Eur. Phys. J. D (2017) 71: 176
https://doi.org/10.1140/epjd/e2017-80068-y

Regular Article

Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model^*

¹ Department of Applied Physics and Photonics (IR-TONA), Vrije Universiteit Brussels, Pleinlaan 2, 1050 Brussels, Belgium
² Institute of Solid State Physics, 72 Tzarigradsko Chaussee Blvd., 1784 Sofia, Bulgaria
³ Departamento de Física, FCFM, Universidad de Chile, Casilla 487-3, Santiago, Chile
⁴ Faculté des Sciences, Optique Nonlinéaire Thérorique, Université Libre de Bruxelles (U.L.B.), C.P. 231, Campus Plaine, 1050 Bruxelles, Belgium

^a e-mail: kpanajot@b-phot.org

Received: 31 January 2017
Received in final form: 6 April 2017
Published online: 4 July 2017

Abstract

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height.