{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "996ae31d-192b-4988-bd6b-649c833ae967",
   "metadata": {},
   "source": [
    "# Initializing a flying-focus laser from an axiparabola"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f25efcc9-1ed0-4f9a-8c62-da36f56ba02f",
   "metadata": {},
   "source": [
    "In this example, we generate a \"flying-focus\" laser from an axiparabola. This is done by sending a super-Gaussian laser (in the near-field) onto an axiparabola and propagating it to the far field."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f076564-8330-4af0-ad92-708e1825596f",
   "metadata": {},
   "source": [
    "## Generate a super-Gaussian laser"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb5e1364-1b92-42de-9518-dedf62be4544",
   "metadata": {},
   "source": [
    "Define the physical profile, as combination of a longitudinal and transverse profile."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ed0a409c-3c02-4fc4-b41b-ef41d0fb5a3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from lasy.laser import Laser\n",
    "from lasy.profiles.combined_profile import CombinedLongitudinalTransverseProfile\n",
    "from lasy.profiles.longitudinal import GaussianLongitudinalProfile\n",
    "from lasy.profiles.transverse import SuperGaussianTransverseProfile\n",
    "\n",
    "wavelength = 800e-9  # Laser wavelength in meters\n",
    "polarization = (1, 0)  # Linearly polarized in the x direction\n",
    "energy = 1.5  # Energy of the laser pulse in joules\n",
    "spot_size = 1e-3  # Spot size in the near-field: millimeter-scale\n",
    "pulse_duration = 30e-15  # Pulse duration of the laser in seconds\n",
    "t_peak = 0.0  # Location of the peak of the laser pulse in time\n",
    "\n",
    "laser_profile = CombinedLongitudinalTransverseProfile(\n",
    "    wavelength,\n",
    "    polarization,\n",
    "    GaussianLongitudinalProfile(wavelength, pulse_duration, t_peak),\n",
    "    SuperGaussianTransverseProfile(spot_size, n_order=16),\n",
    "    laser_energy=energy,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c303d3b6-2422-445b-a332-bc3f48388612",
   "metadata": {},
   "source": [
    "Define the grid on which this profile is evaluated. \n",
    "\n",
    "**The grid needs to be wide enough to contain the millimeter-scale spot size, but also fine enough to resolve the micron-scale laser wavelength.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "84cb6fd2-2f44-4cc9-a5c1-6dd1e0d72c67",
   "metadata": {},
   "outputs": [],
   "source": [
    "dimensions = \"rt\"  # Use cylindrical geometry\n",
    "lo = (0, -2.5 * pulse_duration)  # Lower bounds of the simulation box\n",
    "hi = (1.1 * spot_size, 2.5 * pulse_duration)  # Upper bounds of the simulation box\n",
    "num_points = (3000, 30)  # Number of points in each dimension\n",
    "\n",
    "laser = Laser(dimensions, lo, hi, num_points, laser_profile)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb8dc634-b3c4-4448-834b-fe9acb6c9645",
   "metadata": {},
   "outputs": [],
   "source": [
    "laser.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f588477-90c0-45c3-a47c-2b57733b462f",
   "metadata": {},
   "source": [
    "## Propagate the laser through the axiparabola, and to the far field.\n",
    "\n",
    "First, define the parameters of the axiparabola."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e3eae91f-edb7-44ac-9b92-5c1a1328a4b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from lasy.optical_elements import Axiparabola\n",
    "\n",
    "f0 = 3e-2  # Focal distance\n",
    "delta = 1.5e-2  # Focal range\n",
    "R = spot_size  # Radius\n",
    "axiparabola = Axiparabola(f0, delta, R)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "292c6e63-0480-4fb9-b1ad-6b679a3472d0",
   "metadata": {},
   "source": [
    "Apply the effect of the axiparabola, and then propagate the laser for a distance `z=f0` (beginning of the focal range)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3158e51d-e331-438d-90c1-5f8c63bf9841",
   "metadata": {},
   "outputs": [],
   "source": [
    "laser.apply_optics(axiparabola)\n",
    "laser.propagate(f0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa581cef-fc3d-414b-9f19-df8545d3b62f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "laser.show()\n",
    "plt.ylim(-0.25e-3, 0.25e-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5582bfe-ce2d-4aec-a757-03a48d4f16f2",
   "metadata": {},
   "source": [
    "At this point, the laser can be saved to file, and used e.g. as input to a PIC simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b8c068a-715b-400f-b6ed-7711a60c0f1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "laser.write_to_file(\"flying_focus\", \"h5\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "192cabcd-b96b-4bff-80b0-2c59d5a780cb",
   "metadata": {},
   "source": [
    "## Check that the electric field on axis remains high over many Rayleigh ranges\n",
    "\n",
    "An axiparabola can maintain a high laser field over a long distance (larger than the Rayleigh length).\n",
    "Here, we can check that the laser field remains high over several Rayleigh length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ef0d6f2e-3aac-47a0-baef-39b42d4c5749",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "\n",
    "ZR = math.pi * wavelength * f0**2 / spot_size**2\n",
    "print(\"Rayleigh length: %.f mm\" % (1.0e3 * ZR))\n",
    "print(\"Focal range: %.f mm\" % (1.0e3 * delta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e2113f14-3ec7-4392-8d91-96f6e28dcc71",
   "metadata": {},
   "outputs": [],
   "source": [
    "laser.propagate(2 * ZR)\n",
    "laser.show()\n",
    "plt.ylim(-0.25e-3, 0.25e-3)\n",
    "plt.title(\"Laser field after 2 Rayleigh range\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3cb4bd3b-ad8d-471f-a2c0-1257c1b3bd39",
   "metadata": {},
   "outputs": [],
   "source": [
    "laser.propagate(2 * ZR)\n",
    "laser.show()\n",
    "plt.ylim(-0.25e-3, 0.25e-3)\n",
    "plt.title(\"Laser field after 4 Rayleigh range\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}