Self-synchronization phenomena in the Lugiato-Lefever equation
Abstract
The damped driven nonlinear Schrödinger equation (NLSE) has been used to understand a range of physical phenomena in diverse systems. Studying this equation in the context of optical hyperparametric oscillators in anomalous-dispersion dissipative cavities, where NLSE is usually referred to as the Lugiato-Lefever equation, we are led to a reduced nonlinear oscillator model that uncovers the essence of the spontaneous creation of sharply peaked pulses in optical resonators. We identify attracting solutions for this model, which correspond to stable cavity solitons and Turing patterns, and study their degree of stability. The reduced model embodies the fundamental connection between mode synchronization and spatiotemporal pattern formation and represents a class of self-synchronization processes in which coupling between nonlinear oscillators is governed by energy and momentum conservation.
- Publication:
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Physical Review A
- Pub Date:
- July 2017
- DOI:
- 10.1103/PhysRevA.96.013828
- arXiv:
- arXiv:1707.05705
- Bibcode:
- 2017PhRvA..96a3828T
- Keywords:
-
- Nonlinear Sciences - Pattern Formation and Solitons;
- Condensed Matter - Statistical Mechanics;
- Physics - Optics
- E-Print:
- This manuscript is published in Physical Review A. Copyright 2017 by the American Physical Society. arXiv admin note: text overlap with arXiv:1602.08523