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Author: Demircan, Ayhan × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik ×

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Now showing 1 - 10 of 26
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    Transient pulse compression at a group velocity horizon
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Babushkin, Ihar; Amiranashvili, Shalva; Brée, Carsten; Morgner, Uwe; Steinmeyer, Günter; Demircan, Ayhan
    Group-velocity matched cross-phase modulation between a fundamental soliton and a dispersive wave-packet has been previously suggested for optical switching applications similar to an optical transistor. Moreover, the nonlinear interaction in the resulting groupvelocity horizon can be exploited for adiabatic compression of the soliton down into the fewcycle regime. Here we show that both mechanisms can be combined. In such a transient compressor, parameters of the dispersive wave may then serve to actively control the soliton compression and adjust the pulse duration in the presence of disturbances. While a certain amount of control is already enabled by the delay between soliton and dispersive wave, the means of controlling the compression process are substantially enhanced by additionally manipulating the chirp of the dispersive wave. Moreover, controlling the chirp of the dispersive wave also enables correction for limitations of the compression scheme due to a self-frequency shift of the soliton or for uncompensated dispersion in the scheme. This substantially widens the practicality of the compression scheme and other applications of the highly efficient nonlinear interaction at the group-velocity horizon.
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    Simulation of pulse propagation in nonlinear optical fibers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2003) Bandelow, Uwe; Demircan, Ayhan; Kesting, Martin
    We solve numerically a generalized nonlinear Schroedinger equation by using a pseudospectral method. Integration is performed by using an eight-order Runge-Kutta scheme. The numerical method therefore differs from the commonly used split-step method. Effects such as the impact of group velocity dispersion (GVD) up to fourth-order dispersion, self phase modulation (SPM), self-steepening and intrapulse Raman scattering can be investigated with the code. Examples for the above effects are demonstrated, as well as their interplay in the context of soliton propagation and sub-picosecond pulses.
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    Ocean rogue waves and their phase space dynamics in the limit of a linear interference model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Birkholz, Simon; Brée, Carsten; Veselic, Ivan; Demircan, Ayhan; Steinmeyer, Günter
    We reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these formation becomes increasingly likely, with appearance frequencies that may even exceed long-term observations by an order of magnitude. For estimation of the effective number of interfering waves, we suggest the Grassberger-Procaccia dimensional analysis of individual time series. For the ocean system, it is further shown that the resulting phase space dimension may vary, such that the threshold for rogue wave formation is not always reached. Time series analysis as well as the appearance of particular focusing wind conditions may enable an effective forecast of such rogue-wave prone situations. In particular, extracting the dimension from ocean time series allows much more specific estimation of the rogue wave probability.
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    Asymptotic pulse shapes in filamentary propagation of intense femtosecond pulses
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Krüger, Carsten; Demircan, Ayhan; Steinmeyer, Günter
    Self-compression of intense ultrashort laser pulses inside a self-guided filament is discussed. The filament self-guiding mechanism requires a balance between diffraction, plasma self-defocusing and Kerr-type self-focusing, which gives rise to asymptotic intensity profiles on axis of the filament. The asymptotic solutions appear as the dominant pulse shaping mechanism in the leading part of the pulse, causing a pinch of the photon density close to zero delay, which substantiates as pulse compression. The simple analytical model is backed up by numerical simulations, confirming the prevalence of spatial coupling mechanisms and explaining the emerging inhomogeneous spatial structure. Numerical simulations confirm that only spatial effects alone may already give rise to filament formation. Consequently, self-compression is explained by a dynamic balance between two optical nonlinearities, giving rise to soliton-like pulse formation inside the filament.
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    Effect of higher-order dispersion on modulation instability, soliton propagation and pulse splitting
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Demircan, Ayhan; Pietrzyk, Monika; Bandelow, Uwe
    By solving numerically the extended nonlinear Schrödinger equation we investigate the influence of higher-order dispersion effects on the propagation of optical pulses in highly nonlinear fibers. In the anomalous dispersion regime third-order dispersion can, in general, induce soliton fission and yields asymmetric spectra, whereas modulation instability can be slightly suppressed. In the normal dispersion regime we demonstrate pulse splitting by third-order dispersion, as well as its later suppression by fourth-order dispersion.
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    Hamiltonian structure of propagation equations for ultrashort optical pulses
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Amiranashvili, Shalva; Demircan, Ayhan
    A Hamiltonian framework is developed for a sequence of ultrashort optical pulses propagating in a nonlinear dispersive medium. To this end a second-order nonlinear wave equation is first simplified using an unidirectional approximation. All non-resonant nonlinear terms are then rigorously eliminated using a suitable change of variables in the spirit of the canonical perturbation theory. The derived propagation equation operates with a properly defined complexification of the real electric field. It accounts for arbitrary dispersion, four-wave mixing processes, weak absorption, and arbitrary pulse duration. Thereafter the so called normal variables, i.e., classical fields corresponding to the quantum creation and annihilation operators, are introduced. Neglecting absorption we finally derive the Hamiltonian formulation. The latter yields the most essential integrals of motion for the pulse propagation. These integrals reflect the time-averaged fluxes of energy, momentum, and classical photon number transferred by the pulse. The conservation laws are further used to control the numerical solutions when calculating supercontinuum generation by an ultrashort optical pulse.
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    Kramers-Kronig relations and high order nonlinear susceptibilities
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Brée, Carsten; Demircan, Ayhan; Steinmeyer, Günter
    As previous theoretical results recently revealed, a Kramers-Kronig transform of multiphoton absorption rates allows for a precise prediction on the dispersion of the nonlinear refractive index $n_2$ in the near IR. It was shown that this method allows to reproduce recent experimental results on the importance of the higher-order Kerr effect. Extending these results, the current manuscript provides the dispersion of $n_2$ for all noble gases in excellent agreement with reference data. It is furthermore established that the saturation and inversion of the nonlinear refractive index is highly dispersive with wavelength, which indicates the existence of different filamentation regimes. While shorter laser wavelengths favor the well-established plasma clamping regime, the influence of the higher-order Kerr effect dominates in the long wavelength regime.
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    Compression limit by third-order dispersion in the normal dispersion regime
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Demircan, Ayhan; Kroh, Marcel; Bandelow, Uwe; Hüttl, Bernd; Weber, Hans-Georg
    Broad-band continua at gigahertz rates generated in high-nonlinear dispersion flattened fibers in the normal dispersion regime near the zero-dispersion wavelength can be used for a subsequent efficient pulse compression, leading to stable high-repetition-rate trains of femtosecond pulses. We show experimentally and theoretically that third-order dispersion defines a critical power, where beyond further compression is inhibited. This fundamental limit is caused by a pulse-breakup.
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    Cascaded self-compression of femtosecond pulses in filaments
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Brée, Carsten; Bethge, Jens; Skupin, Stefan; Demircan, Ayhan; Steinmeyer, Günter
    Highly nonlinear wave propagation scenarios hold the potential to serve for energy concentration or pulse duration reduction of the input wave form, provided that a small range of input parameters be maintained. In particular when phenomena like rogue-wave formation or few-cycle optical pulses generation come into play, it becomes increasingly difficult to maintain control of the waveforms. Here we suggest an alternative approach towards the control of waveforms in a highly nonlinear system. Cascading pulse self-compression cycles at reduced nonlinearity limits the increase of input parameter sensitivity while still enabling an enhanced compression effect. This cascaded method is illustrated by experiments and in numerical simulations of the Nonlinear Schrödinger Equation, simulating the propagation of short optical pulses in a self-generated plasma.
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    Method for computing the nonlinear refractive index via Keldysh theory
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Brée, Carsten; Demircan, Ayhan; Steinmeyer, Günter
    By making use of the multiphoton limit of Keldysh theory, we show that for the case of two-photon absorption a Kramers-Kronig expansion can be used to calculate the nonlinear refractive index for different wavelenghts. We apply this method to various inert gases and compare the obtained numerical values to different experimental and theoretical results for the dispersion of the Kerr nonlinearity.