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

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

.. _sphx_glr_auto_gallery_nonlinear_plot_nonlinear.py:


The second hyperpolarizability: every process on one curve
==========================================================

For each gas, gamma / gamma_0 of the fitted model (line, the Kerr process) against the
dispersion variable W2 = sum of the squared wavenumbers of the four frequencies. The
data of every process are shown against their own W2:

- the fitted ESHG (circles);
- the validators: measured n2 as the Kerr gamma (squares), third-harmonic generation
  (triangles), CARS (diamonds), dc Kerr (crosses).

Because gamma depends on the frequencies almost only through W2 (Bishop; Shelton), one
curve serves every process; the small B' term separates them at fourth order. The
measured n2 lie 1-15 % below the ESHG-based curve, and Lehmeier's THG up to 31 % below
(see the *Third-order nonlinearity* page).

.. GENERATED FROM PYTHON SOURCE LINES 24-81



.. image-sg:: /auto_gallery/nonlinear/images/sphx_glr_plot_nonlinear_001.svg
   :alt: Ar: gamma_0 = 1168 au, N2: gamma_0 = 920.3 au, H2: gamma_0 = 684.9 au, Xe: gamma_0 = 6836 au
   :srcset: /auto_gallery/nonlinear/images/sphx_glr_plot_nonlinear_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python

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

    from optmat.datasets import datasets
    from optmat.exceptions import DataError
    from optmat.gas.gases import Gas
    from optmat.gas.nonlinear import (
        gamma_observation,
        hyperpolarizability_models,
        load_nonlinear_config,
    )

    GASES = [Gas.Ar, Gas.N2, Gas.H2, Gas.Xe]
    MARKERS = {"eshg": "o", "pump_probe": "s", "kerr": "s", "thg": "^", "cars": "D"}
    models = hyperpolarizability_models()
    by_key = {d.key: d for d in datasets()}

    fig, axes = plt.subplots(2, 2, figsize=(11, 8), layout="constrained")
    for axis, gas in zip(axes.flat, GASES, strict=True):
        model = models[gas]
        gamma0 = model.parameters[0]
        w2 = np.linspace(0.0, 2.5e9, 200)
        wavelength = np.where(w2 > 0, 2.0 / np.sqrt(np.maximum(w2, 1e-30)) * 1e-2, np.inf)
        curve = model.gamma_au("kerr", wavelength) / gamma0
        axis.plot(w2, curve, color=LINE_COLOURS[0], linewidth=1.2, label="model (Kerr)")
        config = load_nonlinear_config(gas.value)
        config_keys = [(o, True) for o in config.fitted] + [
            (o, False) for o in config.validators
        ]
        for index, (options, fitted) in enumerate(config_keys):
            if options.scale_group or options.free_scale:
                continue  # theory with a free scale: shape only
            try:
                obs = gamma_observation(by_key[options.key], options)
            except DataError:
                continue
            keep = obs.w2 <= 2.5e9
            if not np.any(keep):
                continue
            marker = "x" if obs.process == "dc_kerr" else MARKERS.get(obs.process, "v")
            axis.errorbar(
                obs.w2[keep],
                obs.gamma[keep] / gamma0,
                yerr=obs.sigma[keep] / gamma0,
                fmt=marker,
                color=COLOURS[0] if fitted else COLOURS[1 + index % 7],
                markersize=4,
                linewidth=0.8,
                label=options.key if not fitted else options.key + " (fitted)",
            )
        axis.set_title(f"{gas.value}: gamma_0 = {gamma0:.4g} au")
        axis.set_xlabel("W2 (cm^-2)")
        axis.set_ylabel("gamma / gamma_0")
        axis.set_ylim(0.6, 1.6)
        axis.grid(alpha=0.25)
        axis.legend(fontsize=5.5, loc="upper left")


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

   **Total running time of the script:** (0 minutes 1.528 seconds)


.. _sphx_glr_download_auto_gallery_nonlinear_plot_nonlinear.py:

.. only:: html

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

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

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

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

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

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

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