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- ItemAsymptotic pulse shapes in filamentary propagation of intense femtosecond pulses(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Krüger, Carsten; Demircan, Ayhan; Steinmeyer, GünterSelf-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.
- ItemEffect 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, UweBy 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.
- ItemHamiltonian structure of propagation equations for ultrashort optical pulses(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Amiranashvili, Shalva; Demircan, AyhanA 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.
- ItemKramers-Kronig relations and high order nonlinear susceptibilities(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Brée, Carsten; Demircan, Ayhan; Steinmeyer, GünterAs 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.
- 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.
- ItemCascaded 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, GünterHighly 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.
- ItemMethod for computing the nonlinear refractive index via Keldysh theory(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Brée, Carsten; Demircan, Ayhan; Steinmeyer, GünterBy 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.
- ItemFilamentary pulse self-compression : the impact of the cell windows(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Brée, Carsten; Demircan, Ayhan; Bethge, Jens; Nibbering, Erik T.J.; Skupin, Stefan; Bergé, Luc; Steinmeyer, GünterSelf-compression of multi-millijoule laser pulses during filamentary propagation is usually explained by the interplay of self-focusing and defocusing effects, causing a substantial concentration of energy on the axis of the propagating optical pulse. Recently, it has been argued that cell windows may play a decisive role in the self-compression mechanism. As such windows have to be used for media other than air their presence is often unavoidable, yet they present a sudden non-adiabatic change in dispersion and nonlinearity that should lead to a destruction of the temporal and spatial integrity of the light bullets generated in the self-compression mechanism. We now experimentally prove that there is in fact a self-healing mechanism that helps to overcome the potentially destructive consequences of the cell windows. We show in two carefully conducted experiments that the cell window position decisively influences activation or inhibition of the self-healing mechanism. A comparison with a windowless cell shows that presence of this mechanism is an important prerequisite for the exploitation of self-compression effects in windowed cells filled with inert gases.
- ItemModulation instability in filamentary self-compression(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Brée, Carsten; Demircan, Ayhan; Steinmeyer, GünterWe numerically analyze filamentary propagation for various medium- and input pulse parameters and show that temporal self-compression can greatly benefit from refocusing events. Analyzing the dynamical behavior in the second focal spot, it turns out that a dispersive temporal break-up may appear due to the emission of a hyperbolic shock-wave from the self-steepened trailing edge of the pulse. This break-up event enhances the self-compression capabilities of laser filaments, enabling up to 12-fold temporal compression. Only slightly perturbing the input pulse parameters, we further identify a regime in which refocusing events give rise to extended subdiffractive propagation in a weakly ionized channel.
- 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.