.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/gallery_01/g_four_pulse_interaction_ESM.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_four_pulse_interaction_ESM.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_gallery_01_g_four_pulse_interaction_ESM.py:


Four pulse interaction in a ESM PCF
===================================

This examples demonstrates the interaction between a fundamental soliton and a
three dispersive wave with pairwise distinct center frequencies in an
"endlessly single mode" (ESM) photonic crystal fiber. For the numerical
simualtion the simplified forward model for the analytic signal is used [3].

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

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

.. GENERATED FROM PYTHON SOURCE LINES 18-100



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


    def define_beta_fun_ESM():
        r"""Custom propagation constant for an ESM photonic crystal fiber.

        Implements rational Pade-approximant of order [8/8] for the refractive
        index of a endlessly single mode (ESM) nonlinear photonic crystal fiber
        (PCF), see Ref. [1].

        References:
            [1] Visibly 'white' light generation in uniform photonic crystal fiber
            using a microchip laser Stone, J.M. and Knight, J.C.  Optics Express 16
            (2007) 2670.

        Returns:
            :obj:`callable`: Propagation constant for ESM PCF.
        """
        p = np.poly1d(
            (16.89475, 0., -319.13216, 0., 34.82210, 0., -0.992495, 0., 0.0010671)[::-1])
        q = np.poly1d(
            ( 1.00000, 0., -702.70157, 0., 78.28249, 0., -2.337086, 0., 0.0062267)[::-1])
        n_idx = lambda w: 1+p(w)/q(w) # (-)
        c0 = 0.29979                    # (micron/fs)
        return lambda w: n_idx(w)*w/c0   # (1/micron)


    def main():

        # -- DEFINE SIMULATION PARAMETERS
        # ... COMPUTATIONAL DOMAIN
        t_max = 4000.       # (fs)
        t_num = 2**14       # (-)
        z_max = 4.0e6       # (micron)
        z_num = 50000       # (-)
        z_skip =100         # (-)
        n2 = 3.0e-8         # (micron^2/W)

        beta_fun = define_beta_fun_ESM()
        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(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
        # ... FUNDAMENTAL NSE SOLITON
        w0_S, t0_S = 1.5, 20.   # (rad/fs), (fs)
        A0 = np.sqrt(abs(pc.beta2(w0_S))*model.c0/w0_S/n2)/t0_S
        A0_S = A0/np.cosh(t/t0_S)*np.exp(1j*w0_S*t)
        # ... 1ST DISPERSIVE WAVE; UNITS (rad/fs), (fs), (fs), (-)
        w0_DW1, t0_DW1, t_off1, s1 = 2.06, 60., -600., 0.35
        A0_DW1 = s1*A0/np.cosh((t-t_off1)/t0_DW1)*np.exp(1j*w0_DW1*t)
        # ... 2ND DISPERSIVE WAVE; UNITS (rad/fs), (fs), (fs), (-)
        w0_DW2, t0_DW2, t_off2, s2 = 2.05, 60., -1200., 0.35
        A0_DW2 = s2*A0/np.cosh((t-t_off2)/t0_DW2)*np.exp(1j*w0_DW2*t)
        # ... 3RD DISPERSIVE WAVE; UNITS (rad/fs), (fs), (fs), (-)
        w0_DW3, t0_DW3, t_off3, s3 = 2.04, 60., -1800., 0.35
        A0_DW3 = s3*A0/np.cosh((t-t_off3)/t0_DW3)*np.exp(1j*w0_DW3*t)
        # ... ANALYTIC SIGNAL OF FULL ININITIAL CONDITION
        Eps_0w = AS(np.real(A0_S + A0_DW1 + A0_DW2 + A0_DW3)).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
        v0 = pc.vg(w0_S)
        utz = change_reference_frame(solver.w, solver.z, solver.uwz, v0)
        plot_evolution( solver.z, grid.t, utz, t_lim=(-4000,1000), w_lim=(1.1,2.4))


    if __name__=='__main__':
        main()


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

   **Total running time of the script:** ( 4 minutes  42.481 seconds)


.. _sphx_glr_download_auto_examples_gallery_01_g_four_pulse_interaction_ESM.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_four_pulse_interaction_ESM.py <g_four_pulse_interaction_ESM.py>`



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

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


.. only:: html

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

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