Engineering Fano resonances in discrete arrays

We study transmission properties of discrete arrays composed of a linear waveguide coupled to a system of N side defect states. This simple system can be used to model discrete networks of coupled defect modes in photonic crystals, complex waveguide arrays in two-dimensional nonlinear lattices, and ring-resonator structures. We demonstrate the basic principles of the resonant scattering management through engineering Fano resonances and find exact results for the wave transmission coefficient. We reveal conditions for perfect reflections and transmissions due to either destructive or constructive interferences, and associate them with Fano resonances, also demonstrating how these resonances can be tuned by nonlinear defects

Matter-wave gap solitons in atomic band-gap structures

We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic crystal for light waves. We study in detail the case of a two-dimensional square optical lattice and show that this atomic band-gap structure allows nonlinear localization of atomic Bloch waves in the form of two-dimensional matter-wave gap solitons

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

Experimental studies of the internal Goos-Hanchen shift for self-collimated beams in two-dimensional microwave photonic crystals

We study experimentally the Goos-Hanchen effect observed at the reflection of a self-collimated beam from the surface of a two-dimensional photonic crystal and describe a method for controlling the beam reflection through surface engineering. The microwave photonic crystal, fabricated from alumina rods, allows control of the output position of a reflected beam undergoing an internal Goos-Hanchen shift by changing the rod diameter at the reflection surface. The experimental data is in good agreement with the results of the finite-difference time-domain numerical calculations.Comment: 3 pages 4 figures, submitted to AP

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