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

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

.. _sphx_glr_auto_gallery_nonlinear_plot_raman_response_gases.py:


Raman: the response functions of the gases
==========================================

The gases' Raman responses (:func:`optmat.gas.raman_response.raman_response`), at
295 K.

**Left:** the rotational response of N2, O2 and dry air at 1 amagat: the alignment in
the first picoseconds and the revivals, every 8.4 ps for N2 and every 2.9 ps for O2,
whose levels are all odd. Each line keeps its own width, so the revivals of air are
the two gases' in proportion.

**Centre:** the envelope of N2's vibrational response at 0.5 and 2 amagat. Its Q(J)
lines are spread below the band origin by the difference of the two levels' rotational
constants, so the lines' sum first dephases on the branch's approximately 6 ps
envelope time (TC-491), and then persists at about a tenth,
beating, until the collisional widths of the lines (some 100 ps at 1 amagat) damp it.
Above 2 amagat the lines overlap and their mixing, not modelled, narrows the branch
(TC-527, TC-688).

**Right:** H2's gain, :math:`\mathrm{Im}\, H(\Omega)`, about the Q(1) line at 1, 10 and
30 amagat, against the shift from the zero-density line. The width is least near 2.4
amagat, where the Dicke narrowing and the collisional broadening balance, and 1.6 GHz
at 30 amagat; the centre moves by -96 MHz/amagat (Bischel & Dyer's Eq. (4), TC-688).

.. GENERATED FROM PYTHON SOURCE LINES 32-97



.. image-sg:: /auto_gallery/nonlinear/images/sphx_glr_plot_raman_response_gases_001.svg
   :alt: rotation, 1 amagat, N2, Q branch, H2, Q(1)
   :srcset: /auto_gallery/nonlinear/images/sphx_glr_plot_raman_response_gases_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python

    import math
    import warnings

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

    from optmat.exceptions import ModelRangeWarning
    from optmat.gas.linewidths import AMAGAT
    from optmat.gas.raman_response import raman_response

    warnings.simplefilter("ignore", ModelRangeWarning)
    fig, axes = plt.subplots(1, 3, figsize=(14, 4.6), layout="constrained")

    t = np.linspace(0.0, 25e-12, 25001)
    for colour, gas in zip(COLOURS, ("N2", "O2", "dry air"), strict=False):
        response = raman_response(gas, 295.0)
        h = response.response(t, AMAGAT, "anisotropic")
        axes[0].plot(t * 1e12, h, color=colour, lw=0.8, label=gas)
    axes[0].set_xlabel("delay (ps)")
    axes[0].set_ylabel("rotational response h (m$^5$ V$^{-2}$ s$^{-1}$)")
    axes[0].set_title("rotation, 1 amagat")
    axes[0].legend()

    nitrogen = raman_response("N2", 295.0)
    q = np.array(nitrogen.branch) == "Q"
    t = np.linspace(0.0, 60e-12, 3001)
    for colour, amagat in zip(COLOURS, (0.5, 2.0), strict=False):
        density = amagat * AMAGAT
        omega = nitrogen.frequencies(density)[q]
        rate = nitrogen.decay_rates(density)[q]
        amplitude = nitrogen.amplitude[q]
        # The envelope: the modulus of the lines' complex sum, about the band origin.
        centre = float(omega[np.argmax(amplitude)])
        envelope = np.abs(
            np.sum(
                amplitude * np.exp(1j * (omega - centre) * t[:, None] - rate * t[:, None]),
                axis=1,
            )
        )
        axes[1].plot(
            t * 1e12, envelope / envelope[0], color=colour, label=f"{amagat:g} amagat"
        )
    axes[1].plot(
        t * 1e12, np.exp(-t / 6e-12), color="#52514e", ls="--", label="one line, 6 ps"
    )
    axes[1].set_xlabel("delay (ps)")
    axes[1].set_ylabel("vibrational envelope (relative)")
    axes[1].set_title("N2, Q branch")
    axes[1].legend()

    hydrogen = raman_response("H2", 295.0)
    line = int(np.flatnonzero((np.array(hydrogen.branch) == "Q") & (hydrogen.j == 1))[0])
    centre = hydrogen.frequency[line]
    detuning = np.linspace(-6e9, 2e9, 4001)  # Hz
    for colour, amagat in zip(COLOURS, (1.0, 10.0, 30.0), strict=False):
        gain = np.imag(hydrogen.spectrum(centre + 2 * math.pi * detuning, amagat * AMAGAT))
        axes[2].plot(
            detuning / 1e9, gain / gain.max(), color=colour, label=f"{amagat:g} amagat"
        )
    axes[2].set_xlabel("shift from the zero-density Q(1) line (GHz)")
    axes[2].set_ylabel("Im H (relative)")
    axes[2].set_title("H2, Q(1)")
    axes[2].legend()
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.877 seconds)


.. _sphx_glr_download_auto_gallery_nonlinear_plot_raman_response_gases.py:

.. only:: html

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

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

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

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

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

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

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