Self-trapping and stable localized modes in nonlinear photonic crystals

We predict the existence of stable nonlinear localized modes near the band edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr nonlinearity. Employing the technique based on the Green function, we reveal a physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystal

Discreteness-induced oscillatory instabilities of dark solitons

We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyze how it may occur for dark solitons of the discrete nonlinear Schrödinger and generalized Ablowitz-Ladik equations. [S0031-9007(98)08088-0

Second-harmonic generation in subwavelength graphene waveguides

We suggest a novel approach for generating second-harmonic radiation in subwavelength graphene waveguides. We demonstrate that quadratic phase matching between the plasmonic guided modes of different symmetries can be achieved in a planar double-layer geometry when conductivity of one of the layers becomes spatially modulated. We predict theoretically that, owing to graphene nonlocal conductivity, the second-order nonlinear processes can be actualized for interacting plasmonic modes with an effective grating coupler to allow external pumping of the structure and output of the radiation at the double frequency.Comment: 5 pages, 3 figure

Necklace-ring vector solitons

We introduce novel classes of optical vector solitons that consist of incoherently coupled self-trapped “necklace” beams carrying zero, integer, and even fractional angular momentum. Because of the stabilizing mutual attraction between the components, such stationary localized structures exhibit quasistable propagation for much larger distances than the corresponding scalar vortex solitons and expanding scalar necklace beams

Nonlinear Systems with Parity-Time Symmetry

We review our recent progress in the study of nonlinear systems with balanced gain and loss described by the models with parity-time (PT) symmetry. We discuss the nonlinear dynamics in optical waveguide couplers and show that for intensities below a threshold, the field oscillates between the waveguides, whereas above the threshold the symmetry breaking is observed. This nonlinearity-induced effect can be generalized to other systems, as well as can be observed experimentally. We then move to the systems with continuous variables and study the soliton dynamics and soliton scattering in the systems with PT-symmetric potentials. In particular, we demonstrate that both single and multiple soliton scattering can exhibit almost perfect unidirectional flows associated with an energy exchange between the soliton center of mass and its internal mode

Self-trapping of light and nonlinear localized modes in 2D photonic crystals and waveguides

We overview our recent results on the nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we describe the existence domains for nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.Comment: 20 pages (LaTeX) with 12 figures (EPS

Broadband light coupling to dielectric slot waveguides with tapered plasmonic nanoantennas

We propose and theoretically verify an efficient mechanism of broadband coupling between incident light and on-chip dielectric slot waveguide by employing a tapered plasmonic nanoantenna. Nanoantenna receives free space radiation and couples it to a dielectric slot waveguide with the efficiency of up to 20% in a broad spectral range, having a small footprint as compared with the currently used narrowband dielectric grating couplers. We argue that the frequency selective properties of such nanoantennas also allow for using them as ultrasmall on-chip multiplexer/demultiplexer devices