Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type

Nonlinear localized modes in one-dimensional nanoscale dark-state optical lattices

Optical lattices (OLs) with conventional spatial periodic λ/2, formed by interfering the counterpropagating laser beams with wavelength λ, are versatile tools to study the dynamical and static properties of ultracold atoms. OLs with subwavelength spatial structure have been realized in recent quantum-gas experiment, offering new possibility for nonlinear and quantum control of ultracold atoms at the nano scale. Herein, we study theoretically and numerically the formation, property, and dynamics of matter-wave localized gap modes of Bose-Einstein condensates loaded in a one-dimensional nanoscale dark-state OL consisted of an array of optical subwavelength barriers. The nonlinear localized modes, in the forms of on- and off-site fundamental gap solitons, and dipole ones, are demonstrated; and we uncover that, counterintuitively, these modes exhibit always a cusplike (side peaks) mode even for a deeply subwavelength adiabatic lattice, contrary to the previously reported results in conventional deep OLs where the localized gap modes are highly confined in a single lattice cell. The (in)stability features of all the predicted localized modes are verified through the linear-stability analysis and direct perturbed simulations. Our predicted results are attainable in current ultracold atoms experiments with the cutting-edge technique, pushing the nonlinear control of ultracold atoms with short-period OLs as an enabling technology into subwavelength structures.

Controllable Gaussian-shaped soliton clusters in strongly nonlocal media

In this paper, we discuss the evolution of the Gaussian-shaped soliton clusters in strongly nonlocal nonlinear media, which is modeled by the nonlinear Schrödinger equation. The influences of three initial incident parameters (the initial transverse velocity, the initial position, the input power) on propagation dynamics of the soliton clusters are all discussed in detail. The results show that the intensity distribution, the trajectory, the center distance, and the angular velocity of the clusters can be controlled by adjusting the initial incident parameters. A series of analytical solutions on the propagation dynamics of the clusters are derived by borrowing ideas from classical physics. The results in this paper may have potential applications in the beam controlling and all-optical interconnection with the interacting characteristics of (2+1)-dimensional soliton clusters.

Aberrated surface soliton formation in a nonlinear 1D and 2D photonic crystal

We discuss a novel type of surface soliton-aberrated surface soliton-appearance in a nonlinear one dimensional photonic crystal and a possibility of this surface soliton formation in two dimensional photonic crystal. An aberrated surface soliton possesses a nonlinear distribution of the wavefront. We show that, in one dimensional photonic crystal, the surface soliton is formed at the photonic crystal boundary with the ambient medium. Essentially, that it occupies several layers at the photonic crystal boundary and penetrates into the ambient medium at a distance also equal to several layers, so that one can infer about light energy localization at the lateral surface of the photonic crystal. In the one dimensional case, the surface soliton is formed from an earlier formed soliton that falls along the photonic crystal layers at an angle which differs slightly from the normal to the photonic crystal face. In the two dimensional case, the soliton can appear if an incident Gaussian beam falls on the photonic crystal face. The influence of laser radiation parameters, optical properties of photonic crystal layers and ambient medium on the one dimensional surface soliton formation is investigated. We also discuss the influence of two dimensional photonic crystal configuration on light energy localization near the photonic crystal surface. It is important that aberrated surface solitons can be created at relatively low laser pulse intensity and for close values of alternating layers dielectric permittivity which allows their experimental observation.

Dynamics of nonlinear waves in two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and potentials

We derive analytical solutions to the cubic-quintic nonlinear Schrödinger equation with potentials and nonlinearities depending on both propagation distance and transverse space. Among other, circle solitons and multi-peaked vortex solitons are found. These solitary waves propagate self-similarly and are characterized by three parameters, the modal numbers m and n, and the modulation depth of intensity. We find that the stable fundamental solitons with m = 0 and the low-order solitons with m = 1, n ≤ 2 can be supported with the energy eigenvalues E = 0 and E ≠ 0. However, higher-order solitons display unstable propagation over prolonged distances. The stability of solutions is examined by numerical simulations.