Introduction

Tobisch, Elena

doi:10.1007/978-3-319-20690-5_1

Cited by 2 publications

(2 citation statements)

References 42 publications

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“…• The above scenario of a rogue wave formation as a result of focusing dispersion packets and a small number of solitons (one or two) is apparently typical for the equations in which the interaction of solitons leads to their repulsion in space (as in the classical Korteweg-de Vries equation). It is closely related to the phenomenon of modulation instability, [7,12,[29][30][31], or rather its absence in systems with repulsive solitons, [20,34]. Such equations are called defocusing, and for them, in our opinion, the dispersive focusing mechanism is fundamental for the occurrence of rogue waves.…”

Section: Discussionmentioning

confidence: 99%

Dispersive focusing in fractional Korteweg–de Vries-type equations

Tobisch

Pelinovsky

2020

J. Phys. A: Math. Theor.

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In this paper we study dispersive enhancement of a wave train in systems described by the fractional Korteweg–de Vries-type equations of the form u t + α n u n u x + β m ( D m { u } ) x = 0 , D m { u } = − | k | m u ( k ) where the operator D m {u} is written in the Fourier space, α n , β m are arbitrary constants and n, m being rational numbers (positive or negative). Using both approximate and exact solutions of these wave equations we describe constructively the process of dispersive focusing. It is based on a time-reversing approach with the expected rogue wave chosen as the initial condition for a solution of these equations. We demonstrate the qualitative difference in the shape of the focused wavetrains for various n and m. Our results can be used for prediction of the rogue wave appearance arising in many types of weakly nonlinear and weakly dispersive wave systems in physical context.

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Section: Discussionmentioning

confidence: 99%

Dispersive focusing in fractional Korteweg–de Vries-type equations

Tobisch

Pelinovsky

2020

J. Phys. A: Math. Theor.

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“…31 However, the GNLSE accuracy becomes debatable when employing few-or subcycle pulses with a spectrum comparable to the carrier frequency, which are accessible with modern mode-locked lasers. 32 Moreover, using the Taylor expansion coefficients approximation makes the GNLSE invalid when investigating the propagation of multiple optical pulses with distinctive central frequencies. [33][34][35] A nonenvelope formulation based on the description of the pulse dynamics in terms of the analytic signal for the electric field has been proposed to overcome the shortcomings of the GNLSE.…”

Section: Modeling Of Few-cycle Pulses Propagationmentioning

confidence: 99%

Numerical investigation of coherent supercontinuum generation via soliton implosion in ZBLAN photonic crystal fiber

Medjouri¹,

Abed

2022

Opt. Eng.

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We numerically investigate coherent supercontinuum (SC) generation extending from the deep ultraviolet to the mid-infrared spectral region using few-cycle optical pulses, pumped into a ZBLAN photonic crystal fiber. The finite difference method is used to optimize the fiber structure and achieve two zero dispersion wavelengths, with a broad anomalous dispersion region. The propagation of ultrashort pulses and their nonlinear dynamics is accurately modeled by employing the forward unidirectional propagation equation for the analytic signal of the pulse electric field. We show that by pumping in the anomalous regime of dispersion, the high-order solitons undergo an implosion process and spectral broadening is achieved via the contribution of self-phase modulation, self-steepening, and shock formation, along with a strong transfer of energy into a nonsolitonic resonant Cherenkov-like radiation in the normal dispersion region. Furthermore, numerical results indicate that broadband supercontinua spanning the region from 0.22 to 4.6 μm is successfully achieved with a pulse having a soliton order and duration of 12 and 6 fs, respectively. In addition, the deterministic feature of the implosion mechanism exhibits very low sensitivity to the input quantum noise and achieves excellent coherence properties. The proposed multioctave SC source is found promising for various potential applications, such as two-photon excited autofluorescence, bioimaging, spectroscopy, optical signal processing, and medicine.

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Introduction

Cited by 2 publications

References 42 publications

Dispersive focusing in fractional Korteweg–de Vries-type equations

Dispersive focusing in fractional Korteweg–de Vries-type equations

Numerical investigation of coherent supercontinuum generation via soliton implosion in ZBLAN photonic crystal fiber

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