linspace(-30,30,1000)*u.um\n",
    "trap.get_axial_occ_analytic(z,plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options = {\n",
    "    \"prop_dir\" : \"v\", #direction of beam propagation, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"wavelength\" : 532*u.nm,\n",
    "    \"alpha\" : 184.4, # Dy polarizability in terms of a_0\n",
    "    \"dy_mass\" : 164*u.u,\n",
    "    \"dy_mag_moment\" : 9.93 * ac.muB,\n",
    "    \"power\" : 3*u.mW,\n",
    "    \"w_0\" : 2*u.um, #beam waist in transverse-plane\n",
    "    \"gravity\" : True, #bool for gravity in z direction\n",
    "    \"mag_dir\" : \"v\", #direction of magnetic field and gradient, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"mag_grad\" : 120*u.G/u.cm, #magnetic gradient\n",
    "    \"mag_offset\" : 0*u.G, #magnetic offset\n",
    "    \"mJ\" : 0, #magnetic quantum number\n",
    "    \"ref_ind\" : 1  #refractive index\n",
    "}\n",
    "trap = ODP_1D(options)\n",
    "\n",
    "z = np.linspace(-50,50,1000)*u.um\n",
    "#power = np.linspace(0.1,1,10)*u.mW\n",
    "power = np.linspace(2.8,3,40)*u.mW\n",
    "freq = np.zeros(len(power))*u.Hz\n",
    "#mag_grad = np.linspace(4.5,4.9,10)*u.G/u.cm\n",
    "mag_grad = np.linspace(4.8,5.2,40)*u.G/u.cm\n",
    "power2D, mag_grad2D = np.meshgrid(power,mag_grad)\n",
    "\n",
    "occupation = np.zeros_like(power2D).value\n",
    "\n",
    "for i,p in enumerate(power):\n",
    "    for j,grad in enumerate(mag_grad):\n",
    "        trap.power = p\n",
    "        trap.mag_grad = grad\n",
    "        try:\n",
    "            n = trap.get_axial_occ_analytic(z,plot=False)\n",
    "        except:\n",
    "            n = np.nan\n",
    "        occupation[i,j] = n\n",
    "    freq[i] = trap.nu_z\n",
    "    #print(i)\n",
    "\"\"\"  \n",
    "plt.imshow(occupation,extent=[np.min(mag_grad).to(u.G/u.cm).value,np.max(mag_grad).to(u.G/u.cm).value,\n",
    "                                                        np.min(power).to(u.mW).value,np.max(power).to(u.mW).value]\n",
    "                                                        ,aspect=\"auto\",origin=\"lower\",vmax=10)\n",
    "plt.colorbar()\n",
    "plt.title(f\"w_0={trap.w_0}, alpha={184}a_0\")\n",
    "plt.ylabel(\"beam power [mW]\")\n",
    "plt.xlabel(\"magnetic gradient [G/cm]\")\n",
    "plt.show()\n",
    "#print(occupation)\"\"\"\n",
    "\n",
    "# Plot the main data\n",
    "fig, ax1 = plt.subplots()\n",
    "im = ax1.imshow(\n",
    "    occupation,\n",
    "    extent=[\n",
    "        np.min(mag_grad).to(u.G / u.cm).value,\n",
    "        np.max(mag_grad).to(u.G / u.cm).value,\n",
    "        np.min(power).to(u.mW).value,\n",
    "        np.max(power).to(u.mW).value\n",
    "    ],\n",
    "    aspect=\"auto\",\n",
    "    origin=\"lower\"\n",
    ")\n",
    "\n",
    "# Add colorbar\n",
    "plt.colorbar(im, ax=ax1, label=\"Occupation\")\n",
    "#divider = make_axes_locatable(ax1)\n",
    "#cax = divider.append_axes(\"right\", size=\"5%\", pad=0.5)  # Offset colorbar to the right\n",
    "#cbar = plt.colorbar(im, cax=cax, label=\"Occupation\")\n",
    "\n",
    "# Primary axis labels\n",
    "ax1.set_xlabel(\"Magnetic gradient [G/cm]\")\n",
    "ax1.set_ylabel(\"Beam power [mW]\")\n",
    "ax1.set_title(f\"w_0={trap.w_0}, alpha={184}a_0\")\n",
    "\n",
    "# Add secondary y-axis for trap.nu_z\n",
    "ax2 = ax1.twinx()\n",
    "\n",
    "# Compute nu_z for given power values (example using trap)\n",
    "nu_z_vals = freq\n",
    "\n",
    "# Map power to nu_z for the second axis\n",
    "ax2.set_ylim(ax1.get_ylim())  # Align y-axis limits\n",
    "ax2.set_yticks(np.linspace(np.min(power).to(u.mW).value, np.max(power).to(u.mW).value, 5))  # Match tick locations\n",
    "ax2.set_yticklabels([f\"{nu_z:.1f}\" for nu_z in np.interp(\n",
    "    np.linspace(np.min(power).to(u.mW).value, np.max(power).to(u.mW).value, 5),\n",
    "    power.to(u.mW).value,\n",
    "    nu_z_vals\n",
    ")])  # Map ticks to nu_z values\n",
    "ax2.set_ylabel(r\"$\\nu_z$ [Hz]\")  # Second axis label\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.055960553528076495 Hz\n"
     ]
    },
    {
     "ename": "Exception",
     "evalue": "fit was unsuccessful :(",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "File \u001b[1;32mc:\\Users\\peter\\Uni-Bulk\\FerDy_Chomaz\\spilling_code\\ODT.py:105\u001b[0m, in \u001b[0;36mODP_1D.get_axial_occ\u001b[1;34m(self, z, fit_fac, p0, plot, plot_fac)\u001b[0m\n\u001b[0;32m    104\u001b[0m n_max \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mint\u001b[39m(np\u001b[38;5;241m.\u001b[39mceil((E_max\u001b[38;5;241m/\u001b[39m(ac\u001b[38;5;241m.\u001b[39mhbar\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39mpi\u001b[38;5;241m*\u001b[39mnu)\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m0.5\u001b[39m)\u001b[38;5;241m.\u001b[39mvalue))\n\u001b[1;32m--> 105\u001b[0m temps \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([((ac\u001b[38;5;241m.\u001b[39mhbar\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39mpi\u001b[38;5;241m*\u001b[39mnu\u001b[38;5;241m*\u001b[39m(n \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m0.5\u001b[39m)\u001b[38;5;241m+\u001b[39mV_0)\u001b[38;5;241m/\u001b[39mac\u001b[38;5;241m.\u001b[39mk_B)\u001b[38;5;241m.\u001b[39mto(u\u001b[38;5;241m.\u001b[39muK)\u001b[38;5;241m.\u001b[39mvalue \u001b[38;5;28;01mfor\u001b[39;00m n \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(n_max)])\n\u001b[0;32m    106\u001b[0m \u001b[38;5;66;03m#print(f\"{n_max} modes of trap frequncy {nu} were found in potential well.\")\u001b[39;00m\n\u001b[0;32m    107\u001b[0m \u001b[38;5;66;03m#plot results\u001b[39;00m\n",
      "File \u001b[1;32mc:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\astropy\\units\\quantity.py:667\u001b[0m, in \u001b[0;36mQuantity.__array_ufunc__\u001b[1;34m(self, function, method, *inputs, **kwargs)\u001b[0m\n\u001b[0;32m    666\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m input_, converter \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(inputs, converters):\n\u001b[1;32m--> 667\u001b[0m     input_ \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(input_, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mvalue\u001b[39m\u001b[38;5;124m\"\u001b[39m, input_)\n\u001b[0;32m    668\u001b[0m     arrays\u001b[38;5;241m.\u001b[39mappend(converter(input_) \u001b[38;5;28;01mif\u001b[39;00m converter \u001b[38;5;28;01melse\u001b[39;00m input_)\n",
      "File \u001b[1;32mc:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\astropy\\units\\quantity.py:949\u001b[0m, in \u001b[0;36mQuantity.to_value\u001b[1;34m(self, unit, equivalencies)\u001b[0m\n\u001b[0;32m    947\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_new_view(value, unit)\n\u001b[1;32m--> 949\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mto_value\u001b[39m(\u001b[38;5;28mself\u001b[39m, unit\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, equivalencies\u001b[38;5;241m=\u001b[39m[]):\n\u001b[0;32m    950\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[0;32m    951\u001b[0m \u001b[38;5;124;03m    The numerical value, possibly in a different unit.\u001b[39;00m\n\u001b[0;32m    952\u001b[0m \n\u001b[1;32m   (...)\u001b[0m\n\u001b[0;32m    975\u001b[0m \u001b[38;5;124;03m    to : Get a new instance in a different unit.\u001b[39;00m\n\u001b[0;32m    976\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: ",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mException\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[3], line 19\u001b[0m\n\u001b[0;32m     16\u001b[0m trap \u001b[38;5;241m=\u001b[39m ODP_1D(options)\n\u001b[0;32m     18\u001b[0m z \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinspace(\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m20\u001b[39m,\u001b[38;5;241m20\u001b[39m,\u001b[38;5;241m1000\u001b[39m)\u001b[38;5;241m*\u001b[39mu\u001b[38;5;241m.\u001b[39mum\n\u001b[1;32m---> 19\u001b[0m trap\u001b[38;5;241m.\u001b[39mget_axial_occ(z,fit_fac\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m2\u001b[39m,p0\u001b[38;5;241m=\u001b[39m[\u001b[38;5;241m2e3\u001b[39m,\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1.5e-27\u001b[39m,\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1e6\u001b[39m],plot\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m,plot_fac\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m1\u001b[39m)\n",
      "File \u001b[1;32mc:\\Users\\peter\\Uni-Bulk\\FerDy_Chomaz\\spilling_code\\ODT.py:119\u001b[0m, in \u001b[0;36mODP_1D.get_axial_occ\u001b[1;34m(self, z, fit_fac, p0, plot, plot_fac)\u001b[0m\n\u001b[0;32m    117\u001b[0m         plt\u001b[38;5;241m.\u001b[39mshow()\n\u001b[0;32m    118\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m:\n\u001b[1;32m--> 119\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mfit was unsuccessful :(\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m    120\u001b[0m     \u001b[38;5;66;03m#plot potential for trouble shooting\u001b[39;00m\n\u001b[0;32m    121\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m plot:\n",
      "\u001b[1;31mException\u001b[0m: fit was unsuccessful :("
     ]
    },
    {
     "data": {
      "image/png": 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+H499vgOAO/s04f4BLVRkvJTKjIiIuJ2XVu5lzhc7Abj7sqZM6NdcRcaLqcyIiIhbefHbPTzx5c8A3Ht5M8Zf0UxFxsupzIiIiNt4YcUenvyqvMjcd0Vz7r2imcmJxBWozIiIiFt4+bu9FUVmUv/mjLtMRUbKaX5nERFxeQv+l8bspeVjZCb0U5GRylRmRETEpb2x5gAzPi2//fruy5pyz+UqMlKZyoyIiLis99Zl8PBH5UsU/LV3Yyb0a25yInFFKjMiIuKSPvzpIA9+uAWAv1yapAnx5KxUZkRExOV8sjmTSe9vxjDg5u6JPHJVaxUZOSuVGRERcSlfpGZx37ubcBowvEsCM4emqMjIOZleZqZPn47FYqm0xcXFVTxvGAbTp08nPj6eoKAg+vTpw7Zt20xMLCIiNeW/2w9z99sbcTgNhnVsyOxr2+LjoyIj52Z6mQFo06YNWVlZFVtqamrFc0888QTPPPMM8+bNY926dcTFxdGvXz/y8/NNTCwiItXtf3uOcuebP1HmNLi6QzxP/KmdioycF5coM35+fsTFxVVsMTExQPlVmeeee46pU6dy3XXXkZKSwqJFiygsLOStt94yObWIiFSXjel5jF28nhKHkwFtYnn6+vb4qsjIeXKJMrN7927i4+NJTk5m+PDh7Nu3D4C0tDSys7Pp379/xb5Wq5XevXuzatWqs3694uJi7HZ7pU1ERFzTjiw7oxeso7DEQa9m0fzzpkvw83WJlydxE6b/39KtWzcWL17MV199xb///W+ys7Pp2bMnubm5ZGdnAxAbG1vpc2JjYyueO5M5c+YQHh5esSUkJNToMYiISNXsP1rAyFfXYjtZSsfEurw0shNWP1+zY4mbMb3MDBo0iGHDhtG2bVuuuOIKPv/8cwAWLVpUsc+po9gNwzjnyPbJkydjs9kqtoyMjJoJLyIiVZZlO8mfX/mRoyeKaRkXyoLRXQkO0JKBcuFMLzOnCgkJoW3btuzevbvirqZTr8Lk5OScdrXmt6xWK2FhYZU2ERFxHbknirn5lR85dPwkSVHBvH5bN8KD/c2OJW7K5cpMcXExO3bsoH79+iQnJxMXF8fy5csrni8pKWHlypX07NnTxJQiIlJV9qJSRi1Yy94jBcSHB/LGmG7EhFrNjiVuzPTreZMmTWLIkCEkJiaSk5PDY489ht1uZ9SoUVgsFsaPH8/s2bNp1qwZzZo1Y/bs2QQHBzNixAizo4uIyAU6WeJgzML1bD1kJyokgNfHdKNhRLDZscTNmV5mDh48yE033cTRo0eJiYmhe/furFmzhkaNGgHwwAMPcPLkSe68807y8vLo1q0by5YtIzQ01OTkIiJyIcocTsa99RNr9x8jNNCPRbd2pUlMHbNjiQewGIZhmB2iptntdsLDw7HZbBo/IyJiAsMwePCDLby3/iBWPx/eGNONLkmRZscSF3e+r98uN2ZGREQ8z9PLdvHe+oP4WOD5my5RkZFqpTIjIiI1avHq/cxbsQeAWde2pX+buN/5DJELozIjIiI1ZmlqFtM+KV8c+L4rmnNT10STE4knUpkREZEasWZfLuPf2YRhwIhuidxzeVOzI4mHUpkREZFqtyPLzthF5QtH9m8dy6NXp5xz5naRi6EyIyIi1epgXiGjF6wlv7iMLkkR/POmS7QCttQolRkREak2tsJSRi9Yx2F7Mc1j6/DKLV0I9NfCkVKzVGZERKRalJQ5ueONDezJOUFsmJVFt3bVektSK1RmRETkohmGweQPU1m9L5eQAF9eG92F+uFBZscSL6EyIyIiF23eN3v44KfySfHmjehIm/hwsyOJF1GZERGRi/LxpkM8vXwXADOuTqFvy3omJxJvozIjIiJVtjbtGPe/vwWAsb2SGdm9kcmJxBupzIiISJXsO3KC218vn0tmYJs4Jg9qZXYk8VIqMyIicsGOFZTwl4XrOF5YSvuEujx7Ywd8NJeMmERlRkRELsivt2AfyC2kYUQQr9zSmaAAzSUj5lGZERGR82YYBo98vJW1aceoY/VjweguxIRazY4lXk5lRkREztvCVft5Z10GFgs8f9MlNIsNNTuSiMqMiIicn+92HeHRz7YDMGVQK92CLS5DZUZERH7XviMnGPfWTzgN+FOnhozplWx2JJEKKjMiInJOtsJSxixaj72ojI6JdZl1bQoWi+5cEtehMiMiImdV5nAy7u2f2He0gPjwQF4a2Rmrn+5cEteiMiMiImc1e+lOvt99lCB/X/49qrPuXBKXpDIjIiJntGTjQV77XxoAz9zQXotHistSmRERkdNsy7Qx+cNUAO6+rCmD2tY3OZHI2anMiIhIJccLS7jjjQ0UlTrp3TyG8Vc0NzuSyDmpzIiISAWH0+CedzaRcewkiZHB/GN4B3y15pK4OJUZERGp8OzyXXy36wiB/j7Mv7kTdYMDzI4k8rtUZkREBICvtmUzb8UeAOYOa0fr+DCTE4mcH5UZERFhT84JJr63GYBbL03m6g4NTE4kcv5UZkREvNyJ4jL++vp6ThSX0S05kslXtjQ7ksgFUZkREfFihmEw5cNU9h4pIC4skHkjOuLvq5cGcS/6P1ZExIu9tTadTzZn4utjYd6ISzTDr7gllRkRES+19ZCNGZ9uB+CBAS3onBRpciKRqlGZERHxQvaiUu566ydKypxc0aoeY3s1NjuSSJWpzIiIeBnDMHjogy0cyC2kQd0gnrq+PT6aGE/cmMqMiIiXWbz6AEtTs/H3LR8no4nxxN2pzIiIeJHNGcd57PPycTKTB7XiksQIkxOJXDyVGRERL2ErLB8nU+owGNgmjr9cmmR2JJFqoTIjIuIFDMPgoQ+3cDCvfAHJuX9qh8WicTLiGVRmRES8wDvrMvhiazZ+v8wnEx7kb3YkkWqjMiMi4uH25OQz49NtANw/oAXtGtY1N5BINVOZERHxYEWlDu5+exNFpU56NYvWfDLikVRmREQ82Nwvd7Ijy05kSABPaz4Z8VAqMyIiHmrFzhwW/G8/AE/+qR31wgLNDSRSQ1RmREQ8UE5+EZPe3wzA6J5JXN4q1uREIjVHZUZExMM4nQYT39tMbkEJLeNCeWhQS7MjidQolRkREQ+zYNV+vt99lEB/H56/6RIC/X3NjiRSo1RmREQ8yO7D+cz9cicAU69sRbPYUJMTidQ8lRkREQ9R6nAy4b3NlJQ56d08hpu7NzI7kkitUJkREfEQz3+9m9RDNsKD/HlCyxWIF3GbMvPiiy+SnJxMYGAgnTp14vvvvzc7koiIy9iYnscL3+4F4LFrUojVbdjiRdyizLz77ruMHz+eqVOnsnHjRnr16sWgQYNIT083O5qIiOlOljiY+N5mHE6Doe3jGdI+3uxIIrXKLcrMM888w2233caYMWNo1aoVzz33HAkJCfzrX/8yO5qIiOnmfLGDfUcLiAsL5NGrU8yOI1LrXL7MlJSUsGHDBvr371/p8f79+7Nq1aozfk5xcTF2u73SJiLiib7bdYTFqw8A8OT17QgP1mrY4n1cvswcPXoUh8NBbGzl2StjY2PJzs4+4+fMmTOH8PDwii0hIaE2ooqI1CpbYSkP/GcLALf0aESvZjEmJxIxh8uXmV+dOirfMIyzjtSfPHkyNputYsvIyKiNiCIitWr6p9vIthfRODqEyYNamR1HxDR+Zgf4PdHR0fj6+p52FSYnJ+e0qzW/slqtWK3W2ognImKK/24/zJKNh/CxwNM3tCcoQLP8ivdy+SszAQEBdOrUieXLl1d6fPny5fTs2dOkVCIi5rEVljJlSSoAY3s15pLECJMTiZjL5a/MAEyYMIGRI0fSuXNnevTowcsvv0x6ejp33HGH2dFERGrdo59vJye/mMbRIdzXr7nZcURM5xZl5sYbbyQ3N5eZM2eSlZVFSkoKS5cupVEjTdUtIt5lxc85/GfDQSyW8ruXtIikCFgMwzDMDlHT7HY74eHh2Gw2wsLCzI4jIlIl9qJSBjz7HVm2Im69NJlHhrQ2O5JIjTrf12+XHzMjIiLl5izdSZatiEZRwdw/oIXZcURchsqMiIgb+N+eo7y9tnwJl8eva6e7l0R+Q2VGRMTFFRSX8eAH5ZPjjezeiB5NokxOJOJaVGZERFzc3C93cjDvJA3qBvHQoJZmxxFxOSozIiIubP3+YxVrL80d1o4Qq1vchCpSq1RmRERcVHGZg8kflk+Od0PnhvyhWbTJiURck8qMiIiLemnlPnbnnCAqJIApV2rtJZGzUZkREXFBe4+cYN43ewB4ZEhr6gYHmJxIxHWpzIiIuBin02Dyh6mUOJz0bh7D0PbxZkcScWkqMyIiLua99RmsTTtGkL8vj12TgsViMTuSiEtTmRERcSE5+UXMXroDgIn9m5MQGWxyIhHXpzIjIuJCZn66HXtRGSkNwhjdM8nsOCJuQWVGRMRFfLPzMJ9tycLXx8Lj17XDz1e/okXOh35SRERcQEFxGQ8v2QrAbX9IJqVBuMmJRNyHyoyIiAt4etkuMm1FNIwIYvwVzcyOI+JWVGZEREy2LdPGwlVpADx2TQrBAVqyQORCqMyIiJjI6TR4+KOtOA0Y3LY+fVrUMzuSiNtRmRERMdF76zPYmH6ckABf/n5Va7PjiLgllRkREZMcKyjh8S93AnBfv+bEhQeanEjEPanMiIiYZO4XOzleWErLuFDNKSNyEVRmRERMsH7/Md5dnwGUD/rVnDIiVaefHhGRWlbmcPLwR+VzytzYOYHOSZEmJxJxbyozIiK1bOGq/ezMzqdusD8PDmppdhwRt6cyIyJSi7JtRTy7fBcADw1sSWRIgMmJRNyfyoyISC169LPtFJQ46JhYlxs6J5gdR8QjqMyIiNSSlbuO8HlqFj4WeOyatvj4WMyOJOIRVGZERGpBUamDaR+XD/od3TOZ1vFhJicS8RwqMyIiteCllfvYn1tIvVAr9/XTQpIi1UllRkSkhu0/WsAL3+4B4O9XtSY00N/kRCKeRWVGRKQGGYbBI59so6TMyR+aRnNVu/pmRxLxOCozIiI16Mut2Xy36wgBvj7MvLoNFosG/YpUN5UZEZEaUlBcxszPtgNwR+/GNI6pY3IiEc+kMiMiUkP+8fVusmxFJEQGcWffpmbHEfFYKjMiIjVg1+F8XvshDYAZQ9sQ6O9rciIRz6UyIyJSzQzD4OGPtlLmNOjXOpbLWsaaHUnEo6nMiIhUs482HWJt2jEC/X2YNqS12XFEPJ7KjIhINbKdLGXW5zsBuPuyZjSMCDY5kYjnU5kREalGzyz7maMnimkcE8LYXo3NjiPiFVRmRESqydZDNl5fcwCAR69OIcBPv2JFaoN+0kREqoHTWT7o12nAVe3qc2nTaLMjiXgNlRkRkWrw3voMNmUcJyTAl4cHa9CvSG1SmRERuUh5BSXM/bJ80O99/ZoTFx5ociIR76IyIyJykZ74aid5haW0jAtlVM8ks+OIeB2VGRGRi/BTeh7vrMsA4NFrUvD31a9VkdqmnzoRkSpyOA3+/tFWDAOGdWxIl6RIsyOJeCWVGRGRKnpjzQG2ZdoJC/Rj8pUtzY4j4rVUZkREquBIfjFPLfsZgPsHtCC6jtXkRCLeS2VGRKQKZi/dQX5RGW0bhDOiWyOz44h4NZUZEZEL9P3uIyzZeAiLBR67JgVfH4vZkUS8msqMiMgFKCp18PBHWwEY1SOJ9gl1zQ0kIuaWmaSkJCwWS6XtoYceqrRPeno6Q4YMISQkhOjoaO655x5KSkpMSiwi3m7eN3s4kFtIXFggE/s3NzuOiAB+ZgeYOXMmY8eOrfi4Tp06FX92OBwMHjyYmJgYfvjhB3Jzcxk1ahSGYfD888+bEVdEvNiuw/nMX7kXgOlD2xAa6G9yIhEBFygzoaGhxMXFnfG5ZcuWsX37djIyMoiPjwfg6aefZvTo0cyaNYuwsLDajCoiXszpNJjyYSplToMrWsUyoE2s2ZFE5Bemj5mZO3cuUVFRdOjQgVmzZlV6C2n16tWkpKRUFBmAAQMGUFxczIYNG876NYuLi7Hb7ZU2EZGL8e76DNYfyCM4wJeZV7fBYtGgXxFXYeqVmXvvvZeOHTsSERHB2rVrmTx5MmlpabzyyisAZGdnExtb+V8/ERERBAQEkJ2dfdavO2fOHGbMmFGj2UXEe+TkFzFn6Q4AJvZvQXzdIJMTichvVfuVmenTp582qPfUbf369QDcd9999O7dm3bt2jFmzBjmz5/Pq6++Sm5ubsXXO9O/fgzDOOe/iiZPnozNZqvYMjIyqvswRcSLPPbZDuy/zCkzWgtJiricar8yM27cOIYPH37OfZKSks74ePfu3QHYs2cPUVFRxMXF8eOPP1baJy8vj9LS0tOu2PyW1WrFatVsnCJy8f67/TCfbM7ExwKzr22rOWVEXFC1l5no6Giio6Or9LkbN24EoH79+gD06NGDWbNmkZWVVfHYsmXLsFqtdOrUqXoCi4iche1kKVM/SgVgbK/GtG0YbnIiETkT08bMrF69mjVr1tC3b1/Cw8NZt24d9913H0OHDiUxMRGA/v3707p1a0aOHMmTTz7JsWPHmDRpEmPHjtWdTCJS4x77bDuH7cU0jg7hvn6aU0bEVZlWZqxWK++++y4zZsyguLiYRo0aMXbsWB544IGKfXx9ffn888+58847ufTSSwkKCmLEiBE89dRTZsUWES/x7c85vL/hIBYLPPGndgT6+5odSUTOwmIYhmF2iJpmt9sJDw/HZrPpio6I/K78olL6P/sdWbYi/nJpEtOGtDE7kohXOt/Xb9PnmRERcTVzvthJlq2IxMhg7h/Qwuw4IvI7VGZERH7jf3uO8taP6QDMHdaO4ADTJ0oXkd+hMiMi8gtbYSmT3t8MwM3dE+nRJMrkRCJyPlRmREQon4xz6kepZNmKSI4OYcqVrcyOJCLnSWVGRAT4eFMmn23JwtfHwrM3dtDbSyJuRGVGRLzewbxC/v7xVgDuuawZHRLqmhtIRC6IyoyIeDWH02Die5vJLyrjksS63NW3idmRROQCqcyIiFf759e7+THtGMEBvjx3Ywf8fPVrUcTd6KdWRLzW97uP8M9vdgMw69oUGkWFmJxIRKpCZUZEvNJhexHj39mEYcDwLglce0lDsyOJSBWpzIiI1ylzOLn7rY3kFpTQMi6U6UO1XIGIO1OZERGv8+Syn1m7/xh1rH68+OeOWkRSxM2pzIiIV/lo4yFeWrkPgMeHtaVxTB2TE4nIxVKZERGvsSnjOA98sAWAO3o34ap28SYnEpHqoDIjIl4h21bE7YvXU1Lm5PKW9bQatogHUZkREY93oriMsYvXk5NfTPPYOjw3vAO+PhazY4lINVGZERGPVlLm5G9vbCD1kI2IYH9euaULoYH+ZscSkWqkMiMiHsvpNJj0/ma+332UIH9fFvylK4lRwWbHEpFqpjIjIh7JMAymfbKNTzZn4udj4V83d9QCkiIeSmVGRDyOYRg88vE2Xl9zAIsFnry+HX1a1DM7lojUEJUZEfEopxaZucPaaakCEQ/nZ3YAEZHqUlLm5MEPtrBk46GKInND5wSzY4lIDVOZERGPkF9Uyt/e+Ikf9hzF18fCE8PaMayTrsiIeAOVGRFxewdyC/jr6xvYmZ1PcIAvL/65o8bIiHgRlRkRcWvLtmUz8f3N5BeVEV3HyoLRXWjbMNzsWCJSi1RmRMQtnSxx8NSyn3n1hzQAOjWK4IURHYkLDzQ5mYjUNpUZEXE7a9OO8cB/NrM/txCAv1yaxJQrW+Hvqxs0RbyRyoyIizIMA3tRGYftRb9sxdhOlnKiqIwTxaXkF5VRWOLAaRgYBjicBk7DwN/PhyB/3/ItwJfgAF8iQwKICrESGRJAdJ0AoutYqRvsj8XiXusTZdlO8tRXu/hw40EMA2LDrMy+ti2Xt4o1O5qImEhlRsRk+UWl7Dqcz94jBaQdLWDfkROkHS0g/VghRaXOGvu+IQG+NIwIpmFEEAmR5f9NigqhWWwdGkYEu9RCjNm2Il79YR+vrzlQ8XdyQ+eGTB3cmvAgrbMk4u1UZkRqUWFJGVsO2kg9aCP1kI2th2zsO1pwzs+pG+xPbGgg9cKsRAQHUCfQj9BAP0KtfgQF+OFrAR8fCxaLBQtQ6nBSVOrkZKmDolIH+UVl5BWUkFtQTG5BCccKSjheWEpBiYOfD+fz8+H8075ngJ8PjaNDaFqvTqUtKSqEQH/fGvrbqczhNFizL5f/bDjIZ1syKXUYAHRJimDKla24JDGiVnKIiOtTmRGpQfaiUjbsz+PHtGP8mJZL6kEbZU7jtP3iwgJpUi+ExtF1aBwTQnJ0CElRIcSFB9ZIeSgqdZB5/CQZeSc5mFfIwbyTpB8rZG/OCfYdLaCkzMnO7Hx2ZlcuOj4WSIgMpklMeblpEhNS8ee6wQEXnSu/qJTVe3P5Yc9R/rv9MJm2oornuiZH8rfeTejTIsbt3h4TkZplMQzj9N+sHsZutxMeHo7NZiMsLMzsOOLBnE6D7Vl2VuzMYcXPOWzKOM6p3aV+eCDtGobTtkE4Kb9s0XWs5gQ+A4fT4GBeIXtyTvz/dqT8v/lFZWf9vKiQABKjgokLCyQ2LJD64eVXk0IC/Aix+hEU4IuvxUKpw0lJmZMTxWUczi8mx17E3iMn2JGVz/7cAn77Gyks0I8h7eO5vnOCFokU8ULn+/qtKzMiF+lkiYNvf87h6505fPvzEY6eKK70fFJUMF2TI+mWHEXX5EgaRgS59JUFXx8LjaJCaBQVUmlgrWEYHDlRzN6cAvYcOcHenBPs/eW/mbYicgtKyC0ouejvnxwdwh+aRtOrWTR/bB5Ta29riYj7UpkRqYLCkjK+2ZnDF6nZfLMzh5OljornQgJ8ubRpNH1b1qN38xji6waZmLT6WCwW6oUGUi80kB5Noio9V1Bcxr4jBRw6Xki2rYgsexGHbUUcOVFMQbGDkyUOCkrKcDoNAvx8CPDzISjAj9hQK7FhgSREBtGqfhgt48KICXWdq1Qi4h5UZkTOU1Gpg2925vDp5kxW/JxT6U6jhhFBDGwTR9+W9eicFIHVz7uuJoRY/WjbMFwz74qIKVRmRM7BMAw2ZRzng58O8unmLGwnSyueS4wM5sq29bmybRxtG4S79FtHIiKeTGVG5AwO24v44KeDfLDhIHuP/P+t0/XDA7m6QwOualefNvFhKjAiIi5AZUbkF06nwaq9ubyx5gDLdxzG8cttSIH+PgxsE8efOiXQo0mUS00mJyIiKjMiHC8s4T8bDvLmj+mk/WYCu86NIri+c0OubFuf0EDNMisi4qpUZsRr7ciy89oPaXyyOZPisvLBvHWsflx7SQP+3D2RlnGak0hExB2ozIhXcToNVu4+wqvfp/HDnqMVj7eqH8bN3RO5pkMDQqz6sRARcSf6rS1eoajUwUcbD/HKD2nsyTkBlE/NP6htfW69NImOiREazCsi4qZUZsSj2QpLWbhqP4tX76+YnbaO1Y/hXRIY1TOJhMhgkxOKiMjFUpkRj3Qkv5hXf0jjjTUHOFFcvp5Qg7pB/OXSJG7skqABvSIiHkRlRjxK5vGTvPzdPt5em14xqLdlXCh39m3KlSlx+Pn6mJxQRESqm8qMeIT9Rwv417d7+XDjQUod5fPDdEioy7i+Tbm8VT2NhxER8WAqM+LWDuQW8I+vd/PRxkP8MscdPRpHMe6ypvRsEqUSIyLiBVRmxC0dOn6Sed/s5v31Byn7pcX0bRHDuMua0qlRpMnpRESkNqnMiFvJsRfxwoo9vL02gxJH+ZiY3s1jmNCvOe0T6pobTkRETKEyI24h90Qx81fuZfHqAxUDe3s0jmJi/+Z0TtKVGBERb1ajt3bMmjWLnj17EhwcTN26dc+4T3p6OkOGDCEkJITo6GjuueceSkpKKu2TmppK7969CQoKokGDBsycORPDMGoyuriIE8VlPLPsZ3o9sYJ/f59GcZmTTo0ieGtMN96+vbuKjIiI1OyVmZKSEq6//np69OjBq6++etrzDoeDwYMHExMTww8//EBubi6jRo3CMAyef/55AOx2O/369aNv376sW7eOXbt2MXr0aEJCQpg4cWJNxhcTlZQ5eXttOv/8enfFZHdtG4QzsX9zejeP0cBeERGpUKNlZsaMGQAsXLjwjM8vW7aM7du3k5GRQXx8PABPP/00o0ePZtasWYSFhfHmm29SVFTEwoULsVqtpKSksGvXLp555hkmTJigFzUPYxgGS1OzefKrnezPLQSgcXQIDwxswYA2cTrfIiJyGlNnEFu9ejUpKSkVRQZgwIABFBcXs2HDhop9evfujdVqrbRPZmYm+/fvP+PXLS4uxm63V9rE9a3Zl8s1L67irrd+Yn9uIdF1rDx2TQpf3fdHBqbUV5EREZEzMnUAcHZ2NrGxsZUei4iIICAggOzs7Ip9kpKSKu3z6+dkZ2eTnJx82tedM2dOxVUhcX27Ducz94udfL0zB4DgAF9u/2NjxvZqrBWsRUTkd13wlZnp06djsVjOua1fv/68v96Z/rVtGEalx0/d59fBv2f7l/rkyZOx2WwVW0ZGxnnnkdpzJL+YyR9uYeBz3/H1zhx8fSzc3D2Rb+/vw/grmqvIiIjIebngV4tx48YxfPjwc+5z6pWUs4mLi+PHH3+s9FheXh6lpaUVV1/i4uIqrtL8Kien/F/wp17V+ZXVaq30tpS4luIyBwv+t5953+ypWARyYJs47h/YgiYxdUxOJyIi7uaCy0x0dDTR0dHV8s179OjBrFmzyMrKon79+kD5oGCr1UqnTp0q9pkyZQolJSUEBARU7BMfH3/epUlcg2EYfLXtMLOX7iD9WPng3rYNwnlkSGu66BZrERGpohodAJyens6mTZtIT0/H4XCwadMmNm3axIkTJwDo378/rVu3ZuTIkWzcuJGvv/6aSZMmMXbsWMLCwgAYMWIEVquV0aNHs3XrVpYsWcLs2bN1J5Ob2Z5pZ8S/f+SONzaQfqyQeqFWnrq+PR/fdamKjIiIXBSLUYOzz40ePZpFixad9viKFSvo06cPUF547rzzTr755huCgoIYMWIETz31VKW3iVJTU7nrrrtYu3YtERER3HHHHTzyyCPnXWbsdjvh4eHYbLaKkiS14+iJYp5etot316XjNCDAz4fbezXmb32aaEyMiIic0/m+ftdomXEVKjO1r7jMwaJV+3n+6z3k/zIuZnC7+jw0sCUJkcEmpxMREXdwvq/f+qexVLuVu44w/ZNtpB0tACClQRiPXNWGrsl6O0lERKqfyoxUm4N5hTz62Xa+2nYYgOg6Vh4Y2II/dWyIj4/GN4mISM1QmZGLVlTq4N/f7eOFb/dQVOrE18fCqB5JjO/XjLBAf7PjiYiIh1OZkYuyYmcOMz7dVrGOUtfkSB69OoUWcaEmJxMREW+hMiNVknGskBmfbue/O8rfUqoXamXq4FYMbR+vW+ZFRKRWqczIBSkqdTB/5V7+9e1eisuc+PlYuPUPydxzeTPq6FZrERExgV595Lyt+DmHaR9vq5i9t2eTKGYMbUOzWL2lJCIi5lGZkd912F7EjE+3sTS1fI2suLBAHr6qFYPb1tdbSiIiYjqVGTkrh9Pg9dX7eWrZLk4Ul+HrY+G2PyRz7+XNNHuviIi4DL0iyRltPWRjypJUthy0AdAhoS6zr21L63jNoCwiIq5FZUYqyS8q5ellu1i8ej9OA0ID/XhwYEtGdE3UxHciIuKSVGYEAMMw+HJrNtM/3cZhezEAQ9vH8/BVragXGmhyOhERkbNTmREyjhUy7ZNtfLMzB4BGUcE8enUKf2weY3IyERGR36cy48VKHU5e+T6Nf3y9i6JSJ/6+Fv7Wuwl39m1KoL+v2fFERETOi8qMl9qccZwHP9jCzux8ALolRzLr2rY0rVfH5GQiIiIXRmXGyxSWlPHMsl289r80nAZEBPszdXBrhnVsoDljRETELanMeJHvdh1hypJUDuadBOCaDvH8/arWRNWxmpxMRESk6lRmvEBeQQmPfr6dD386BECDukE8dm0KfVvUMzmZiIjIxVOZ8WCGYfDJ5kxmfrqd3IISLBYY1SOJ+we00Ay+IiLiMfSK5qEOHT/J3z/aWnG7dfPYOjw+rB0dEyNMTiYiIlK9VGY8jNNp8PqaAzzx5U4KShwE+Pow7rKm3NG7CQF+PmbHExERqXYqMx5k9+F8HvxgCz+lHwegU6MIHr+uLc1iQ80NJiIiUoNUZjxASZmTF7/dwwsr9lDqMAgJ8OWhQS35c7dGWk9JREQ8nsqMm9ty8Dj3v7+Fnw+XT353ect6PHpNCvF1g0xOJiIiUjtUZtxUUamD5/67m5e/24vTgKiQAKYPbcNV7epr8jsREfEqKjNu6Kf0PO5/fzN7jxQAMKR9PDOGtiEyJMDkZCIiIrVPZcaNFJU6eHrZz7z6Q/lSBNF1rMy6NoUBbeLMjiYiImIalRk3sW7/MR74zxbSjpZfjbnukgY8MqQ1dYN1NUZERLybyoyLKywp44kvf2bR6v0YBsSGWZl9bVsubxVrdjQRERGXoDLjwlbvzeXBD7aQfqwQgBs6N2Tq4NaEB/mbnExERMR1qMy4oBPFZTz+xQ7eWJMOQHx4IHOGtaN38xiTk4mIiLgelRkX8/3uIzz0QSqHjp8EYES3RCYPaklooK7GiIiInInKjIuwF5Uy+/MdvLMuA4CGEUHMHdaOS5tGm5xMRETEtanMuICVu47w0AdbyLIVAXBLj0Y8OLAlIVadHhERkd+jV0sTnSguY9bn23l7bfnVmEZRwcwd1o7ujaNMTiYiIuI+VGZMsmrvUR74zxYO5pWPjRndM4kHBrYgOECnRERE5ELolbOWnSxxMPfLnSxctR+ABnWDePL6dvRsorExIiIiVaEyU4s2HDjGxPc2sz+3fN6Ym7omMnVwK+pobIyIiEiV6VW0FhSVOnh2+S5e/n4fhgFxYYE8PqwtfVrUMzuaiIiI21OZqWFbDh5n4nub2Z1zAoDrOjZg2pA2msVXRESkmqjM1JCSMifPf7ObF7/di8NpEF3Hypzr2tKvtdZUEhERqU4qMzVgR5adCe9tZkeWHYCr2tVn5tUpRIZohWsREZHqpjJTjcocTuav3Ms/vt5NqcMgItifR69J4ap28WZHExER8VgqM9VkT04+E9/bzOaDNgD6tY5l9rVtiQm1mpxMRETEs6nMXCSH0+C1H9J4ctnPlJQ5CQ30Y8bQNlx7SQMsFovZ8URERDyeysxF2H+0gEnvb2b9gTwA/tg8hrnD2lI/PMjkZCIiIt5DZeYizFq6g/UH8ggJ8OXhq1ozvEuCrsaIiIjUMpWZizBjaBsAHrmqNQmRwSanERER8U4qMxchvm4Q/76ls9kxREREvJqP2QFERERELkaNlplZs2bRs2dPgoODqVu37hn3sVgsp23z58+vtE9qaiq9e/cmKCiIBg0aMHPmTAzDqMnoIiIi4iZq9G2mkpISrr/+enr06MGrr7561v0WLFjAwIEDKz4ODw+v+LPdbqdfv3707duXdevWsWvXLkaPHk1ISAgTJ06syfgiIiLiBmq0zMyYMQOAhQsXnnO/unXrEhcXd8bn3nzzTYqKili4cCFWq5WUlBR27drFM888w4QJE3T3kIiIiJdziTEz48aNIzo6mi5dujB//nycTmfFc6tXr6Z3795Yrf8/k+6AAQPIzMxk//79JqQVERERV2L63UyPPvool19+OUFBQXz99ddMnDiRo0eP8vDDDwOQnZ1NUlJSpc+JjY2teC45Ofm0r1lcXExxcXHFx3a7veYOQEREREx1wVdmpk+ffsZBu7/d1q9ff95f7+GHH6ZHjx506NCBiRMnMnPmTJ588slK+5z6VtKvg3/P9hbTnDlzCA8Pr9gSEhIu8ChFRETEXVzwlZlx48YxfPjwc+5z6pWUC9G9e3fsdjuHDx8mNjaWuLg4srOzK+2Tk5MD/P8VmlNNnjyZCRMmVHxst9tVaERERDzUBZeZ6OhooqOjayILABs3biQwMLDiVu4ePXowZcoUSkpKCAgIAGDZsmXEx8eftTRZrdZKY2xERETEc9XomJn09HSOHTtGeno6DoeDTZs2AdC0aVPq1KnDp59+SnZ2Nj169CAoKIgVK1YwdepUbr/99ooyMmLECGbMmMHo0aOZMmUKu3fvZvbs2TzyyCO6k0lERESwGDU4+9zo0aNZtGjRaY+vWLGCPn368OWXXzJ58mT27NmD0+mkcePGjBkzhrvuugs/v//vWampqdx1112sXbuWiIgI7rjjjgsqM3a7nfDwcGw2G2FhYdV2fCIiIlJzzvf1u0bLjKtQmREREXE/5/v67RLzzIiIiIhUlenzzNSGXy8+ab4ZERER9/Hr6/bvvYnkFWUmPz8fQLdni4iIuKH8/PxK6zaeyivGzDidTjIzMwkNDa32O6B+ncMmIyPDI8fj6Pjcn6cfo47P/Xn6Mer4qs4wDPLz84mPj8fH5+wjY7ziyoyPjw8NGzas0e8RFhbmkf+T/krH5/48/Rh1fO7P049Rx1c157oi8ysNABYRERG3pjIjIiIibk1l5iJZrVamTZvmscsn6Pjcn6cfo47P/Xn6Mer4ap5XDAAWERERz6UrMyIiIuLWVGZERETEranMiIiIiFtTmRERERG3pjJTBfv37+e2224jOTmZoKAgmjRpwrRp0ygpKam0X3p6OkOGDCEkJITo6Gjuueee0/ZxZbNmzaJnz54EBwdTt27dM+5jsVhO2+bPn1+7QavofI7P3c/hqZKSkk47Xw899JDZsarsxRdfJDk5mcDAQDp16sT3339vdqRqM3369NPOVVxcnNmxquy7775jyJAhxMfHY7FY+Oijjyo9bxgG06dPJz4+nqCgIPr06cO2bdvMCVtFv3eMo0ePPu2cdu/e3ZywVTBnzhy6dOlCaGgo9erV45prruHnn3+utI9Z51Flpgp27tyJ0+nkpZdeYtu2bTz77LPMnz+fKVOmVOzjcDgYPHgwBQUF/PDDD7zzzjt88MEHTJw40cTkF6akpITrr7+ev/3tb+fcb8GCBWRlZVVso0aNqqWEF+f3js8TzuGZzJw5s9L5evjhh82OVCXvvvsu48ePZ+rUqWzcuJFevXoxaNAg0tPTzY5Wbdq0aVPpXKWmppodqcoKCgpo37498+bNO+PzTzzxBM888wzz5s1j3bp1xMXF0a9fv4q19dzB7x0jwMCBAyud06VLl9ZiwouzcuVK7rrrLtasWcPy5cspKyujf//+FBQUVOxj2nk0pFo88cQTRnJycsXHS5cuNXx8fIxDhw5VPPb2228bVqvVsNlsZkSssgULFhjh4eFnfA4wlixZUqt5qtvZjs+TzuGvGjVqZDz77LNmx6gWXbt2Ne64445Kj7Vs2dJ46KGHTEpUvaZNm2a0b9/e7Bg14tTfG06n04iLizMef/zxiseKioqM8PBwY/78+SYkvHhn+t04atQo4+qrrzYlT03IyckxAGPlypWGYZh7HnVlpprYbDYiIyMrPl69ejUpKSnEx8dXPDZgwACKi4vZsGGDGRFrzLhx44iOjqZLly7Mnz8fp9NpdqRq4anncO7cuURFRdGhQwdmzZrllm+blZSUsGHDBvr371/p8f79+7Nq1SqTUlW/3bt3Ex8fT3JyMsOHD2ffvn1mR6oRaWlpZGdnVzqfVquV3r17e9T5BPj222+pV68ezZs3Z+zYseTk5JgdqcpsNhtAxWufmefRKxaarGl79+7l+eef5+mnn654LDs7m9jY2Er7RUREEBAQQHZ2dm1HrDGPPvool19+OUFBQXz99ddMnDiRo0ePuu1bF7/liefw3nvvpWPHjkRERLB27VomT55MWloar7zyitnRLsjRo0dxOBynnZ/Y2Fi3PTen6tatG4sXL6Z58+YcPnyYxx57jJ49e7Jt2zaioqLMjletfj1nZzqfBw4cMCNSjRg0aBDXX389jRo1Ii0tjb///e9cdtllbNiwwe1mBzYMgwkTJvCHP/yBlJQUwNzzqCszv3GmAXenbuvXr6/0OZmZmQwcOJDrr7+eMWPGVHrOYrGc9j0Mwzjj47WlKsd4Lg8//DA9evSgQ4cOTJw4kZkzZ/Lkk0/W4BGcW3Ufnyuew1NdyDHfd9999O7dm3bt2jFmzBjmz5/Pq6++Sm5urslHUTWnngdXOzcXY9CgQQwbNoy2bdtyxRVX8PnnnwOwaNEik5PVHE8+nwA33ngjgwcPJiUlhSFDhvDFF1+wa9euinPrTsaNG8eWLVt4++23T3vOjPOoKzO/MW7cOIYPH37OfZKSkir+nJmZSd++fenRowcvv/xypf3i4uL48ccfKz2Wl5dHaWnpaa21Nl3oMV6o7t27Y7fbOXz4sCnHWZ3H56rn8FQXc8y/3kmxZ88et/rXfnR0NL6+vqddhcnJyXGpc1OdQkJCaNu2Lbt37zY7SrX79S6t7Oxs6tevX/G4J59PgPr169OoUSO3O6d33303n3zyCd999x0NGzaseNzM86gy8xvR0dFER0ef176HDh2ib9++dOrUiQULFuDjU/kiV48ePZg1axZZWVkVJ3XZsmVYrVY6depU7dnP14UcY1Vs3LiRwMDAs97qXNOq8/hc9Rye6mKOeePGjQCVfvG4g4CAADp16sTy5cu59tprKx5fvnw5V199tYnJak5xcTE7duygV69eZkepdsnJycTFxbF8+XIuueQSoHxc1MqVK5k7d67J6WpObm4uGRkZbvPzZxgGd999N0uWLOHbb78lOTm50vNmnkeVmSrIzMykT58+JCYm8tRTT3HkyJGK535tpv3796d169aMHDmSJ598kmPHjjFp0iTGjh1LWFiYWdEvSHp6OseOHSM9PR2Hw8GmTZsAaNq0KXXq1OHTTz8lOzubHj16EBQUxIoVK5g6dSq33367W7z/+3vH5wnn8LdWr17NmjVr6Nu3L+Hh4axbt4777ruPoUOHkpiYaHa8CzZhwgRGjhxJ586dK66Opqenc8cdd5gdrVpMmjSJIUOGkJiYSE5ODo899hh2u91tpj441YkTJ9izZ0/Fx2lpaWzatInIyEgSExMZP348s2fPplmzZjRr1ozZs2cTHBzMiBEjTEx9Yc51jJGRkUyfPp1hw4ZRv3599u/fz5QpU4iOjq5UyF3ZXXfdxVtvvcXHH39MaGhoxZXR8PBwgoKCsFgs5p3HGr1XykMtWLDAAM64/daBAweMwYMHG0FBQUZkZKQxbtw4o6ioyKTUF27UqFFnPMYVK1YYhmEYX3zxhdGhQwejTp06RnBwsJGSkmI899xzRmlpqbnBz9PvHZ9huP85/K0NGzYY3bp1M8LDw43AwECjRYsWxrRp04yCggKzo1XZCy+8YDRq1MgICAgwOnbsWHGLqCe48cYbjfr16xv+/v5GfHy8cd111xnbtm0zO1aVrVix4ow/b6NGjTIMo/y23mnTphlxcXGG1Wo1/vjHPxqpqanmhr5A5zrGwsJCo3///kZMTIzh7+9vJCYmGqNGjTLS09PNjn3ezva6t2DBgop9zDqPll8CioiIiLgl3c0kIiIibk1lRkRERNyayoyIiIi4NZUZERERcWsqMyIiIuLWVGZERETEranMiIiIiFtTmRERERG3pjIjIiIibk1lRkRERNyayoyIiIi4NZUZERERcWv/B1ndenYLkF6RAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options = {\n",
    "    \"prop_dir\" : \"v\", #direction of beam propagation, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"wavelength\" : 532*u.nm,\n",
    "    \"alpha\" : 184.4, # Dy polarizability in terms of a_0\n",
    "    \"dy_mass\" : 164*u.u,\n",
    "    \"dy_mag_moment\" : 9.93 * ac.muB,\n",
    "    \"power\" : 2.9*u.mW,\n",
    "    \"w_0\" : 1*u.um, #beam waist in transverse-plane\n",
    "    \"gravity\" : True, #bool for gravity in z direction\n",
    "    \"mag_dir\" : \"v\", #direction of magnetic field and gradient, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"mag_grad\" : 100*u.G/u.cm, #magnetic gradient\n",
    "    \"mag_offset\" : 0*u.G, #magnetic offset\n",
    "    \"mJ\" : 0, #magnetic quantum number\n",
    "    \"ref_ind\" : 1  #refractive index\n",
    "}\n",
    "trap = ODP_1D(options)\n",
    "\n",
    "z = np.linspace(-20,20,1000)*u.um\n",
    "trap.get_axial_occ(z,fit_fac=2,p0=[2e3,-1.5e-27,-1e6],plot=True,plot_fac=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "435.5842083790574 Hz\n",
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\peter\\Uni-Bulk\\FerDy_Chomaz\\spilling_code\\ODT.py:97: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  popt, pcov = curve_fit(self.harm_pot, z_fit,pot_fit,p0=p0)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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    }
   ],
   "source": [
    "options = {\n",
    "    \"prop_dir\" : \"v\", #direction of beam propagation, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"wavelength\" : 532*u.nm,\n",
    "    \"alpha\" : 184.4, # Dy polarizability in terms of a_0\n",
    "    \"dy_mass\" : 164*u.u,\n",
    "    \"dy_mag_moment\" : 9.93 * ac.muB,\n",
    "    \"power\" : 3*u.mW,\n",
    "    \"w_0\" : 1*u.um, #beam waist in transverse-plane\n",
    "    \"gravity\" : True, #bool for gravity in z direction\n",
    "    \"mag_dir\" : \"v\", #direction of magnetic field and gradient, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"mag_grad\" : 120*u.G/u.cm, #magnetic gradient\n",
    "    \"mag_offset\" : 0*u.G, #magnetic offset\n",
    "    \"mJ\" : 0, #magnetic quantum number\n",
    "    \"ref_ind\" : 1  #refractive index\n",
    "}\n",
    "trap = ODP_1D(options)\n",
    "\n",
    "z = np.linspace(-30,30,1000)*u.um\n",
    "power = np.linspace(.1,2,50)*u.mW\n",
    "mag_grad = np.linspace(0.1,50,50)*u.G/u.cm\n",
    "power2D, mag_grad2D = np.meshgrid(power,mag_grad)\n",
    "\n",
    "occupation = np.zeros_like(power2D).value\n",
    "\n",
    "for i,p in enumerate(power):\n",
    "    for j,grad in enumerate(mag_grad):\n",
    "        trap.power = p\n",
    "        trap.mag_grad = grad\n",
    "        try:\n",
    "            n = trap.get_axial_occ(z,plot=False)\n",
    "        except:\n",
    "            n = np.nan\n",
    "        occupation[i,j] = n\n",
    "    \n",
    "plt.imshow(occupation,extent=[np.min(mag_grad).to(u.G/u.cm).value,np.max(mag_grad).to(u.G/u.cm).value,\n",
    "                                                        np.min(power).to(u.mW).value,np.max(power).to(u.mW).value]\n",
    "                                                        ,aspect=\"auto\",origin=\"lower\")\n",
    "plt.colorbar()\n",
    "plt.title(f\"w_0={trap.w_0}, alpha={184}a_0\")\n",
    "plt.ylabel(\"beam power [mW]\")\n",
    "plt.xlabel(\"magnetic gradient [G/cm]\")\n",
    "plt.show()\n",
    "#print(occupation)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\peter\\Uni-Bulk\\FerDy_Chomaz\\spilling_code\\ODT.py:97: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  popt, pcov = curve_fit(self.harm_pot, z_fit,pot_fit,p0=p0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options = {\n",
    "    \"prop_dir\" : \"v\", #direction of beam propagation, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"wavelength\" : 532*u.nm,\n",
    "    \"alpha\" : 184.4, # Dy polarizability in terms of a_0\n",
    "    \"dy_mass\" : 164*u.u,\n",
    "    \"dy_mag_moment\" : 9.93 * ac.muB,\n",
    "    \"power\" : 3*u.mW,\n",
    "    \"w_0\" : 2*u.um, #beam waist in transverse-plane\n",
    "    \"gravity\" : True, #bool for gravity in z direction\n",
    "    \"mag_dir\" : \"v\", #direction of magnetic field and gradient, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"mag_grad\" : 120*u.G/u.cm, #magnetic gradient\n",
    "    \"mag_offset\" : 0*u.G, #magnetic offset\n",
    "    \"mJ\" : 0, #magnetic quantum number\n",
    "    \"ref_ind\" : 1  #refractive index\n",
    "}\n",
    "trap = ODP_1D(options)\n",
    "\n",
    "z = np.linspace(-30,30,1000)*u.um\n",
    "power = np.linspace(.5,5,40)*u.mW\n",
    "mag_grad = np.linspace(0.1,12,40)*u.G/u.cm\n",
    "power2D, mag_grad2D = np.meshgrid(power,mag_grad)\n",
    "\n",
    "occupation = np.zeros_like(power2D).value\n",
    "\n",
    "for i,p in enumerate(power):\n",
    "    for j,grad in enumerate(mag_grad):\n",
    "        trap.power = p\n",
    "        trap.mag_grad = grad\n",
    "        try:\n",
    "            n = trap.get_axial_occ(z,plot=False)\n",
    "        except:\n",
    "            n = np.nan\n",
    "        occupation[i,j] = n\n",
    "    \n",
    "plt.imshow(occupation,extent=[np.min(mag_grad).to(u.G/u.cm).value,np.max(mag_grad).to(u.G/u.cm).value,\n",
    "                                                        np.min(power).to(u.mW).value,np.max(power).to(u.mW).value]\n",
    "                                                        ,aspect=\"auto\",origin=\"lower\",vmax=50)\n",
    "plt.colorbar()\n",
    "plt.title(f\"w_0={trap.w_0}, alpha={184}a_0\")\n",
    "plt.ylabel(\"beam power [mW]\")\n",
    "plt.xlabel(\"magnetic gradient [G/cm]\")\n",
    "plt.show()\n",
    "#print(occupation)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\peter\\Uni-Bulk\\FerDy_Chomaz\\spilling_code\\ODT.py:97: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  popt, pcov = curve_fit(self.harm_pot, z_fit,pot_fit,p0=p0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options = {\n",
    "    \"prop_dir\" : \"v\", #direction of beam propagation, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"wavelength\" : 532*u.nm,\n",
    "    \"alpha\" : 184.4, # Dy polarizability in terms of a_0\n",
    "    \"dy_mass\" : 164*u.u,\n",
    "    \"dy_mag_moment\" : 9.93 * ac.muB,\n",
    "    \"power\" : 3*u.mW,\n",
    "    \"w_0\" : 2*u.um, #beam waist in transverse-plane\n",
    "    \"gravity\" : True, #bool for gravity in z direction\n",
    "    \"mag_dir\" : \"v\", #direction of magnetic field and gradient, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"mag_grad\" : 120*u.G/u.cm, #magnetic gradient\n",
    "    \"mag_offset\" : 0*u.G, #magnetic offset\n",
    "    \"mJ\" : 0, #magnetic quantum number\n",
    "    \"ref_ind\" : 1  #refractive index\n",
    "}\n",
    "trap = ODP_1D(options)\n",
    "\n",
    "z = np.linspace(-30,30,1000)*u.um\n",
    "power = np.linspace(2.7,3.3,40)*u.mW\n",
    "mag_grad = np.linspace(4.5,5.5,40)*u.G/u.cm\n",
    "power2D, mag_grad2D = np.meshgrid(power,mag_grad)\n",
    "\n",
    "occupation = np.zeros_like(power2D).value\n",
    "\n",
    "for i,p in enumerate(power):\n",
    "    for j,grad in enumerate(mag_grad):\n",
    "        trap.power = p\n",
    "        trap.mag_grad = grad\n",
    "        try:\n",
    "            n = trap.get_axial_occ(z,plot=False)\n",
    "        except:\n",
    "            n = np.nan\n",
    "        occupation[i,j] = n\n",
    "    \n",
    "plt.imshow(occupation,extent=[np.min(mag_grad).to(u.G/u.cm).value,np.max(mag_grad).to(u.G/u.cm).value,\n",
    "                                                        np.min(power).to(u.mW).value,np.max(power).to(u.mW).value]\n",
    "                                                        ,aspect=\"auto\",origin=\"lower\",vmax=50)\n",
    "plt.colorbar()\n",
    "plt.title(f\"w_0={trap.w_0}, alpha={184}a_0\")\n",
    "plt.ylabel(\"beam power [mW]\")\n",
    "plt.xlabel(\"magnetic gradient [G/cm]\")\n",
    "plt.show()\n",
    "#print(occupation)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "options = {\n",
    "    \"prop_dir\" : \"v\", #direction of beam propagation, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"wavelength\" : 532*u.nm,\n",
    "    \"alpha\" : 184.4, # Dy polarizability in terms of a_0\n",
    "    \"dy_mass\" : 164*u.u,\n",
    "    \"dy_mag_moment\" : 9.93 * ac.muB,\n",
    "    \"power\" : 3*u.mW,\n",
    "    \"w_0\" : 2*u.um, #beam waist in transverse-plane\n",
    "    \"gravity\" : True, #bool for gravity in z direction\n",
    "    \"mag_dir\" : \"v\", #direction of magnetic field and gradient, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"mag_grad\" : 5*u.G/u.cm, #magnetic gradient\n",
    "    \"mag_offset\" : 0*u.G, #magnetic offset\n",
    "    \"mJ\" : 0, #magnetic quantum number\n",
    "    \"ref_ind\" : 1  #refractive index\n",
    "}\n",
    "trap = ODP_1D(options)\n",
    "\n",
    "z = np.linspace(-30,30,1000)*u.um\n",
    "trap.get_axial_occ(z,fit_fac=2,p0=[1e8,-1.5e-27,0],plot=True,plot_fac=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 9\n",
    "\n",
    "plt.plot(mag_grad,occupation[n,:],\".\")\n",
    "plt.title(f\"power={power[n]}\")\n",
    "plt.xlabel(\"magnetic gradient [G/cm]\")\n",
    "plt.ylabel(\"occupation number\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 25\n",
    "\n",
    "plt.plot(power,occupation[:,n],\".\")\n",
    "plt.title(f\"magnetic gradien ={mag_grad[n]}\")\n",
    "plt.xlabel(\"power [mW]\")\n",
    "plt.ylabel(\"occupation number\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options = {\n",
    "    \"prop_dir\" : \"v\", #direction of beam propagation, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"wavelength\" : 532*u.nm,\n",
    "    \"alpha\" : 400,#184.4, # Dy polarizability in terms of a_0\n",
    "    \"dy_mass\" : 164*u.u,\n",
    "    \"dy_mag_moment\" : 9.93 * ac.muB,\n",
    "    \"power\" : 3*u.mW,\n",
    "    \"w_0\" : 1*u.um, #beam waist in transverse-plane\n",
    "    \"gravity\" : True, #bool for gravity in z direction\n",
    "    \"mag_dir\" : \"v\", #direction of magnetic field and gradient, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"mag_grad\" : 120*u.G/u.cm, #magnetic gradient\n",
    "    \"mag_offset\" : 0*u.G, #magnetic offset\n",
    "    \"mJ\" : 0, #magnetic quantum number\n",
    "    \"ref_ind\" : 1  #refractive index\n",
    "}\n",
    "trap = ODP_1D(options)\n",
    "\n",
    "power = np.linspace(.1,6,50)*u.mW\n",
    "mag_grad = np.linspace(0.1,250,50)*u.G/u.cm\n",
    "power2D, mag_grad2D = np.meshgrid(power,mag_grad)\n",
    "\n",
    "occupation = np.zeros_like(power2D).value\n",
    "\n",
    "for i,p in enumerate(power):\n",
    "    for j,grad in enumerate(mag_grad):\n",
    "        trap.power = p\n",
    "        trap.mag_grad = grad\n",
    "        try:\n",
    "            n = trap.get_axial_occ(z,plot=False)\n",
    "        except:\n",
    "            n = np.nan\n",
    "        occupation[i,j] = n\n",
    "    \n",
    "plt.imshow(occupation,extent=[np.min(mag_grad).to(u.G/u.cm).value,np.max(mag_grad).to(u.G/u.cm).value,\n",
    "                                                        np.min(power).to(u.mW).value,np.max(power).to(u.mW).value]\n",
    "                                                        ,aspect=\"auto\",origin=\"lower\")\n",
    "plt.colorbar()\n",
    "plt.title(f\"w_0={trap.w_0}, alpha={400}a_0\")\n",
    "plt.ylabel(\"beam power [mW]\")\n",
    "plt.xlabel(\"magnetic gradient [G/cm]\")\n",
    "plt.show()\n",
    "#print(occupation)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options = {\n",
    "    \"prop_dir\" : \"v\", #direction of beam propagation, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"wavelength\" : 532*u.nm,\n",
    "    \"alpha\" : 184.4, # Dy polarizability in terms of a_0\n",
    "    \"dy_mass\" : 164*u.u,\n",
    "    \"dy_mag_moment\" : 9.93 * ac.muB,\n",
    "    \"power\" : 3*u.mW,\n",
    "    \"w_0\" : 2*u.um, #beam waist in transverse-plane\n",
    "    \"gravity\" : True, #bool for gravity in z direction\n",
    "    \"mag_dir\" : \"v\", #direction of magnetic field and gradient, \"v\" for vertical and \"h\" for horizontal\n",
    "    \"mag_grad\" : 120*u.G/u.cm, #magnetic gradient\n",
    "    \"mag_offset\" : 0*u.G, #magnetic offset\n",
    "    \"mJ\" : 0, #magnetic quantum number\n",
    "    \"ref_ind\" : 1  #refractive index\n",
    "}\n",
    "trap = ODP_1D(options)\n",
    "\n",
    "z = np.linspace(-40,40,1000)*u.um\n",
    "\n",
    "power = np.linspace(.1,25,50)*u.mW\n",
    "mag_grad = np.linspace(0.1,80,50)*u.G/u.cm\n",
    "power2D, mag_grad2D = np.meshgrid(power,mag_grad)\n",
    "\n",
    "occupation = np.zeros_like(power2D).value\n",
    "\n",
    "for i,p in enumerate(power):\n",
    "    for j,grad in enumerate(mag_grad):\n",
    "        trap.power = p\n",
    "        trap.mag_grad = grad\n",
    "        try:\n",
    "            n = trap.get_axial_occ(z,plot=False)\n",
    "        except:\n",
    "            n = np.nan\n",
    "        occupation[i,j] = n\n",
    "    \n",
    "plt.imshow(occupation,extent=[np.min(mag_grad).to(u.G/u.cm).value,np.max(mag_grad).to(u.G/u.cm).value,\n",
    "                                                        np.min(power).to(u.mW).value,np.max(power).to(u.mW).value]\n",
    "                                                        ,aspect=\"auto\",origin=\"lower\")\n",
    "plt.colorbar()\n",
    "plt.title(f\"w_0={trap.w_0}, alpha={184}a_0\")\n",
    "plt.ylabel(\"beam power [mW]\")\n",
    "plt.xlabel(\"magnetic gradient [G/cm]\")\n",
    "plt.show()\n",
    "#print(occupation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "only integers, slices (`:`), ellipsis (`...`), numpy.newaxis (`None`) and integer or boolean arrays are valid indices",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[5], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m pot  \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinspace(\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m2\u001b[39m)\n\u001b[1;32m----> 2\u001b[0m peaks \u001b[38;5;241m=\u001b[39m pot[find_peaks(np\u001b[38;5;241m.\u001b[39mlinspace(\u001b[38;5;241m0\u001b[39m,\u001b[38;5;241m1\u001b[39m))]\n\u001b[0;32m      3\u001b[0m peaks\n",
      "\u001b[1;31mIndexError\u001b[0m: only integers, slices (`:`), ellipsis (`...`), numpy.newaxis (`None`) and integer or boolean arrays are valid indices"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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