Multiple breakup of high-order spatial solitons

High-speed soliton ejection generated from the scattering of bright solitons by modulated reflectionless potential wells

We investigate numerically and theoretically the conditions leading to soliton ejection stimulated through the scattering of bright solitons by modulated reflectionless potential wells. Such potential wells allow for the possibility of controlled ejection of solitons with significantly high speeds. At the outset, we describe the scattering setup and characterize the soliton ejection in terms of the different parameters of the system. Then, we formulate a theoretical model revealing the underlying physics of soliton ejection. The model is based on energy and norm exchange between the incident soliton and a stable trapped mode corresponding to an exact solution of the governing nonlinear Schrödinger equation. Remarkably, stationary solitons can lead to high-speed soliton ejection where part of the nonlinear interaction energy transforms to translational kinetic energy of the ejected soliton. Our investigation shows that soliton ejection always occurs whenever the incident soliton norm is greater than that of the trapped mode whereas their energy is almost the same. Once the incident soliton is trapped, the excess in norm turns to an ejected soliton in addition to a small amount of radiation that share translational kinetic energy. We found that higher ejection speeds are obtained with multinode trapped modes that have higher binding energy. Simultaneous two-soliton ejection has been also induced by two solitons scattering with the potential from both of its sides. An ejection speed almost twice as that of single soliton ejection was obtained. Ejection outcome and ejection speed turn out to be sensitive to the relative phase between the two incoming solitons, which suggests a tool for soliton phase interferometry.

Many-body interaction in fast soliton collisions

We study n-pulse interaction in fast collisions of N solitons of the cubic nonlinear Schrödinger (NLS) equation in the presence of generic weak nonlinear loss. We develop a generalized reduced model that yields the contribution of the n-pulse interaction to the amplitude shift for collisions in the presence of weak (2m+1)-order loss, for any n and m. We first employ the reduced model and numerical solution of the perturbed NLS equation to analyze soliton collisions in the presence of septic loss (m=3). Our calculations show that the three-pulse interaction gives the dominant contribution to the collision-induced amplitude shift already in a full-overlap four-soliton collision, and that the amplitude shift strongly depends on the initial soliton positions. We then extend these results for a generic weak nonlinear loss of the form G(|ψ|2)ψ, where ψ is the physical field and G is a Taylor polynomial of degree mc. Considering mc=3, as an example, we show that three-pulse interaction gives the dominant contribution to the amplitude shift in a six-soliton collision, despite the presence of low-order loss. Our study quantitatively demonstrates that n-pulse interaction with high n values plays a key role in fast collisions of NLS solitons in the presence of generic nonlinear loss. Moreover, the scalings of n-pulse interaction effects with n and m and the strong dependence on initial soliton positions lead to complex collision dynamics, which is very different from that observed in fast NLS soliton collisions in the presence of cubic loss.

Stationary one-dimensional dispersive shock waves

We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defects in defocusing media with linear gain and two-photon absorption. We found that, in contrast to conservative media where one-dimensional dispersive shock waves usually exist only as nonstationary objects expanding away from a defect or generating beam, the competition between gain and two-photon absorption in a dissipative medium results in the formation of localized stationary dispersive shock waves, whose transverse extent may considerably exceed that of the refractive index defect. One-dimensional dispersive shock waves are stable if the defect strength does not exceed a certain critical value.

Rotating vortex solitons supported by localized gain

We show that ringlike localized gain landscapes imprinted in focusing cubic (Kerr) nonlinear media with strong two-photon absorption support new types of stable higher-order vortex solitons containing multiple phase singularities nested inside a single core. The phase singularities are found to rotate around the center of the gain landscape, with the rotation period being determined by the strength of the gain and the nonlinear absorption.

Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain

We discover that a spatially localized gain supports stable vortex solitons in media with cubic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying rings results in the suppression of otherwise ubiquitous azimuthal modulation instabilities of radially symmetric vortex solitons. We find that the topology of the gain profile imposes restrictions on the maximal possible charge of vortex solitons. Symmetry breaking occurs at high gain levels, resulting in the formation of necklace vortex solitons composed of asymmetric bright spots.