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

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

.. _sphx_glr_auto_gallery_accuracy_plot_gvd_comparison.py:


Group-velocity dispersion: the fits against the formulas in use
===============================================================

The group-velocity dispersion :math:`\beta_2 = (\lambda^3/2\pi
c^2)\,\mathrm{d}^2n/\mathrm{d}\lambda^2` of each noble gas at 1 bar and 20 °C, from
the fitted model, and the ratio to it of every published, legacy and comparison formula
over its stated range. The dispersion of a gas-filled hollow fibre is the gas's
:math:`\beta_2` against the waveguide's anomalous term, so these ratios move
zero-dispersion wavelengths and phase-matching points directly.

For helium the fit reproduces the ab initio dispersion (Puchalski et al.; Stone &
Stejskal's formula agrees to 1e-5). The recorded Ermolov formula gives about 12 %
less dispersion in the visible and near infrared; Börzsönyi's differs by +2 %
at 400 nm and -6 % at 800 nm. Each curve is labelled by its model identifier.

.. GENERATED FROM PYTHON SOURCE LINES 23-88



.. image-sg:: /auto_gallery/accuracy/images/sphx_glr_plot_gvd_comparison_001.svg
   :alt: Group-velocity dispersion at 1 bar, 20 °C
   :srcset: /auto_gallery/accuracy/images/sphx_glr_plot_gvd_comparison_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python

    import warnings

    import matplotlib.pyplot as plt
    import numpy as np

    from optmat.conditions import State
    from optmat.constants import C
    from optmat.exceptions import ModelRangeWarning
    from optmat.gas.comparison import database_models
    from optmat.gas.models.fitted import fitted_models
    from optmat.gas.models.formulas import published_models

    STATE = State(1e5, 293.15)
    LINES = ["#0b0b0b", "#52514e", "#2a78d6", "#eb6834", "#1baf7a", "#e87ba4", "#4a3aa7"]


    def gvd(model, wavelength):
        """Return beta_2 in fs^2/m by a central second difference in wavelength."""
        step = wavelength * 1e-3
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", ModelRangeWarning)
            n = [model.refractivity(wavelength + k * step, STATE) for k in (-1, 0, 1)]
        second = (n[0] - 2 * n[1] + n[2]) / step**2
        return wavelength**3 / (2 * np.pi * C**2) * second * 1e30


    gases = ["He", "Ne", "Ar", "Kr", "Xe"]
    fig, axes = plt.subplots(len(gases), 2, figsize=(11, 15), layout="constrained")
    for row, gas in enumerate(gases):
        fit = fitted_models()[f"fit/{gas}"]
        grid = np.geomspace(max(fit.wavelength_range[0] * 1.3, 150e-9), 2.5e-6, 300)
        reference = gvd(fit, grid)
        axes[row, 0].plot(grid * 1e9, reference, color="#2a78d6", linewidth=2, label="fit")
        others = [m for m in published_models().values() if m.gas == gas]
        others += [m for m in database_models().values() if m.gas == gas]
        for number, model in enumerate(others):
            low, high = model.wavelength_range
            inside = (grid >= low) & (grid <= high)
            if np.count_nonzero(inside) < 3:
                continue
            ratio = gvd(model, grid[inside]) / reference[inside]
            style = {
                "color": LINES[number % len(LINES)],
                "linestyle": {"comparison": ":", "legacy": "--"}.get(model.kind, "-"),
                "linewidth": 1.1,
            }
            axes[row, 1].plot(
                grid[inside] * 1e9, (ratio - 1) * 100, label=model.name, **style
            )
        axes[row, 0].set_ylabel(f"{gas}: GVD (fs$^2$/m)")
        axes[row, 1].set_ylabel("formula / fit - 1 (%)")
        axes[row, 1].axhline(0, color="#2a78d6", linewidth=1)
        axes[row, 1].set_ylim(-20, 20)
        axes[row, 1].legend(fontsize=6, loc="upper left", bbox_to_anchor=(1.01, 1.0))
        for axis in axes[row]:
            axis.set_xscale("log")
            ticks = [200, 300, 500, 1000, 2000]
            axis.set_xticks(ticks, [str(t) for t in ticks])
            axis.xaxis.set_minor_formatter(plt.NullFormatter())
            axis.grid(which="both", alpha=0.25)
        axes[row, 0].set_yscale("log")
    axes[-1, 0].set_xlabel("vacuum wavelength (nm)")
    axes[-1, 1].set_xlabel("vacuum wavelength (nm)")
    fig.suptitle("Group-velocity dispersion at 1 bar, 20 °C")
    plt.show()


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

   **Total running time of the script:** (0 minutes 2.306 seconds)


.. _sphx_glr_download_auto_gallery_accuracy_plot_gvd_comparison.py:

.. only:: html

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

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

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

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

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

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

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