Browsing by Author "Amiranashvili, Shalva"
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- 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]
- ItemAdditive splitting methods for parallel solution of evolution problems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Amiranashvili, Shalva; Radziunas, Mindaugas; Bandelow, Uwe; Busch, Kurt; Čiegis, RaimondasWe demonstrate how a multiplicative splitting method of order P can be used to construct an additive splitting method of order P + 3. The weight coefficients of the additive method depend only on P, which must be an odd number. Specifically we discuss a fourth-order additive method, which is yielded by the Lie-Trotter splitting. We provide error estimates, stability analysis, and numerical examples with the special discussion of the parallelization properties and applications to nonlinear optics.
- ItemAdiabatic theory of champion solitons(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, ShalvaWe consider scattering of small-amplitude dispersive waves at an intense optical soliton which constitutes a nonlinear perturbation of the refractive index. Specifically, we consider a single-mode optical fiber and a group velocity matched pair: an optical soliton and a nearly perfectly reflected dispersive wave, a fiber-optical analogue of the event horizon. By combining (i) an adiabatic approach that is used in soliton perturbation theory and (ii) scattering theory from Quantum Mechanics, we give a quantitative account for the evolution of all soliton parameters. In particular, we quantify the increase in the soliton peak power that may result in spontaneous appearance of an extremely large, so-called champion soliton. The presented adiabatic theory agrees well with the numerical solutions of the pulse propagation equation. Moreover, for the first time we predict the full frequency band of the scattered dispersive waves and explain an emerging caustic structure in the space-time domain.
- 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.
- ItemAsymptotically stable compensation of soliton self-frequency shift(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, ShalvaWe report the cancellation of the soliton self-frequency shift in nonlinear optical fibers. A soliton which interacts with a group velocity matched low intensity dispersive pump pulse, experiences a continuous blue-shift in frequency, which counteracts the soliton selffrequency shift due to Raman scattering. The soliton self-frequency shift can be fully compensated by a suitably prepared dispersive wave. We quantify this kind of soliton-dispersive wave interaction by an adiabatic approach and demonstrate that the compensation is stable in agreement with numerical simulations.
- 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.
- 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.
- ItemDispersion of nonlinear group velocity determines shortest envelope solitons(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Amiranashvili, Shalva; Bandelow, Uwe; Akhmediev, Nail N.We demonstrate that a generalized nonlinear Schrödinger equation (NSE), that includes dispersion of the intensity-dependent group velocity, allows for exact solitary solutions. In the limit of a long pulse duration, these solutions naturally converge to a fundamental soliton of the standard NSE. In particular, the peak pulse intensity times squared pulse duration is constant. For short durations this scaling gets violated and a cusp of the envelope may be formed. The limiting singular solution determines then the shortest possible pulse duration and the largest possible peak power. We obtain these parameters explicitly in terms of the parameters of the generalized NSE.
- 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.
- ItemEfficient all-optical control of solitons(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, ShalvaWe consider the phenomenon of an optical soliton controlled (e.g. amplified) by a much weaker second pulse which is efficiently scattered at the soliton. An important problem in this context is to quantify the small range of parameters at which the interaction takes place. This has been achieved by using adiabatic ODEs for the soliton characteristics, which is much faster than an empirical scan of the full propagation equations for all parameters in question.
- 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.
- ItemFew-cycle optical solitons in dispersive media beyond the envelope approximation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Amiranashvili, Shalva; Bandelow, Uwe; Akhmediev, NailWe study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our theory extends beyond the slowly varying envelope approximation. The optical field is derived directly from the Maxwell equations under the assumption that generation of the third harmonic is a non-resonant process or at least cannot destroy the pulse prior to inevitable linear damping. The solitary wave solutions are obtained numerically up to nearly single-cycle duration using a modification of the spectral renormalisation method originally developed for the envelope solitons.
- 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.
- ItemGeneralized Lighthill criterion for the modulation instability(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Amiranashvili, Shalva; Tobisch, ElenaAn @universal modulation instability is subject to Lighthill criterion: nonlinearity and dispersion should make opposite contributions to the wave frequency. Recent studies of wave instabilities in optical fibers with the minimum chromatic dispersion revealed situations in which the criterion is violated and fast unstable modulations appear due to the four wave mixing process. We derive a generalized criterion, it applies to an arbitrary dispersion and to both slow and fast unstable modulations. Since the fast modulations depend on nonlinear dispersion, we also demonstrate how to describe them in the framework of a single generalized nonlinear Schrödinger equation.
- ItemHamiltonian framework for short optical pulses(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Amiranashvili, ShalvaPhysics of short optical pulses is an important and active research area in nonlinear optics. In what follows we theoretically consider the most extreme representatives of short pulses that contain only several oscillations of electromagnetic field. Description of such pulses is traditionally based on envelope equations and slowly varying envelope approximation, despite the fact that the envelope is not ?slow? and, moreover, there is no clear definition of such a ?fast? envelope. This happens due to another paradoxical feature: the standard (envelope) generalized nonlinear Schrödinger equation yields very good correspondence to numerical solutions of full Maxwell equations even for few-cycle pulses, a thing that should not be. In what follows we address ultrashort optical pulses using Hamiltonian framework for nonlinear waves. As it appears, the standard optical envelope equation is just a reformulation of general Hamiltonian equations. In a sense, no approximations are required, this is why the generalized nonlinear Schrödinger equation is so effective. Moreover, the Hamiltonian framework greatly contributes to our understanding of ?fast? envelope, ultrashort solitons, stability and radiation of optical pulses. Even the inclusion of dissipative terms is possible making the Hamiltonian approach an universal theoretical tool also in extreme nonlinear optics.
- 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.
- 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.
- ItemModeling of ultrashort optical pulses in nonlinear fibers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Amiranashvili, ShalvaThis work deals with theoretical aspects of pulse propagation. The core focus is on extreme, few-cycle pulses in optical fibers, pulses that are strongly affected by both dispersion and nonlinearity. Using Hamil- tonian methods, we discuss how the meaning of pulse envelope changes, as pulses become shorter and shorter, and why an envelope equation can still be used. We also discuss how the standard set of dispersion coefficients yields useful rational approximations for the chromatic dispersion in optical fibers. Three more specific problems are addressed thereafter. First, we present an alternative framework for ultra- short pulses in which non-envelope propagation models are used. The approach yields the limiting, shortest solitons and reveals their universal features. Second, we describe how one can manipulate an ultrashort pulse, i.e., to change its amplitude and duration in a predictable manner. Quantitative theory of the manipu- lation is presented based on perturbation theory for solitons and analogy between classical fiber optics and quantum mechanics. Last but not least, we consider a recently found alternative to the standard split-step approach for numerical solutions of the pulse propagation equations.
- ItemNumerical methods for accurate description of ultrashort pulses in optical fibers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Amiranashvili, Shalva; Radziunas, Mindaugas; Bandelow, Uwe; C̆iegis, RaimondasWe consider a one-dimensional first-order nonlinear wave equation (the so-called forward Maxwell equation, FME) that applies to a few-cycle optical pulse propagating along a preferred direction in a nonlinear medium, e.g., ultrashort pulses in nonlinear fibers. The model is a good approximation to the standard second-order wave equation under assumption of weak nonlinearity. We compare FME to the commonly accepted generalized nonlinear Schrödinger equation, which quantifies the envelope of a quickly oscillating wave field based on the slowly varying envelope approximation. In our numerical example, we demonstrate that FME, in contrast to the envelope model, reveals new spectral lines when applied to few-cycle pulses. We analyze and compare pseudo-spectral numerical schemes employing symmetric splitting for both models. Finally, we adopt these schemes to a parallel computation and discuss scalability of the parallelization.
- ItemPadé approximant for refractive index and nonlocal envelope equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Amiranashvili, Shalva; Mielke, Alexander; Bandelow, UwePadé approximant is superior to Taylor expansion when functions contain poles. This is especially important for response functions in complex frequency domain, where singularities are present and intimately related to resonances and absorption. Therefore we introduce a diagonal Padé approximant for the complex refractive index and apply it to the description of short optical pulses. This yields a new nonlocal envelope equation for pulse propagation. The model offers a global representation of arbitrary medium dispersion and absorption, e.g., the fulfillment of the Kramers-Kronig relation can be established. In practice, the model yields an adequate description of spectrally broad pulses for which the polynomial dispersion operator diverges and can induce huge errors.