Adiabatic theory of champion solitons
Please always quote using this URN:urn:nbn:de:0296-matheon-14010
- We 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.
Author: | Shalva Amiranashvili |
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URN: | urn:nbn:de:0296-matheon-14010 |
Referee: | Benjamin Kunz |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2016/12/16 |
Release Date: | 2016/12/16 |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
Project: | D Optics and Electronics (Electronic and photonic devices) / D-OT2 Turbulence and extreme events in non-linear optics |
MSC-Classification: | 78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78-02 Research exposition (monographs, survey articles) |
Preprint Number: | 1119 |