Two-dimensional optical chimera states in an array of coupled waveguide resonators

Abstract

Two-dimensional arrays of coupled waveguides or coupled microcavities allow to confine and manipulate light. Based on a paradigmatic envelope equation, we show that these devices, subject to a coherent optical injection, support coexistence between a coherent and incoherent emission. In this regime, we show that two-dimensional chimera state can be generated. Depending on initial conditions, the system exhibits a family of two-dimensional chimera states and interaction between them. We characterize these two-dimensional structures by computing their Lyapunov spectrum, and Yorke-Kaplan dimension. Finally, we show that two-dimensional chimera states are of spatiotemporal chaotic nature.One-dimensional nonlinear coupled microcavities exhibit a rich spatiotemporal dynamics. In particular, these coupled microcavities have fully synchronized or incoherent light emission of a spatiotemporal chaotic nature. Also, depending on the initial conditions, these devices show coexistence between desynchronized and synchronized domains, often called optical chimera states. In this contribution, we show evidence of optical chimeras in a twodimensional array of coupled waveguide resonators. Due to the additional degrees of freedom, the smaller localized solutions exhibit a chaotic spatiotemporal evolutionwhich is not the case of the one-dimensional counterpart. Lyapunov spectrum and Yorke-Kaplan dimensions are calculated to characterize these intriguing localized states.

Rogue waves in nonlinear optics

“…The latter was first derived to describe the dynamics in passive resonators [60], which was later on extended to fiber optics [149], left-handed materials [150], whispering gallery mode cavities [144], integrated ring resonators [69], and chains of coupled silver nanoparticles embedded in glass [151]. A discrete version of the LLE has been established to model coupled-waveguide resonators [152][153][154][155], or extended Josephson junction [156]. The LLE constitutes a paradigm for the study and for the understanding of various dynamical properties of laser fields confined in nonlinear optical resonators such as hard-mode symmetry-breaking instability and self-organization either in time and/or space (see a recent overview [157]).…”

Discrete vector light bullets in coupled χ3 nonlinear cavities

“…Such discrete solitons, both in 1D and in 2D waveguides arrays, have been realized experimentally via Kerr nonlinearity [39,40], quadratic nonlinearity [41], and photorefractive effect [42]. The stability of time-periodically oscillating (breather) solutions in the discretized LLE has been studied in [43,44]. Only quite recently, discrete LBs have been predicted theoretically for the discrete LLE [35].…”

Snakes on Lieb lattice

“…If in the continuous case the snaking is due to front locking mediated by spatially periodic solutions, in the discrete systems it is due to the imposed lattice, i.e., a discreteness-induced effective potential on the front dynamics, which is characterized by the overlap of the attractive interaction of fronts and the Peierls-Nabarro potential [10]. Further discussion about discreteness effect that generates a set of bound states also have been studied by Egorov et al [27] and Clerc et al [19,20]. The pinning region in the discrete case was first approximated analytically by Matthews and Susanto [48] and Dean et al [23].…”