.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/gallery_01/g_specialized_model_NLPM.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_gallery_01_g_specialized_model_NLPM.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_gallery_01_g_specialized_model_NLPM.py:


Two pulse interaction in a NLPM750 PCF
======================================

This examples demonstrates the interaction between a fundamental soliton and a
dispersive wave in a NL-PM-750 photonic crystal fiber. For the numerical
simualtion the forward model for the analytic signal including the Raman effect
is used [3].

In particular, this example reproduces the propagation scenario for
:math:`t_0=250\,\mathrm{fs}`, shown in Fig.~2(b) of Ref. [2].  Note that here
we use a polynomial expansion of the propagation constant, obtained for the
reference frequency :math:`\omega_{\rm{ref}}=1.85\,\mathrm{rad/fs}`.
For a more detailed discussion, see Ref. [2].

References:
    [1] A. Demircan, Sh. Amiranashvili, C. Bree, C. Mahnke, F. Mitschke, G.
    Steinmeyer, Rogue wave formation by accelerated solitons at an optical
    event horizon, Appl. Phys. B 115 (2014) 343,
    http://dx.doi.org/10.1007/s00340-013-5609-9

    [2] O. Melchert, C. Bree, A. Tajalli, A. Pape, R. Arkhipov, S. Willms, I.
    Babushkin, D. Skryabin, G. Steinmeyer, U. Morgner, A. Demircan, All-optical
    supercontinuum switching, Communications Physics 3 (2020) 146,
    https://doi.org/10.1038/s42005-020-00414-1.

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

.. GENERATED FROM PYTHON SOURCE LINES 29-96



.. image:: /auto_examples/gallery_01/images/sphx_glr_g_specialized_model_NLPM_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 FMAS_S_R
    from fmas.solver import IFM_RK4IP
    from fmas.analytic_signal import AS
    from fmas.propagation_constant import PropConst
    from fmas.tools import change_reference_frame, plot_evolution


    def define_beta_fun_poly_NLPM750():
        # -- EXPANSION COEFFIENTS
        coeffs =[-7.47658629e-08, 2.07925891e-06, -2.50978046e-05, 1.70783580e-04,
            -7.06498505e-04 ,  1.74251689e-03 , -2.05510570e-03, -1.02991785e-03,
            7.44467252e-03,  -1.15714412e-02,   1.06894885e-02, -1.03866947e-02,
            1.11828958e-02,   8.28155802e-04 , -1.51886109e-02 , 4.97000000e+00,
            8.90000000e+00]
        # -- FREQUENCY FOR WHICH EXPANSION COEFFICIENTS ARE VALID
        w_ref = 1.85      # (rad/fs)
        # -- PROPAGATION CONSTANT FOR DETUNING (1/micron)
        _beta = np.poly1d(coeffs);
        return lambda w: _beta(w-w_ref)


    def main():

        # -- DEFINE SIMULATION PARAMETERS
        # ... COMPUTATIONAL DOMAIN
        t_max = 2000.       # (fs)
        t_num = 2**13       # (-)
        z_max = 1.0e6       # (micron)
        z_num = 10000       # (-)
        z_skip = 10         # (-)
        n2 = 3.0e-8         # (micron^2/W)
        c0 = 0.29979        # (fs/micron)
        lam0 = 0.860        # (micron)
        w0_S = 2*np.pi*c0/lam0 # (rad/fs)
        t0_S = 20.0         # (fs)
        w0_DW = 2.95        # (rad/fs)
        t0_DW = 70.0        # (fs)
        t_off = -250.0      # (fs) 
        sFac = 0.75         # (-)

        beta_fun = define_beta_fun_poly_NLPM750()
        pc = PropConst(beta_fun)

        # -- INITIALIZATION STAGE
        grid = Grid( t_max = t_max, t_num = t_num, z_max = z_max, z_num = z_num)
        model = FMAS_S_R(w=grid.w, beta_w=pc.beta(grid.w), n2 = n2)
        solver = IFM_RK4IP( model.Lw, model.Nw, user_action = model.claw)

        # -- SET UP INITIAL CONDITION
        t = grid.t
        A0 = np.sqrt(abs(pc.beta2(w0_S))*c0/w0_S/n2)/t0_S
        A0_S = A0/np.cosh(t/t0_S)*np.exp(1j*w0_S*t)
        A0_DW = sFac*A0/np.cosh((t-t_off)/t0_DW)*np.exp(1j*w0_DW*t)
        Eps_0w = AS(np.real(A0_S + A0_DW)).w_rep
        solver.set_initial_condition( grid.w, Eps_0w)
        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(w0_S))
        plot_evolution( solver.z, grid.t, utz, t_lim=(-1200,1200), w_lim=(1.8,3.2))


    if __name__=='__main__':
        main()


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

   **Total running time of the script:** ( 0 minutes  44.519 seconds)


.. _sphx_glr_download_auto_examples_gallery_01_g_specialized_model_NLPM.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_specialized_model_NLPM.py <g_specialized_model_NLPM.py>`



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

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


.. only:: html

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

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