.. 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_PCF.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_PCF.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_gallery_01_g_specialized_model_PCF.py:


Supercontinuum generation in a PCF
==================================

This examples demonstrates the :math:`z`-propagation of a specialized
propagation model for a specific propagation constant, implemented  using
the simplified forward model for the analytis signal including the Raman
effect.

The propagation scenario schown below, is discussed on several occations in the
scientific literature [1-3]. For example, in Ref. [1], it is used to
demonstrate numerical simulations in terms of the gneralized nonlinear
Schrödinger equation (GNSE) on supercontinuum generation for an instance of a
highly nonlinear photonic crystal fiber (PCF) with an anomalous group-velocity
dispersion regime. In Ref. [2] it is used, again using the GNSE, to introduce a
particular :math:`z`-propagation algorithm referred to as the "Runge-Kutta in
the interacton picture" (RK4IP) method. This algorithm, a particular variant
of an integrating-factor method, is also implemented in `py-fmas`.  In Ref. [3]
it is used to demonstrate the feasibility of an adaptive step-size method for
the simulation of supercontinuum generation in optical fiber.

All the above simulation studies used the generalized nonlinear Schrödinger
equation wich relies on the slowly varying envelope approximation. In contrast
to this, the below example employs a non-envelope model, namely by the
simplified forward model for the analytic signal with added Raman effect
(FMAS-S-R) [4-6].  The :math:`z`-propagation algorithm used with the FMAS-S-R
in conjunction with the RK4IP method.

References:
    [1] J. M. Dudley, G. Genty, S. Coen,
    Supercontinuum generation in photonic crystal fiber,
    Rev. Mod. Phys. 78 (2006) 1135,
    http://dx.doi.org/10.1103/RevModPhys.78.1135

    [2] J. Hult, A Fourth-Order Runge–Kutta in the Inter- action Picture
    Method for Simulating Supercontin- uum Generation in Optical Fibers,
    IEEE J. Light- wave Tech. 25 (2007) 3770,
    https://doi.org/10.1109/JLT.2007.909373.

    [3] A. M. Heidt,
    Efficient Adaptive Step Size Method for the Simulation of
    Supercontinuum Generation in Optical Fibers,
    IEEE J. Lightwave Tech. 27 (2009) 3984,
    https://doi.org/10.1109/JLT.2009.2021538

    [4] 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.

    [5] Sh. Amiranashvili, A. Demircan, Ultrashort Optical Pulse Propagation in
    terms of Analytic Signal, Adv. Opt. Tech. 2011 (2011) 989515,
    http://dx.doi.org/10.1155/2011/989515.

    [6] 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 61-103



.. image:: /auto_examples/gallery_01/images/sphx_glr_g_specialized_model_PCF_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.models import CustomModelPCF
    from fmas.solver import IFM_RK4IP
    from fmas.analytic_signal import AS
    from fmas.grid import Grid
    from fmas.tools import plot_evolution


    def main():
        # -- DEFINE SIMULATION PARAMETERS
        # ... COMPUTATIONAL DOMAIN
        t_max = 3500.       # (fs)
        t_num = 2**14       # (-)
        z_max = 0.10*1e6    # (micron)
        z_num = 8000        # (-)
        z_skip = 10         # (-)
        # ... INITIAL CONDITION
        P0 = 1e4            # (W)
        t0 = 28.4           # (fs)
        w0 = 2.2559         # (rad/fs)
        E_0t_fun = lambda t: np.real(np.sqrt(P0)/np.cosh(t/t0)*np.exp(-1j*w0*t))

        # -- INITIALIZATION STAGE
        # ... COMPUTATIONAL DOMAIN
        grid = Grid( t_max = t_max, t_num = t_num, z_max = z_max, z_num = z_num)
        # ... CUSTOM PROPAGATION MODEL
        model = CustomModelPCF(w=grid.w)
        # ... PROPAGATION ALGORITHM 
        solver = IFM_RK4IP( model.Lw, model.Nw, user_action = model.claw)
        solver.set_initial_condition( grid.w, AS(E_0t_fun(grid.t)).w_rep)

        # -- RUN SIMULATION
        solver.propagate( z_range = z_max, n_steps = z_num, n_skip = z_skip)

        # -- SHOW RESULTS
        plot_evolution( solver.z, grid.t, solver.utz,
            t_lim = (-500,2200), w_lim = (1.,4.))


    if __name__=='__main__':
        main()


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

   **Total running time of the script:** ( 1 minutes  5.424 seconds)


.. _sphx_glr_download_auto_examples_gallery_01_g_specialized_model_PCF.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_PCF.py <g_specialized_model_PCF.py>`



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

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


.. only:: html

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

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