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- ItemSimulation of pulse propagation in nonlinear optical fibers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2003) Bandelow, Uwe; Demircan, Ayhan; Kesting, MartinWe 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.
- ItemCompression 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-GeorgBroad-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.
- ItemHigh-frequency averaging in semi-classical Hartree-type equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Giannoulis, Johannes; Mielke, Alexander; Sparber, ChristofWe investigate the asymptotic behavior of solutions to semi-classical Schröodinger equations with nonlinearities of Hartree type. For a weakly nonlinear scaling, we show the validity of an asymptotic superposition principle for slowly modulated highly oscillatory pulses. The result is based on a high-frequency averaging effect due to the nonlocal nature of the Hartree potential, which inhibits the creation of new resonant waves. In the proof we make use of the framework of Wiener algebras.
- ItemGeneralized integrable evolution equations with an infinite number of free parameters(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Akhmediev, Nail; Ankiewicz, Adrian; Amiranashvili, Shalva; Bandelow, UweEvolution equations such as the nonlinear Schrödinger equation (NLSE) can be extended to include an infinite number of free parameters. The extensions are not unique. We give two examples that contain the NLSE as the lowest-order PDE of each set. Such representations provide the advantage of modelling a larger variety of physical problems due to the presence of an infinite number of higher-order terms in this equation with an infinite number of arbitrary parameters. An example of a rogue wave solution for one of these cases is presented, demonstrating the power of the technique.
- ItemAnalysis of the interplay between soliton fission and modulation instability in supercontinuum generation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Demircan, Ayhan; Bandelow, UweWe investigate the generation mechanisms for ultrawide spectra in nonlinear optical fibers. Soliton fission and modulation instability represent fundamental mechanisms for the generation process. The primary origin of the spectral broadening changes with the pump-pulse duration. Soliton fission dominates for low input power and short pulses. Its efficiency for supercontinuum generation and especially the extend to the blue side can be increased by proper design of the dispersion profile. The modulation instability has a strong impact for high input powers and greatly enhances the generation process, but leads to a degradation of the coherence properties. Also for short pulses with durations of 60 fs the modulation instability is present and can hardly be suppressed. The interplay between these two effects leads to various characteristics of the resulting spectra, which are modified by to the relative impact of the modulation instability.
- ItemLimit for pulse compression by pulse splitting(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Demircan, Ayhan; Bandelow, UweWe have detected a fundamental pulse-compression limit for high-nonlinear fibers in the normal dispersion regime near the zero-dispersion wavelength. The desired generation of a broadband continuum by self-phase modulation is limited by already small amounts of third-order dispersion, which results in pulse splitting above a critical pulse power. We investigate the critical fiber length in dependence on pulse- and fiber parameters.
- ItemSupercontinuum generation by multiple scatterings at a group velocity horizon(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Demircan, Ayhan; Amiranashvli, Shalva; Brée, Carsten; Morgner, Uwe; Steinmeyer, GünterA new scheme for supercontinuum generation covering more than one octave and exhibiting extraordinary high coherence properties has recently been proposed in Phys. Rev. Lett. 110, 233901 (2013). The scheme is based on two-pulse collision at a group velocity horizon between a dispersive wave and a soliton. Here we demonstrate that the same scheme can be exploited for the generation of supercontinua encompassing the entire transparency region of fused silica, ranging from 300 to 2300nm. At this bandwidth extension, the Raman effect becomes detrimental, yet may be compensated by using a cascaded collision process. Consequently, the high degree of coherence does not degrade even in this extreme scenario.