Saddle solitons: a balance between bi-diffraction and hybrid nonlinearity

Abstract

We demonstrate self-trapping of light by simultaneously compensating normal and anomalous (saddleshaped) diffractions with self-focusing and self-defocusing hybrid nonlinearity in optically induced ionic-type photonic lattices. Innovative two-dimensional gap solitons, named "saddle solitons," are established, whose phase and spectrum characteristics are different from all previously observed spatial solitons. © 2009 Optical Society of America OCIS codes: 190.6135, 190.5330, 350.4238. Despite the discovery of a variety of soliton entities in discrete systems [1], to our knowledge, it has not been possible to demonstrate a two-dimensional (2D) spatial soliton in a physical arrangement where an optical beam exhibits simultaneously normal and anomalous diffractions in different transverse directions. First, natural materials typically are not endowed with a saddle-shaped bi-diffractive property; second, it remains a challenge to find a nonlinear material that can support hybrid self-focusing and selfdefocusing nonlinearities without changing experimental conditions. Previous work on nonlinear X waves and light bullets was aimed toward balancing of beam diffraction and pulse dispersion simultaneously, but in spatial domain alone compensation of normal and anomalous diffractions in the same experimental setting has not been realized. Man-made periodic structures have shown many intriguing optical properties. In an optically induced 2D square lattice [2][3][4], for example, the highsymmetry X point in the first Bloch band is akin to a saddle point in diffraction spectrum [see Fig. 1(c)], where normal and anomalous diffractions coexist along orthogonal directions [5]. At this X point, a quasi-1D soliton train can be excited provided that an appropriate type of nonlinearity is used to balance beam diffraction in one particular direction, whereas in the orthogonal direction it is an extended plane wave [6]. The propagation constant of such a 1D soliton train could reside within the first Bloch band, thus named "in-band" or "embedded" solitons [7]. However, to simultaneously balance normal and anomalous diffractions for self-trapping of a 2D-localized optical beam, one needs orientationdependent hybrid nonlinearity. Fortunately, such nonlinearity was found in our recent work with photorefractive nonlinear crystals under nonconventional bias (NCB) condition [8][9][10], in which coexistence of self-focusing and self-defocusing nonlinearities at two orthogonal directions has led to observation of controlled 1D soliton transition from different band edges or subband edges.In this Letter, we employ the hybrid nonlinearity to demonstrate a type of spatial gap solitons, namely, "saddle solitons," by balancing the saddle-shaped diffraction in an optically induced 2D ionic-type lattice [10]. Such solitons have propagation constant residing in the Bragg reflection gap, but they differ from all previously observed solitons supported by a single self-focusing or self-defocusing nonlinearity. In addition, quasi-localized 2D in-band...

Optical spatial solitons: historical overview and recent advances

“…Furthermore, with such hybrid nonlinearity, a new type of spatial gap solitons, namely, 'saddle' solitons, can be established. In fact, Hu et al observed such 'saddle' solitons by balancing the saddle-shaped bi-diffraction with hybrid focusing/defocusing in an optically induced 2D ionic-type lattice [253]. These 'saddle' solitons have a propagation constant residing in the Bragg reflection gap, but they differ from all previously observed solitons supported by a single focusing or defocusing nonlinearity.…”

Interactions of accessible solitons with interfaces in anisotropic media: the case of uniaxial nematic liquid crystals

“…Another type of nonlinearity is associated with the photorefractive response, where non-locality relates to the diffusion of light-induced carriers. In photorefractive media the nonlinear index well is not single-humped for a bell-shaped input and the transition from self-focusing to self-defocusing can be achieved via crystal rotation [21,22].…”

Tunable self-shifting Bloch modes in anisotropic hexagonal photonic lattices

“…According to the Floquet-Bloch theorem, beam propagation in photonic lattices can be analyzed from spatially extended Bloch waves as a complete orthogonal set of allowed eigenmodes of the lattice [2]. In uniform photonic lattices, localized modes characterized by Bloch waves are crucial for understanding the formation of spatial lattice solitons [7][8][9][10][11][12]. Recently, many intriguing linear and nonlinear phenomena have been reported in deformed or anisotropic lattices [5,12].…”

“…Because of the intrinsic anisotropic nonlinearity [13,14], the light-induced photonic lattices possess high anisotropy, which can be tuned by the bias condition [3,11,12]. Under the illumination of the hexagonal lattice beam [see the background of Fig.…”

“…4(c)-4(e) are set to 90°, 0°, and 135°, respectively. The corresponding lattice index profiles are calculated with the anisotropic model [3,[10][11][12], as shown in the insets of Figs. 4(c)-4(e).…”