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- ItemThe Effect of Chirp on Pulse Compression at a Group Velocity Horizon(New York, NY : IEEE, 2016) Babushkin, Ihar; Amiranashvili, Shalva; Bree, Carsten; Morgner, Uwe; Steinmeyer, Gunter; Demircan, AyhanGroup-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 group-velocity horizon can be exploited for adiabatic compression of the soliton down into the few-cycle regime. Here, we study the delicate phase- and frequency-matching mechanism of soliton/dispersive wave interaction by controlling the input chirp of the dispersive wave. We demonstrate that such a modification of the dispersive wave can significantly alter the soliton dynamics. In particular, we show that it allows a decrease of the fiber length needed for the best compression and, to some extent, control of the trajectory of the soliton. The mechanism of such an influence is related to the modification of the phase-matching condition between the soliton and dispersive wave.
- ItemExtended criterion for the modulation instability([London] : IOP, 2019) Amiranashvili, Shalva; Tobisch, ElenaModulation instability, following the classical Lighthill criterion, appears if nonlinearity and dispersion make opposite contributions to the wave frequency, e.g. in the framework of the one-dimensional nonlinear Schrödinger equation (NLSE). Several studies of the wave instabilities in optical fibers revealed four wave mixing instabilities that are not covered by the Lighthill criterion and require use of the generalized NLSE. We derive an extended criterion, which applies to all four wave interactions, covers arbitrary dispersion, and depends neither on the propagation equation nor on the slowly varying envelope approximation. © 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.
- 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.
- ItemUltrashort optical solitons in transparent nonlinear media with arbitrary dispersion(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Amiranashvili, Shalva; Bandelow, Uwe; Akhmediev, NailWe consider the propagation of ultrashort optical pulses in nonlinear fibers and suggest a new theoretical framework for the description of pulse dynamics and exact characterization of solitary solutions. Our approach deals with a proper complex generalization of the nonlinear Maxwell equations and completely avoids the use of the slowly varying envelope approximation. The only essential restriction is that fiber dispersion does not favor both the so-called Cherenkov radiation, as well as the resonant generation of the third harmonics, as these effects destroy ultrashort solitons. Assuming that it is not the case, we derive a continuous family of solitary solutions connecting fundamental solitons to nearly single-cycle ultrashort ones for arbitrary anomalous dispersion and cubic nonlinearity.
- ItemCalculation of ultrashort pulse propagation based on rational approximations for medium dispersion(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Amiranashvili, Shalva; Bandelow, Uwe; Mielke, AlexanderUltrashort optical pulses contain only a few optical cycles and exhibit broad spectra. Their carrier frequency is therefore not well defined and their description in terms of the standard slowly varying envelope approximation becomes questionable. Existing modeling approaches can be divided in two classes, namely generalized envelope equations, that stem from the nonlinear Schrödinger equation, and non-envelope equations which treat the field directly. Based on fundamental physical rules we will present an approach that effectively interpolates between these classes and provides a suitable setting for accurate and highly efficient numerical treatment of pulse propagation along nonlinear and dispersive optical media.
- ItemAccelerated rogue solitons triggered by background radiation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Morgner, Uwe; Steinmeyer, Günter[no abstract available]
- ItemSpatio-temporal pulse propagation in nonlinear dispersive optical media(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Brée, Carsten; Amiranashvili, Shalva; Bandelow, UweWe discuss state-of-art approaches to modeling of propagation of ultrashort optical pulses in one and three spatial dimensions.We operate with the analytic signal formulation for the electric field rather than using the slowly varying envelope approximation, because the latter becomes questionable for few-cycle pulses. Suitable propagation models are naturally derived in terms of unidirectional approximation.
- ItemA model equation for ultrashort optical pulses(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Amiranashvili, Shalva; Vladimirov, Andrei; Bandelow, UweThe nonlinear Schrödinger equation based on the Taylor approximation of the material dispersion can become invalid for ultrashort and few-cycle optical pulses. Instead, we use a rational fit to the dispersion function such that the resonances are naturally accounted for. This approach allows us to derive a simple non-envelope model for short pulses propagating in one spatial dimension. This model is further investigated numerically and analytically.
- ItemCancellation of Raman self-frequency shift for compression of optical pulses(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Pickartz, Sabrina; Brée, Carsten; Bandelow, Uwe; Amiranashvili, ShalvaWe study to which extent a fiber soliton can be manipulated by a specially chosen continuous pump wave. A group velocity matched pump scatters at the soliton, which is compressed due to the energy/momentum transfer. As the pump scattering is very sensitive to the velocity matching condition, soliton compression is quickly destroyed by the soliton self-frequency shift (SSFS). This is especially true for ultrashort pulses: SSFS inevitably impairs the degree of compression. We demonstrate numerically that soliton enhancement can be restored to some extent and the compressed soliton can be stabilized, provided that SSFS is canceled by a second pump wave. Still the available compression degree is considerably smaller than that in the Raman-free nonlinear fibers.
- ItemAdjustable pulse compression scheme for generation of few-cycle pulses in the mid-infrared(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Morgner, Uwe; Steinmeyer, GünterAn novel adjustable adiabatic soliton compression scheme is presented, enabling a coherent pulse source with pedestal-free few-cycle pulses in the infrared or mid-infrared regime. This scheme relies on interaction of a dispersive wave and a soliton copropagating at nearly identical group velocities in a fiber with enhanced infrared transmission. The compression is achieved directly in one stage, without necessity of an external compensation scheme. Numerical simulations are employed to demonstrate this scheme for silica and fluoride fibers, indicating ultimate limitations as well as the possibility of compression down to the single-cycle regime. Such output pulses appear ideally suited as seed sources for parametric amplification schemes in the mid-infrared.
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