Observation of Surface Gap Solitons in Semi-Infinite Waveguide Arrays

Abstract

We report on the first observation of surface gap solitons, recently predicted to exist at the interface between uniform and periodic dielectric media with defocusing nonlinearity [Ya. V. Kartashov et al., Phys. Rev. Lett. 96, 073901 (2006)]. We demonstrate strong self-trapping at the edge of a LiNbO3 waveguide array and the formation of staggered surface solitons with propagation constant inside the first photonic band gap. We study the crossover between linear repulsion and nonlinear attraction at the surface, revealing the mechanism of nonlinearity-mediated stabilization of the surface gap modes.PACS numbers: 42.65. Tg, 42.65.Sf5, 42.65.Wi Interfaces between different physical media can support a special class of localized waves known as surface waves or surface modes. In periodic systems, staggered surface modes are often referred to as Tamm states [1], first identified as localized electronic states at the edge of a truncated periodic potential. Because of the difficulties in observing this type of surface waves in natural materials such as crystals, successful efforts were made to demonstrate their existence in nano-engineered periodic structures or superlattices [2]. An optical analog of linear Tamm states has been described theoretically and demonstrated experimentally for an interface separating periodic and homogeneous dielectric media [3,4].Nonlinear surface waves have been studied in different fields of physics and most extensively in optics where surface TE and TM modes were predicted and analyzed for the interfaces between two different homogeneous nonlinear dielectric media [5,6,7]. In addition, nonlinear effects have been shown to stabilize surface waves in discrete systems, generating different types of modes localized at and near the surface [8]. Self-trapping of light near the boundary of a self-focusing photonic lattice has recently been predicted theoretically [9] and demonstrated in experiment [10] through the formation of discrete surface solitons at the edge of a waveguide array.Recently, Kartashov et al. [11] predicted theoretically the existence of surface gap solitons at the interface between a uniform medium and a photonic lattice with defocusing nonlinearity. In such systems, light localization occurs inside a photonic bandgap in the form of staggered surface modes. This enables us to draw an analogy with the localized electronic Tamm states and extend it to the nonlinear regime, so that the surface gap solitons can be termed as nonlinear Tamm states. They posses a unique combination of properties related to both electronic and optical surface waves and discrete optical gap solitons. The ability to generate such surface gap solitons could provide novel and effective experimental tools for the study of nonlinear effects near surfaces with possible applications in optical sensing and switching.In this Letter we study experimentally self-action of a narrow beam propagating near the edge of a LiNbO 3 waveguide array with defocusing nonlinearity. For the first time to our knowledge, ...

Discrete surface solitons in two-dimensional anisotropic photonic lattices

“…That can be understood as the localization of a discrete optical soliton near the surface [4] for powers exceeding a certain threshold value, for which the repulsive effect of the surface is balanced. A similar effect of light localization near the edge of the waveguide array and the formation of surface gap solitons have been predicted and observed for defocusing nonlinear media [5,6].…”

“…That can be understood as the localization of a discrete optical soliton near the surface [4] for powers exceeding a certain threshold value, for which the repulsive effect of the surface is balanced. A similar effect of light localization near the edge of the waveguide array and the formation of surface gap solitons have been predicted and observed for defocusing nonlinear media [5,6].It is important to analyze how the properties of nonlinear surface waves are modified by the lattice dimensionality, and the first studies of different types of discrete surface solitons in two-dimensional lattices [7,8,9,10] revealed, in particular, that the presence of a surface increases the stability region for two-dimensional (2D) discrete solitons [10] and the threshold power for the edge surface state is slightly higher than that for the corner soliton [9].In this Letter we consider anisotropic semi-infinite twodimensional photonic lattices and study the crossover between one-and two-dimensional surface solitons emphasizing the crucial effect of the lattice dimensionality on the formation of surface solitons.We consider a semi-infinite 2D lattice [shown schematically in Fig.2(a) below], described by the system of coupled-mode equations for the normalized amplitudes u n,m [11,12],where ξ is the normalized propagation distance. We de- fine the lattice coupling as follows:…”

Interaction of highly nonlinear solitary waves with linear elastic media

“…In particular, the study of interfaces between linear and nonlinear optical media has allowed the observation of interesting spatially localized phenomena known as optical Tamm states [7]. In linear lattice structures, acoustic localization has been reported in association with the boundary conditions [4] and with the presence of local defects in an otherwise periodical system [5].…”

Multipole-mode interface solitons in quadratic nonlinear photonic lattices

“…Recently, the interest in the study of electromagnetic surface waves has been renewed after the theoretical prediction [5] and subsequent experimental demonstration [6] of nonlinearity-induced self-trapping of light near the edge of a one-dimensional waveguide array with self-focusing nonlinearity, that can lead to the formation of a discrete surface soliton. A related effect of light localization and the formation of surface gap solitons have been predicted theoretically and observed experimentally for defocusing periodic nonlinear media [7,8]. In addition, the concept of nonlinear surface and gap solitons has been extended to the case of an interface separating two different nonlinear periodic media [9,10,11,12].…”