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

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

.. _sphx_glr_auto_gallery_dispersion_plot_euv_he.py:


Helium in the extreme ultraviolet
=================================

The complex refractive index of helium at 1 bar and 20 °C from 20 to 120 nm, from its
constrained oscillator-strength distribution (``euv/He``): Samson et al.'s measured
photoionisation cross section, Henke's scattering factors above 120 eV and the NIST
Rydberg lines. Above the ionisation threshold (50.4 nm) :math:`\mathrm{Re}\,n - 1` is
negative and the absorption index :math:`\mathrm{Im}\,n` appears; between the first
line (58.4 nm) and the threshold the Rydberg lines make the index singular. For
comparison: the index from Henke's :math:`f_1` and :math:`f_2` (dotted, unreliable below
about 30 eV by Henke et al.'s own account), Liu's ab initio absorption (squares) and the
ab initio fit ``fit/He`` below the first resonance (dashed).

.. GENERATED FROM PYTHON SOURCE LINES 21-105



.. image-sg:: /auto_gallery/dispersion/images/sphx_glr_plot_euv_he_001.svg
   :alt: Helium at 1 bar, 20 °C (shaded: the Rydberg lines)
   :srcset: /auto_gallery/dispersion/images/sphx_glr_plot_euv_he_001.svg
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /home/docs/checkouts/optmat/checkouts/7/src/optmat/gas/models/base.py:439: ModelRangeWarning: fit/He (He) evaluated outside 60-inf nm, the range its source supports
      alpha = self.polarizability(wavelength, warn=warn)






|

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from optmat.conditions import State
    from optmat.constants import AU_POLARIZABILITY, EPS0
    from optmat.datasets import DATA_DIRECTORY, datasets
    from optmat.gas.eos import number_density
    from optmat.gas.euv import EV_PER_HARTREE, euv_model
    from optmat.gas.models.fitted import fitted_models

    state = State(1e5, 293.15)
    model = euv_model("He")
    wavelength = np.concatenate(
        [np.linspace(20e-9, 50.3e-9, 400), np.linspace(58.6e-9, 120e-9, 300)]
    )
    n = model.refractive_index(wavelength, state)
    # Break the curves across the Rydberg lines rather than joining them.
    gap = np.searchsorted(wavelength, 55e-9)
    wavelength = np.insert(wavelength, gap, np.nan)
    n = np.insert(n, gap, np.nan)
    density = number_density("He", state)

    henke = np.loadtxt(DATA_DIRECTORY / "external" / "henke" / "he.nff", skiprows=1)
    keep = (henke[:, 0] > 10.4) & (henke[:, 1] > -9000)
    henke_wavelength = 1239.84198e-9 / henke[keep, 0]
    omega = henke[keep, 0] / EV_PER_HARTREE
    # Henke's n = 1 - delta - i beta; in the package's convention (Im n > 0 absorbs)
    # alpha = -(f1 - i f2) / omega^2.
    alpha = -(henke[keep, 1] - 1j * henke[keep, 2]) / omega**2 * AU_POLARIZABILITY
    henke_n = 1 + density * alpha / (2 * EPS0)
    inside = (henke_wavelength > 20e-9) & (henke_wavelength < 120e-9)

    (liu,) = [d for d in datasets("He") if d.key == "liu_1997/alpha_imaginary"]
    liu_omega = np.array([float(x) for x in liu.abscissae]) / EV_PER_HARTREE
    liu_wavelength = 45.56335e-9 / liu_omega
    liu_im_n = density * liu.scaled_values() * AU_POLARIZABILITY / (2 * EPS0)

    fit = fitted_models()["fit/He"]
    long = np.linspace(60e-9, 120e-9, 100)

    fig, (top, bottom) = plt.subplots(
        2, 1, sharex=True, figsize=(8, 7), layout="constrained"
    )
    top.plot(wavelength * 1e9, (n.real - 1) * 1e6, color="#2a78d6", label="euv/He")
    top.plot(
        henke_wavelength[inside] * 1e9,
        (henke_n.real[inside] - 1) * 1e6,
        ":",
        color="#52514e",
        label="Henke f1",
    )
    top.plot(
        long * 1e9,
        fit.refractivity(long, state) * 1e6,
        "--",
        color="#eb6834",
        label="fit/He (below the first line)",
    )
    top.axhline(0, color="#9a9994", linewidth=0.8)
    top.set_ylim(-40, 150)
    top.set_ylabel(r"Re $n - 1$ ($\times 10^{6}$)")
    top.legend()
    bottom.semilogy(
        wavelength * 1e9, np.maximum(n.imag, 1e-12), color="#2a78d6", label="euv/He"
    )
    bottom.semilogy(
        henke_wavelength[inside] * 1e9,
        henke_n.imag[inside],
        ":",
        color="#52514e",
        label="Henke f2",
    )
    bottom.semilogy(
        liu_wavelength * 1e9, liu_im_n, "s", color="#1baf7a", label="Liu (ab initio)"
    )
    bottom.set_ylim(1e-8, 1e-4)
    bottom.set_ylabel(r"Im $n$")
    bottom.set_xlabel("vacuum wavelength (nm)")
    bottom.legend()
    for axis in (top, bottom):
        axis.axvspan(50.43, 58.43, color="#f0efec", zorder=0)
        axis.grid(alpha=0.25)
    fig.suptitle("Helium at 1 bar, 20 °C (shaded: the Rydberg lines)")
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.543 seconds)


.. _sphx_glr_download_auto_gallery_dispersion_plot_euv_he.py:

.. only:: html

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

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

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

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

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

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

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