pump_evoln.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import imageio\n",
    "from scipy.linalg import expm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Here we consider the pump moving from lab to crystal back to lab, i.e. we take the velocity to be z-dependent. In momentum space the EoMs can be readily solved by matrix exponention\n",
    "#Maybe write up a quick note to show how you do it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "vp = 0.1  # pump velocity\n",
    "c = 1  #speed of light which I take to be one\n",
    "l = 1.0  # amplification region length\n",
    "sig = 10  # pump wave packet spread\n",
    "a = 1.61 / 1.13  # from symmetric grp vel matching\n",
    "\n",
    "nk=800\n",
    "k_ft = 200/l\n",
    "dk = k_ft/nk\n",
    "k = np.arange(-k_ft/2,k_ft/2,dk)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Matrix responsible for time evolution, tyring it differently so that 'k' multiplies the FT before..\n",
    "A = -1j*c*np.diag(k)-1j*(vp-c)*l*np.sinc(-(k-k[:,np.newaxis]*l/(2*np.pi)))*k/(2*np.pi)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#This is for considering GVD, just to see if Im plotting things correctly\n",
    "A2 = -1j*c*np.diag(k)-1j*0.005*np.diag(k**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining gaussian pump pulse at t0 when it is outside the crystal\n",
    "def pump(x, scale=1):\n",
    "    return np.exp(-((x) ** 2) / (2 * ((c/sig)*scale) ** 2)) / np.power(np.pi * ((c/sig)*scale), 1 / 4)\n",
    "\n",
    "Lambda =lambda x,t: pump(x+l-c*t,scale=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc076102070>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the pump pulse to make sure chosen values of z0 and tf are good (i.e. pulse is completely out of crystal before and after)\n",
    "dz=0.005\n",
    "zplot=np.arange(-2,2,dz)\n",
    "hat = (np.heaviside(zplot+0.5,0)-np.heaviside(zplot-0.5,0))\n",
    "plt.plot(Lambda(zplot,4))\n",
    "plt.plot(hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Finding fourier transform of pump pulse\n",
    "FT = np.sum(np.exp(-1j*np.tensordot(k,zplot,axes=0))/np.sqrt(2*np.pi)*dz*Lambda(zplot,0),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0c58d21430>,\n",
       " <matplotlib.lines.Line2D at 0x7f0c58d21460>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Finding fourier transform using fft command.\n",
    "ft = np.fft.fft(Lambda(zplot,0))\n",
    "freq = np.fft.fftfreq(zplot.shape[-1])\n",
    "plt.plot(freq, ft.real, freq, ft.imag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0c588fbc40>,\n",
       " <matplotlib.lines.Line2D at 0x7f0c58b01ac0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Finding fourier transform using fft command.\n",
    "ft2 = np.fft.ifft(np.fft.fft(Lambda(zplot,0)))\n",
    "freq = np.fft.fftfreq(zplot.shape[-1])\n",
    "plt.plot(zplot, ft2.real, zplot, ft2.imag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0c58dc8b80>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Evol = expm(A*0)@FT\n",
    "plt.plot(k/(2*np.pi),np.real(Evol))\n",
    "plt.plot(k/(2*np.pi),np.imag(Evol))\n",
    "plt.plot(k/(2*np.pi),np.abs(Evol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#This is if we keep the velocity constant\n",
    "IFT = lambda t: np.sum(np.exp(1j*np.tensordot(zplot,k,axes=0))/np.sqrt(2*np.pi)*dk*(np.exp(-1j*c*k*t)*FT),axis=1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "#This is if we keep the velocity constant and include small GVD\n",
    "IFTgvd = lambda t: np.sum(np.exp(1j*np.tensordot(zplot,k,axes=0))/np.sqrt(2*np.pi)*dk*(np.exp(-1j*c*k*t-1j*0.005*(k**2)*t)*FT),axis=1) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc075b9bca0>]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t=8\n",
    "plt.plot(zplot,np.real_if_close(IFT(t)))\n",
    "plt.plot(zplot,Lambda(zplot,t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe50f3315e0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Testing for weird periodicity\n",
    "IFTnt=np.sum((FT*np.exp(1j*np.tensordot(zplot,k,axes=0)))*dk/np.sqrt(2*np.pi),axis=1)\n",
    "plt.plot(zplot,np.real(IFTnt))\n",
    "plt.plot(zplot,Lambda(zplot,0))\n",
    "#plt.xlim(-2,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Here I play with the momentum vector to get better inverse fourier transforms while being careful not to introduce periodicity\n",
    "nk=2000*4\n",
    "k_ft = 800/l\n",
    "dk = k_ft/nk\n",
    "k = np.arange(-k_ft/2,k_ft/2,dk)\n",
    "A = -1j*c*np.diag(k)-1j*(vp-c)*l*np.sinc(-(k-k[:,np.newaxis]*l/(2*np.pi)))*k/(2*np.pi)\n",
    "FT = np.sum(np.exp(-1j*np.tensordot(k,zplot,axes=0))/np.sqrt(2*np.pi)*dz*Lambda(zplot,0),axis=1)\n",
    "IFT2 = lambda t: np.sum(np.exp(1j*np.tensordot(zplot,k,axes=0))/np.sqrt(2*np.pi)*dk*(expm(A*t)@(FT)),axis=1)\n",
    "IFT = lambda t: np.sum(np.exp(1j*np.tensordot(zplot,k,axes=0))/np.sqrt(2*np.pi)*dk*(np.exp(-1j*c*k*t)*FT),axis=1) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0c56b5fee0>]"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t=0\n",
    "plt.plot(zplot,Lambda(zplot,t))\n",
    "plt.plot(zplot,np.real(IFT(t)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0c646de6a0>]"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t=2\n",
    "plt.plot(zplot,np.abs(IFT2(t)))\n",
    "plt.plot(zplot,Lambda(zplot,t))\n",
    "#plt.plot(hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "t=2\n",
    "plt.plot(k,np.real(expm(A*t)@(FT)))\n",
    "plt.plot(k,np.imag(expm(A*t)@(FT)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Need to do time evolution properly. By multipying by small steps dt..and then take fourier back. Try this kind of evol to see how it looks like.\n",
    "t=np.arange(0,4,0.1)\n",
    "FTevol=FT\n",
    "for i in t:\n",
    "    FTevol = expm(A*t)@(FTevol)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "IFT2 = np.sum(np.exp(1j*np.tensordot(zplot,k,axes=0))/np.sqrt(2*np.pi)*dk*(FTevol),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Everything after this is for GIF purposes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_frame(t):\n",
    "    fig, ax1 = plt.subplots()\n",
    "    ax1.plot(zplot, np.abs(IFTgvd(t)), label='Pump') #Here we multiply by a phase factor such that the imaginary part is 0 at the origin.\n",
    "    ax1.plot(zplot, hat, label='Crystal')\n",
    "    ax1.set_ylim(-1.4, 1.4)\n",
    "    ax1.set_xlabel(r\"$z$\")\n",
    "    ax1.set_ylabel(r\"$Amplitude$\")\n",
    "    ax1.set_title(r\"$Blob animation$\")\n",
    "    ax1.legend()\n",
    "    plt.savefig(f'img_{t}.png', \n",
    "                transparent = False,  \n",
    "                facecolor = 'white'\n",
    "               )\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots()\n",
    "ax1.plot(zplot, np.abs(IFT(0)), label='Pump') #Here we multiply by a phase factor such that the imaginary part is 0 at the origin.\n",
    "ax1.plot(zplot, hat, label='Crystal')\n",
    "ax1.set_ylim(-1.4, 1.4)\n",
    "ax1.set_xlabel(r\"$z$\")\n",
    "ax1.set_ylabel(r\"$Amplitude$\")\n",
    "ax1.set_title(r\"$Blob animation$\")\n",
    "ax1.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "time = np.arange(0,10,0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "for t in time:\n",
    "    create_frame(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "frames = []\n",
    "for t in time:\n",
    "    image = imageio.v2.imread(f'img_{t}.png')\n",
    "    frames.append(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "imageio.mimsave('example.gif',frames, duration=100)         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "#For what follows I am assuming v has some tanh shape to approximate the Heaviside functions. Doing so allows us to get a general solution\n",
    "v1=1\n",
    "v2=0.3\n",
    "k3=100\n",
    "zplot=np.arange(-2,2,dz)\n",
    "Lambda2 = lambda x,t: pump((v1-v2)*np.log(v2*np.exp(2*k3*x)+v2)/(2*k3*v1*v2)+x/v1-t+1,scale=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(63.24555320336894, 63.24555320336894, 63.24555320336894)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vdot(Lambda2(zplot,0),Lambda2(zplot,0)),np.vdot(Lambda(zplot,0),Lambda(zplot,0)),np.vdot(Lambda(zplot,2),Lambda(zplot,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe50d8ce910>]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(zplot,Lambda(zplot,2))\n",
    "plt.plot(zplot,Lambda2(zplot,0))\n",
    "plt.plot(zplot,Lambda2(zplot,2))\n",
    "plt.plot(zplot,np.heaviside(zplot,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_frame(t):\n",
    "    fig, ax1 = plt.subplots()\n",
    "    ax1.plot(zplot, Lambda2(zplot,t), label='Pump') #Here we multiply by a phase factor such that the imaginary part is 0 at the origin.\n",
    "    ax1.plot(zplot, np.heaviside(zplot,0), label='Crystal')\n",
    "    ax1.set_ylim(-1.4, 1.4)\n",
    "    ax1.set_xlabel(r\"$z$\")\n",
    "    ax1.set_ylabel(r\"$Amplitude$\")\n",
    "    ax1.set_title(r\"$Blob animation$\")\n",
    "    ax1.legend()\n",
    "    plt.savefig(f'img_{t}.png', \n",
    "                transparent = False,  \n",
    "                facecolor = 'white'\n",
    "               )\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "time = np.arange(0,4.5,0.05)\n",
    "for t in time:\n",
    "    create_frame(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "frames = []\n",
    "for t in time:\n",
    "    image = imageio.v2.imread(f'img_{t}.png')\n",
    "    frames.append(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "imageio.mimsave('example.gif',frames, duration=100)   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.8.10"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}