.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/gallery_03/g_BMCF.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_gallery_03_g_BMCF.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_gallery_03_g_BMCF.py:


BMCF -- Backscattered optical field components
==============================================

This examples demonstrates backscattered optical field components using the
bidirectional model for the complex field (BMCF), described in Ref. [1].

In particular, this example reproduces the propagation scenario  shown in Fig.
1(a) of Ref. [1]. The figure shows the evolution of a soliton of duration
:math:`t_{\rm{S}}=50\,\mathrm{fs}`, center frequency
:math:`\omega_{\rm{S}}=2.23548\,\mathrm{rad/fs}`, and soliton order
:math:`N_{\rm{S}}=3.54`. For a detailed discussion, see Ref. [1].

References:
    [1] Sh. Amiranashvili, A. Demircan, Hamiltonian structure of
    propagation equations for ultrashort optical pulses, Phys. Rev. E 10
    (2010) 013812, http://dx.doi.org/10.1103/PhysRevA.82.013812.

.. codeauthor:: Oliver Melchert <melchert@iqo.uni-hannover.de>

.. GENERATED FROM PYTHON SOURCE LINES 21-72



.. image:: /auto_examples/gallery_03/images/sphx_glr_g_BMCF_001.png
    :alt: $|u|^2/{\rm{max}}\left(|u|^2\right)$, $|u_\omega|^2/{\rm{max}}\left(|u_\omega|^2\right)$
    :class: sphx-glr-single-img





.. code-block:: default

    import fmas
    import numpy as np
    from fmas.grid import Grid
    from fmas.models import BMCF
    from fmas.solver import IFM_RK4IP
    from fmas.analytic_signal import AS
    from fmas.propagation_constant import PropConst, define_beta_fun_fluoride_glass_AD2010
    from fmas.tools import change_reference_frame, plot_evolution


    def main():

        # -- INITIALIZATION STAGE
        # ... DEFINE SIMULATION PARAMETERS
        t_max = 3500./2     # (fs)
        t_num = 2**14       # (-)
        z_max = 50.0e3      # (micron)
        z_num = 100000      # (-)
        z_skip = 100        # (-)
        c0 = 0.29979        # (micron/fs)
        n2 = 1.             # (micron^2/W) FICTITIOUS VALUE ONLY
        wS = 2.32548        # (rad/fs)
        tS = 50.0           # (fs)
        NS = 3.54           # (-)
        # ... PROPAGGATION CONSTANT
        beta_fun = define_beta_fun_fluoride_glass_AD2010()
        pc = PropConst(beta_fun)
        chi = (8./3)*pc.beta(wS)*c0/wS*n2

        # ... COMPUTATIONAL DOMAIN, MODEL, AND SOLVER 
        grid = Grid( t_max = t_max, t_num = t_num, z_max = z_max, z_num = z_num)
        model = BMCF(w=grid.w, beta_w=pc.beta(grid.w), chi =  chi)
        solver = IFM_RK4IP( model.Lw, model.Nw)

        # -- SET UP INITIAL CONDITION
        LD = tS*tS/np.abs( pc.beta2(wS) )
        A0 = NS*np.sqrt(8*c0/wS/n2/LD)
        Eps_0w = AS(np.real(A0/np.cosh(grid.t/tS)*np.exp(1j*wS*grid.t))).w_rep
        solver.set_initial_condition( grid.w, Eps_0w)

        # -- PERFORM Z-PROPAGATION
        solver.propagate( z_range = z_max, n_steps = z_num, n_skip = z_skip)

        # -- SHOW RESULTS
        utz = change_reference_frame(solver.w, solver.z, solver.uwz, pc.vg(wS))
        plot_evolution( solver.z, grid.t, utz,
            t_lim = (-500,500), w_lim = (-10.,10.), DO_T_LOG = True, ratio_Iw=1e-15)


    if __name__=='__main__':
        main()


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

   **Total running time of the script:** ( 10 minutes  9.831 seconds)


.. _sphx_glr_download_auto_examples_gallery_03_g_BMCF.py:


.. only :: html

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



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

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



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

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


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_