Control of planar nonlinear guided waves and spatial solitons with a left-handed medium

Dynamics of nonlinear Schrödinger breathers in a potential trap

We consider the evolution of the 2-soliton (breather) of the nonlinear Schrödinger equation on a semi-infinite line with the zero boundary condition and a linear potential, which corresponds to the gravity field in the presence of a hard floor. This setting can be implemented in atomic Bose-Einstein condensates, and in a nonlinear planar waveguide in optics. In the absence of the gravity, repulsion of the breather from the floor leads to its splitting into constituent fundamental solitons, if the initial distance from the floor is smaller than a critical value; otherwise, the moving breather persists. In the presence of gravity, the breather always splits into a pair of "co-hopping" fundamental solitons, which may be frequency locked in the form of a quasi-breather, or unlocked, forming an incoherent pseudo-breather. Some essential results are obtained in an analytical form, in addition to the systematic numerical investigation.

A Unified Approach to Nonlinear Transformation Materials

The advances in geometric approaches to optical devices due to transformation optics has led to the development of cloaks, concentrators, and other devices. It has also been shown that transformation optics can be used to gravitational fields from general relativity. However, the technique is currently constrained to linear devices, as a consistent approach to nonlinearity (including both the case of a nonlinear background medium and a nonlinear transformation) remains an open question. Here we show that nonlinearity can be incorporated into transformation optics in a consistent way. We use this to illustrate a number of novel effects, including cloaking an optical soliton, modeling nonlinear solutions to Einstein’s field equations, controlling transport in a Debye solid, and developing a set of constitutive to relations for relativistic cloaks in arbitrary nonlinear backgrounds.

Gray solitary-wave solutions in nonlinear negative-index materials

We predict the existence of gray (dark) solitary waves in negative-index materials on the basis of a derived higher-order nonlinear Schrödinger equation. The conditions for the formation of three cases of gray solitary waves and exact analytical expressions are presented. Furthermore, we investigate the properties of these gray solitary waves in negative-index materials. The results show that the higher-order linear and nonlinear effects play a crucial role for the formation and properties of the second and third cases of gray solitary waves.

Solitons in anharmonic chains with negative group velocity

We consider the problem of the soliton dynamics in anharmonic chains with nearest-neighbor interactions and negative group velocity. By using the quasicontinuum approach we derive analytic expressions for envelope solitons. We observe that these solitons are stable under collisions and, moreover, in the absence of losses they can propagate with nearly any desired velocity. Energy loss effects are discussed by considering the presence of Stokes and hydrodynamical damping. Numerical simulations are performed showing a good agreement with the theory.