.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_tutorials/free_space/plot_10_radial_kerr.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_tutorials_free_space_plot_10_radial_kerr.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_tutorials_free_space_plot_10_radial_kerr.py:


A radially symmetric beam under the Kerr effect
===============================================

A collimated 800 nm, 30 fs beam of 1 mm waist and 0.2 mJ, in 1 bar of argon, on a
radial (Hankel) grid, below the critical power for self-focusing. Over 50 cm the Kerr
lens offsets about half of the beam's diffraction: its second-moment radius grows by
0.45 %, where diffraction alone (a Rayleigh length of 3.9 m) gives 0.81 %. The run is a
plain :func:`~solprop.driver.interface.prop_radial`, every argument an object a recipe
writes as a table, and it is the call the radial route's example recipe mirrors
(``Recipe.example("radial_kerr")``).

The chart is the fluence across the beam at the entrance and after 50 cm.

.. GENERATED FROM PYTHON SOURCE LINES 19-36

.. code-block:: Python


    from time import perf_counter

    import matplotlib.pyplot as plt
    import numpy as np

    from solprop.driver import SimulationSettings, prop_radial
    from solprop.grid import EnvelopeGrid, RadialGrid
    from solprop.nonlinear.responses import KerrResponse
    from solprop.physdata import gamma3
    from solprop.pulses import GaussianPulse, SpatialPulse
    from solprop.spatial import SpatialFlux, SpatialMedium, spatial_fluence
    from solprop.stats import StatsSpec
    from solprop.stepper import PIController

    started = perf_counter()








.. GENERATED FROM PYTHON SOURCE LINES 37-42

The run
-------
The aperture is four waists, 64 radial samples; the envelope grid leaves out the
third harmonic. Five planes are saved along the 50 cm, the energy and the beam
radius recorded at each.

.. GENERATED FROM PYTHON SOURCE LINES 42-64

.. code-block:: Python


    length = 0.5
    grid = EnvelopeGrid.from_limits(length, 800e-9, (600e-9, 1100e-9), 200e-15, thg=False)
    space = RadialGrid(4e-3, 64)
    argon = SpatialMedium("Ar", pressure=1.0)
    settings = SimulationSettings(
        controller=PIController(rtol=1e-5, atol=1e-12),
        save_planes=[0.1, 0.2, 0.3, 0.4, 0.5],
        dz_init=0.01,
        dz_max=0.05,
        stats=StatsSpec(names=("energy", "beam_radius")),
    )
    result = prop_radial(
        grid,
        space,
        argon,
        [KerrResponse(gamma3("Ar", wavelength=800e-9), thg=False)],
        SpatialPulse(GaussianPulse(wavelength=800e-9, fwhm=30e-15, energy=2e-4), 1e-3),
        settings=settings,
        noise=None,
    )








.. GENERATED FROM PYTHON SOURCE LINES 65-68

The fluence across the beam
---------------------------
The fluence through each plane in the argon, against the radius.

.. GENERATED FROM PYTHON SOURCE LINES 68-82

.. code-block:: Python


    figure, axis = plt.subplots(figsize=(6, 4))
    for index, z in ((0, 0.0), (-1, length)):
        plane = SpatialFlux.resolve(grid, space, argon, z=z)
        fluence = spatial_fluence(result.fields("fft")[index], plane)
        axis.plot(space.r * 1e3, fluence, label=f"z = {z * 100:.0f} cm")
    axis.set(xlabel="r (mm)", ylabel="Fluence (J/m²)", xlim=(0, 3))
    axis.legend()
    figure.tight_layout()
    # The second-moment radius (the statistic's first column, the 1/e^2 radius the second).
    radius = np.asarray(result["stats/beam_radius"])[:, 0] * 1e3
    print(f"Second-moment radius: {radius[0]:.4f} mm -> {radius[-1]:.4f} mm")
    print(f"Complete radial Kerr example: {perf_counter() - started:.3f} s")




.. image-sg:: /auto_tutorials/free_space/images/sphx_glr_plot_10_radial_kerr_001.png
   :alt: plot 10 radial kerr
   :srcset: /auto_tutorials/free_space/images/sphx_glr_plot_10_radial_kerr_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Second-moment radius: 1.0000 mm -> 1.0045 mm
    Complete radial Kerr example: 1.013 s




.. GENERATED FROM PYTHON SOURCE LINES 83-87

Related reading
---------------
:doc:`/guide/free-space/hankel` explains the radial grid, and
:doc:`/guide/setup/recipes` the recipe that builds this run.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.030 seconds)


.. _sphx_glr_download_auto_tutorials_free_space_plot_10_radial_kerr.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_10_radial_kerr.ipynb <plot_10_radial_kerr.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_10_radial_kerr.py <plot_10_radial_kerr.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_10_radial_kerr.zip <plot_10_radial_kerr.zip>`