Observation of Two-Dimensional Surface Solitons

Wang, Qianqian; Bezryadina, Anna; Chen, Zhigang; Makris, Konstantinos G.; Christodoulides, Demetrios N.; Stegeman, George I.

doi:10.1103/physrevlett.98.123903

Cited by 166 publications

(88 citation statements)

References 28 publications

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“…Special attention was given to two-dimensional (2D) geometries [2,9-11]. 2D surface solitons were observed in optically induced lattices [12] and in laser-written waveguide arrays [13,14]. However, up to now the impact of the geometry of the interface on the properties of 2D surface solitons was not addressed properly.…”

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confidence: 99%

Angular surface solitons in sectorial hexagonal arrays

et al. 2008

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We report on the experimental observation of corner surface solitons localized at the edges joining planar interfaces of hexagonal waveguide array with uniform nonlinear medium. The face angle between these interfaces has a strong impact on the threshold of soliton excitation as well as on the light energy drift and diffraction spreading.OCIS codes: 190.0190, 190.6135 Over the last several years there has been growing interest to linear and nonlinear optical surface waves. After the prediction of discrete surface solitons at the interface of uniform material and waveguide array with focusing nonlinearity [1] and at the interface between dissimilar arrays [2] and their subsequent observations [3][4][5], a burst of new findings revolutionized the perception of nonlinear surface waves. For example, solitons were also found at the edge of defocusing lattices [6][7][8]. Special attention was given to two-dimensional (2D) geometries [2,9-11]. 2D surface solitons were observed in optically induced lattices [12] and in laser-written waveguide arrays [13,14]. However, up to now the impact of the geometry of the interface on the properties of 2D surface solitons was not addressed properly. To bridge this gap, we report in this Letter the salient features of 2D solitons localized at the edges joining planar interfaces of a hexagonal waveguide array with a uniform nonlinear medium and show that the face angle is the key parameter defining the power threshold for soliton excitation and the direction of the light energy drift and diffraction spreading.

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confidence: 99%

Angular surface solitons in sectorial hexagonal arrays

et al. 2008

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“…reflection, the discrete diffraction is stronger in the direction perpendicular to the interface than in the direction parallel to it [4][5][6][7][8], therefore the surface modes feature stronger nonlinearity, which is necessary to balance the diffraction.…”

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confidence: 99%

Bulk vortices and half-vortex surface modes in parity-time-symmetric media

Zhu

Shi

et al. 2014

Phys. Rev. A

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We demonstrate that in-bulk vortex localized modes, and their surface half-vortex ("horseshoe") counterparts self-trap in two-dimensional (2D) nonlinear optical systems with PT -symmetric photonic lattices (PLs). The respective stability regions are identified in the underlying parameter space. The in-bulk states are related to truncated nonlinear Bloch waves in gaps of the PL-induced spectrum. The basic vortex and horseshoe modes are built, severally, of four and three beams with appropriate phase shifts between them. Their stable complex counterparts, built of up to 12 beams, are reported too.PACS numbers: 03.65. Ge, 11.30.Er, 42.65.Sf, 42.65.Tg Nonlinear spatially periodic systems support diverse types of self-trapped in-gap states. In particular, spatial gap solitons [1,2] originate from the interplay between the periodicity and nonlinearity. Further, surface gap solitons [4][5][6][7][8] appear at the interface between a uniform medium and a photonic lattice (PL) built into a nonlinear material. Extended self-trapped waves with steep edges also exist in these settings, being related to truncated nonlinear Bloch waves [9,10]. Modes of the latter type provide a link between extended nonlinear Bloch waves [11,12] and tightly localized gap solitons [1][2][3].Recently, a great deal of interest has been drawn to the realization of parity-time (PT ) symmetry in optics. Originally, this concept was developed in quantum mechanics, where it was demonstrated that, beyond the conventional Hermitian Hamiltonians, their PTsymmetric non-Hermitian counterparts may also give rise to purely real (hence physically relevant) spectra [13][14][15][16]. Following the similarity between quantum mechanics and paraxial optics [17,18], PT -symmetric optical systems with complex refractive indices [19,20] have been extensively studied theoretically [21][22][23][24][25][26][27][28][29][30][31][32][33] and experimentally [34][35][36][37][38][39][40][41]. In this context, PT -symmetric PLs play an important role. Taking into account the non-orthogonality of the respective eigenmodes, their coupled-mode description had to be reformulated via the variational principle [21]. The light propagation in PTsymmetric PLs embedded into linear media were analyzed preliminarily [24,42]. Further, it has been found that 1D and 2D spatial gap solitons exist in PLs built into a nonlinear material [23,[43][44][45][46][47].Although PT -symmetric systems combining lattices and nonlinearity was not reported yet. In particular, such self-trapped nonlinear states may serve as a necessary link between spatially localized gap solitons and extended nonlinear Bloch waves under the PT symmetry.Self-trapped vortices and surface modes are of great interest in the context of the PT -symmetric settings. Indeed, the study of nonlinear surface modes pinned on the interface of a PT -symmetric system opens a way to explore the interplay between surface effects, the nonlinearity, and the PT -symmetry. On the other hand, the analysis of localized vortices supported by PT ...

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“…Recent observations of two-dimensional surface solitons in optically-induced photonic lattices [15] and laser-written waveguide arrays in fused silica [16] demonstrated novel features of these nonlinear surface modes in comparison with their counterparts in one-dimensional waveguide arrays.…”

Section: Introductionmentioning

confidence: 99%

Surface solitons in chirped photonic lattices

et al. 2007

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We study surface modes in semi-infinite chirped two-dimensional photonic lattices in the framework of an effective discrete nonlinear model. We demonstrate that the lattice chirp can change dramatically the conditions for the mode localization near the surface, and we find numerically the families of surface modes, in linear lattices, and discrete surface solitons, in nonlinear lattices.We demonstrate that, in a sharp contrast to one-dimensional discrete surface solitons, in twodimensional lattices the mode threshold power is lowered by the action of both the surface and lattice chirp. By manipulating with the lattice chirp, we can control the mode position and its localization.

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Observation of Two-Dimensional Surface Solitons

Cited by 166 publications

References 28 publications

Angular surface solitons in sectorial hexagonal arrays

Angular surface solitons in sectorial hexagonal arrays

Bulk vortices and half-vortex surface modes in parity-time-symmetric media

Surface solitons in chirped photonic lattices

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