Add axiparabola

docs/source/api/index.rst

@@ -9,6 +9,7 @@ The sections below describe the main objects that are accessible in the ``lasy``
 
    laser
    profiles/index
+   optical_elements/index
    utils/index
 
 If you are looking for a specific class or function, see the :ref:`genindex` or use the search bar of this website.

docs/source/api/optical_elements/index.rst

@@ -0,0 +1,8 @@
+Optical elements
+================
+
+.. toctree::
+   :maxdepth: 1
+
+   parabolic_mirror
+   axiparabola

docs/source/api/optical_elements/parabolic_mirror.rst

@@ -0,0 +1,5 @@
+Parabolic mirror
+================
+
+.. autoclass:: lasy.optical_elements.ParabolicMirror
+    :members:

docs/source/tutorials/axiparabola.ipynb

@@ -0,0 +1,240 @@
+{
+ "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.gaussian_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, polarization, energy,\n",
+    "    GaussianLongitudinalProfile(wavelength, pulse_duration, t_peak),\n",
+    "    SuperGaussianTransverseProfile(spot_size, n_order=16)\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",
+    "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": [
+    "Propagate the laser through the axiparabola, and 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.propagate( f0, initial_optical_element=axiparabola )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fa581cef-fc3d-414b-9f19-df8545d3b62f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\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",
+    "ZR = math.pi*wavelength*f0**2/spot_size**2\n",
+    "print('Rayleigh length: ', ZR)\n",
+    "assert delta > 5*ZR"
+   ]
+  },
+  {
+   "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": "3.11.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

lasy/laser.py

@@ -160,6 +160,46 @@ def normalize(self, value, kind="energy"):
         else:
             raise ValueError(f'kind "{kind}" not recognized')
 
+    def apply_optics(self, optical_element):
+        """
+        Propagate the laser pulse through a thin optical element.
+
+        Parameter
+        ---------
+        optical_element: an :class:`.OpticalElement` object (optional)
+            Represents a thin optical element, through which the laser
+            propagates.
+        """
+        # Transform the field from temporal to frequency domain
+        time_axis_indx = -1
+        field_fft = np.fft.ifft(self.grid.field, axis=time_axis_indx, norm="backward")
+
+        # Create the frequency axis
+        dt = self.grid.dx[time_axis_indx]
+        omega0 = self.profile.omega0
+        Nt = self.grid.field.shape[time_axis_indx]
+        omega = 2 * np.pi * np.fft.fftfreq(Nt, dt) + omega0
+
+        # Apply optical element
+        if self.dim == "rt":
+            r, w = np.meshgrid(self.grid.axes[0], omega, indexing="ij")
+            # The line below assumes that amplitude_multiplier
+            # is cylindrically-symmetric, hence we pass
+            # `r` as `x` and 0 as `y`
+            multiplier = optical_element.amplitude_multiplier(r, 0, w)
+            for i_m in range(self.grid.azimuthal_modes.size):
+                field_fft[i_m, :, :] *= multiplier
+        else:
+            x, y, w = np.meshgrid(
+                self.grid.axes[0], self.grid.axes[1], omega, indexing="ij"
+            )
+            field_fft *= optical_element.amplitude_multiplier(x, y, w)
+
+        # Transform field from frequency to temporal domain
+        self.grid.field[:, :, :] = np.fft.fft(
+            field_fft, axis=time_axis_indx, norm="backward"
+        )
+
     def propagate(self, distance, nr_boundary=None, backend="NP", show_progress=True):
         """
         Propagate the laser pulse by the distance specified.
@@ -169,10 +209,16 @@ def propagate(self, distance, nr_boundary=None, backend="NP", show_progress=True
         distance : scalar
             Distance by which the laser pulse should be propagated
 
+        initial_optical_element: an :class:`.OpticalElement` object (optional)
+            Represents a thin optical element, through which the laser
+            propagates, before propagating for `distance` in free space.
+            If this is `None`, no optical element is used.
+
         nr_boundary : integer (optional)
             Number of cells at the end of radial axis, where the field
             will be attenuated (to assert proper Hankel transform).
             Only used for ``'rt'``.
+
         backend : string (optional)
             Backend used by axiprop (see axiprop documentation).
         show_progress : bool (optional)
@@ -212,6 +258,7 @@ def propagate(self, distance, nr_boundary=None, backend="NP", show_progress=True
         omega0 = self.profile.omega0
         Nt = self.grid.field.shape[time_axis_indx]
         omega = 2 * np.pi * np.fft.fftfreq(Nt, dt) + omega0
+
         # make 3D shape for the frequency axis
         omega_shape = (1, 1, self.grid.field.shape[time_axis_indx])
 

lasy/optical_elements/__init__.py

@@ -0,0 +1,4 @@
+from .parabolic_mirror import ParabolicMirror
+from .axiparabola import AxiParabola
+
+__all__ = ["ParabolicMirror", "AxiParabola"]