.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_tutorials/free_space/plot_11_line_beam.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_11_line_beam.py>`
        to download the full example code.

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

.. _sphx_glr_auto_tutorials_free_space_plot_11_line_beam.py:


A line beam under the Kerr effect
=================================

A :class:`~solprop.grid.LineGrid` resolves one transverse direction: the beam is uniform
in y, so its energy is per metre of y. Here a 100 um waist line of 0.1 J/m, at 800 nm
and 30 fs, diffracts through 10 cm of argon at 1 bar. Without the Kerr response its
width follows the Gaussian diffraction law; with it, the Kerr lens narrows it slightly.

The first run is a plain :func:`~solprop.driver.interface.prop_free`, every argument an
object a recipe writes as a table: ``Recipe.example("line_beam")`` is that run.

The launch of the :doc:`line soliton tutorial </auto_tutorials/free_space/plot_03_line>`
is an array, which a recipe does not hold. This one is a
:class:`~solprop.pulses.SpatialPulse`.

.. GENERATED FROM PYTHON SOURCE LINES 21-44

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from solprop.driver import SimulationSettings, prop_free
    from solprop.grid import EnvelopeGrid, LineGrid
    from solprop.nonlinear.responses import KerrResponse
    from solprop.physdata import gamma3
    from solprop.processing import fluence_map
    from solprop.pulses import GaussianPulse, SpatialPulse
    from solprop.spatial import SpatialMedium
    from solprop.stats import StatsSpec
    from solprop.stepper import PIController

    WAVELENGTH = 800e-9
    """Carrier wavelength, m."""

    WAIST = 100e-6
    """Beam waist, m."""

    LENGTH = 0.1
    """Propagation length, m."""





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

 .. code-block:: none


    'Propagation length, m.'



.. GENERATED FROM PYTHON SOURCE LINES 45-47

The run, with the Kerr response and then without it. The half-width is sixteen waists,
so the diffracted beam stays far from the edge of the window.

.. GENERATED FROM PYTHON SOURCE LINES 47-74

.. code-block:: Python

    grid = EnvelopeGrid.from_limits(
        LENGTH, WAVELENGTH, (600e-9, 1100e-9), 200e-15, thg=False
    )
    space = LineGrid(1.6e-3, 256)
    argon = SpatialMedium("Ar", pressure=1.0)
    settings = SimulationSettings(
        controller=PIController(rtol=1e-5, atol=1e-12),
        save_planes=[0.05, 0.1],
        dz_init=1e-3,
        dz_max=5e-3,
        stats=StatsSpec(names=("energy", "beam_radius")),
    )
    beam = SpatialPulse(
        GaussianPulse(wavelength=WAVELENGTH, fwhm=30e-15, energy=0.1), WAIST
    )
    kerr = prop_free(
        grid,
        space,
        argon,
        [KerrResponse(gamma3("Ar", wavelength=WAVELENGTH), thg=False)],
        beam,
        settings=settings,
        noise=None,
    )
    linear = prop_free(grid, space, argon, [], beam, settings=settings, noise=None)









.. GENERATED FROM PYTHON SOURCE LINES 75-78

The width of the fluence, against the Gaussian law ``w(z) = w0 sqrt(1 + (z / z_R)^2)``
with ``z_R = pi w0^2 / lambda``. :func:`~solprop.processing.planes.fluence_map` reads
each plane on its transverse axis.

.. GENERATED FROM PYTHON SOURCE LINES 78-91

.. code-block:: Python

    def width(output, plane):
        """Return the second-moment width ``2 sqrt(<x^2>)`` of one plane's fluence, m."""
        profile = fluence_map(output, plane)
        x = profile.axes[0]
        return 2 * np.sqrt(np.sum(profile.fluence * x**2) / np.sum(profile.fluence))


    rayleigh = np.pi * WAIST**2 / WAVELENGTH
    expected = WAIST * np.sqrt(1 + (LENGTH / rayleigh) ** 2)
    print(f"Gaussian law  {expected * 1e6:.2f} um")
    print(f"without Kerr  {width(linear, -1) * 1e6:.2f} um")
    print(f"with Kerr     {width(kerr, -1) * 1e6:.2f} um")





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

 .. code-block:: none

    Gaussian law  273.58 um
    without Kerr  273.62 um
    with Kerr     267.81 um




.. GENERATED FROM PYTHON SOURCE LINES 92-93

The fluence across the line at the entrance and after 10 cm, in J/m^2.

.. GENERATED FROM PYTHON SOURCE LINES 93-104

.. code-block:: Python

    figure, axis = plt.subplots(figsize=(7, 3.5))
    entrance = fluence_map(kerr, 0)
    axis.plot(entrance.axes[0] * 1e6, entrance.fluence, label="Entrance")
    for output, label in ((linear, "After 10 cm, no Kerr"), (kerr, "After 10 cm, Kerr")):
        profile = fluence_map(output, -1)
        axis.plot(profile.axes[0] * 1e6, profile.fluence, label=label)
    axis.set(xlabel="x (um)", ylabel="Fluence (J/m$^2$)", xlim=(-600, 600))
    axis.legend()
    figure.tight_layout()

    plt.show()



.. image-sg:: /auto_tutorials/free_space/images/sphx_glr_plot_11_line_beam_001.png
   :alt: plot 11 line beam
   :srcset: /auto_tutorials/free_space/images/sphx_glr_plot_11_line_beam_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 3.240 seconds)


.. _sphx_glr_download_auto_tutorials_free_space_plot_11_line_beam.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_11_line_beam.ipynb <plot_11_line_beam.ipynb>`

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

      :download:`Download Python source code: plot_11_line_beam.py <plot_11_line_beam.py>`

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

      :download:`Download zipped: plot_11_line_beam.zip <plot_11_line_beam.zip>`