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

.. only:: html

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

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

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

.. _sphx_glr_auto_gallery_ionisation_plot_two_photon.py:


Two-photon ionisation of the noble gases
========================================

The two-photon ionisation cross sections of the models of
:func:`optmat.gas.two_photon.two_photon_ionisation_model` (OEP 6, Phase 1), each the
curated reference curve the author approved (TC-943):

- helium: Mihelič and Horvat;
- neon and argon: McKenna and van der Hart;
- xenon: Lagutin et al.

Krypton has none (OEP 6, Q2).

**Left:** :math:`\sigma^{(2)}` against the vacuum wavelength of one photon, from the
two-photon threshold :math:`2hc/I_p` to the first one-photon resonance. Solid lines are
supported values; dashed lines are unsupported detail, the resonance wing and, for an
LS-coupled reference, the band between the ion's two thresholds. Gaps are unavailable,
such as xenon between its two thresholds.

**Right:** the intensity of a flat-top plane wave after a path :math:`z` in the gas at
1 bar and 293.15 K, :math:`I(z) = I_0 / (1 + \beta I_0 z)` with :math:`\beta = 2 N
\sigma^{(2)} / \hbar\omega`, for :math:`I_0 = 10^{13}` W/cm² in argon at 155 nm and
helium at 97 nm. This is the two-photon loss of a prescribed field, not a prediction of
resonant-dispersive-wave generation: a propagation model decides how the field evolves.
The time dependence of the loss within a broadband pulse is a documented gap (TC-903).

.. GENERATED FROM PYTHON SOURCE LINES 34-89



.. image-sg:: /auto_gallery/ionisation/images/sphx_glr_plot_two_photon_001.svg
   :alt: the models: supported (solid), unsupported detail (dashed), two-photon loss at 1 bar, $I_0 = 10^{13}$ W/cm$^2$
   :srcset: /auto_gallery/ionisation/images/sphx_glr_plot_two_photon_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python

    import warnings

    import matplotlib.pyplot as plt
    import numpy as np
    from _helpers import COLOURS

    from optmat.constants import BAR, K_B, C
    from optmat.exceptions import ModelRangeWarning
    from optmat.gas.two_photon import two_photon_ionisation_model

    DENSITY = BAR / (K_B * 293.15)  # m^-3
    fig, (left, right) = plt.subplots(1, 2, figsize=(10, 4), constrained_layout=True)
    for colour, gas in zip(COLOURS, ("He", "Ne", "Ar", "Xe"), strict=False):
        model = two_photon_ionisation_model(gas)
        nm = np.linspace(2 * np.pi * C / model.thresholds[0].omega * 1e9 + 0.5, 50, 4000)
        omega = 2 * np.pi * C / (nm * 1e-9)
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", ModelRangeWarning)
            sigma = model.cross_section(omega) * 1e8  # cm^4 s
        labels = model.region(omega)
        for label, style in (("supported", "-"), ("unsupported_detail", "--")):
            shown = np.where(labels == label, sigma, np.nan)
            left.semilogy(
                nm,
                shown,
                style,
                color=colour,
                lw=1.3,
                label=f"{gas} ({model.reference.datasets[0].split('/')[0]})"
                if label == "supported"
                else None,
            )
    left.set_xlim(220, 55)
    left.set_xlabel("photon wavelength (nm)")
    left.set_ylabel(r"$\sigma^{(2)}$ (cm$^4$ s)")
    left.set_title("the models: supported (solid), unsupported detail (dashed)")
    left.legend(fontsize=8)

    z = np.linspace(0, 0.02, 200)  # m
    intensity = 1e17  # W/m^2, 1e13 W/cm^2
    for colour, gas, nm in ((COLOURS[2], "Ar", 155.0), (COLOURS[0], "He", 97.0)):
        model = two_photon_ionisation_model(gas)
        omega = 2 * np.pi * C / (nm * 1e-9)
        beta = float(model.loss_coefficient(omega, DENSITY))
        right.plot(
            z * 1e3,
            1 / (1 + beta * intensity * z),
            color=colour,
            label=f"{gas}, {nm:g} nm: beta = {beta:.2e} m/W",
        )
    right.set_xlabel("path length (mm)")
    right.set_ylabel(r"$I(z) / I_0$")
    right.set_title(r"two-photon loss at 1 bar, $I_0 = 10^{13}$ W/cm$^2$")
    right.legend(fontsize=8)
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.714 seconds)


.. _sphx_glr_download_auto_gallery_ionisation_plot_two_photon.py:

.. only:: html

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

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

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

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

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

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

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