Bistable dark solitons of a cubic-quintic Helmholtz equation

Abstract

We report, to the best of our knowledge, the first exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field, and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and non-degenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit.We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.

Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schrödinger equation

“…While the nonlinear indices n 2 ,n 4 (or equivalently the nonlinear susceptibilities) depend solely on material properties and can be accurately characterized by means of consolidated techniques [3,4], the normalized coefficient α used throughout the paper turns out to depend on the input intensity as well, and hence the impact of the quintic nonlinearity can be tuned by changing the optical power [17]. Another area where the predictions based on the present model can be relevant and can lead to experimental test, is the dynamics of ultracold atoms (Bose-Einstein condensates), where the quintic term arises from higher-order (three-body) atom interactions [28], and tuning of the nonlinearities can be achieved by means of Feshbach resonances.…”

“…Besides being important per se, the knowledge of the dynamics of the whole soliton family of the CQNLS is also important in view of recent studies which extend the investigation of competing nonlinearities to the nonparaxial [17] and nonlocal [18,19] regimes. Moreover, the full characterization of the soliton solutions and their instabilities constitute the starting ground for describing the feature of dispersive shock waves (DSWs, involving multiple solitons in the weakly dispersive regime) [20], which is an active area of research where successful experiments have been recently performed in non-Kerr media under different excitation conditions [21][22][23].…”

Bistable Helmholtz dark spatial optical solitons in materials with self-defocusing saturable nonlinearity

“…We note, in passing, that κ-dependent inequalities determining plane-wave characteristics have also been reported for cubic 28 and cubic-quintic 25 Helmholtz equations. An alternative and often more convenient approach is to associate a conventional transverse velocity parameter V with k ξ .…”

“…An alternative and often more convenient approach is to associate a conventional transverse velocity parameter V with k ξ . 25 In that representation, one may construct k as 6) so that switching between the ± sign in Eq. (3.6) simply reverses the entire wave vector (i.e., k → −k) rather than just its longitudinal projection.…”

“…The spatial asymptotics of these solitons are mapped onto a plane-wave field using similar techniques to those established in Ref. 25, and geometrical transformations 26 are deployed to obtain more general off-axis solutions. A bistability characteristic is also discussed.…”