Interface solitons in two-dimensional photonic lattices

Abstract

We analyze localization of light at the interface separating square and hexagonal photonic lattices, as recently realized experimentally in two-dimensional laser-written waveguide arrays in silica glass with self-focusing nonlinearity [A. Szameit et al., Opt. Lett. 33, 663 (2008)]. We reveal the conditions for the existence of linear and nonlinear surface states substantially influenced by the lattice topology, and study the effect of the different symmetries and couplings on the stability of two-dimensional interface solitons. OCIS codes: 190.4420; 190.5530; 190.5940 Theoretical results on the existence of novel types of discrete surface solitons localized in the corners or at the edges of two-dimensional photonic lattices [1,2,3] have been recently confirmed by the experimental observation of two-dimensional surface solitons in opticallyinduced photonic lattices [4] and two-dimensional waveguide arrays laser-written in fused silica [5,6]. These twodimensional nonlinear surface modes demonstrate novel features in comparison with their counterparts in truncated one-dimensional waveguide arrays [7,8,9]. In particular, in a sharp contrast to one-dimensional discrete surface solitons, the mode threshold is lower at the surface than in a bulk making the mode excitation easier [2].Recently, Szameit et al.[10] reported on the first experimental observation of two-dimensional interface solitons, i.e. spatial optical solitons generated at the interface separating square and hexagonal optical lattices with different refractive index modulation depths. Such twodimensional interface solitons feature asymmetric shapes, while differences in array properties and lattice topology strongly affect the threshold power for soliton existence and excitation as well as soliton stability.In this Letter, we study this problem analytically in a more general setting and analyze localization of light at the interface separating two lattices of different symmetries in the framework of the two-dimensional discrete nonlinear model. We assume that the interface is created between the square and hexagonal two-dimensional optical lattices, similar to the case studied earlier [10], but we assume the coupling parameters to be different and study the effect of different symmetries and lattice topology, as well as the coupling strength of the interface on the existence and stability of both linear and nonlinear surface states. In particular, we determine the conditions for the thresholdless surface states (linear surface modes) that appear due to the breaking of the lattice topology, and also study the nonlinear localization and generation

Vortex solitons at the interface between two photonic lattices

“…In this paper, we extend this analysis to the case of vortex solitons supported by different interfaces separating square and hexagonal photonic lattices [25,26]. We study a more general case and investigate vortex solitons at the interface separating two lattices of different symmetries.…”

Asymmetric defects in one-dimensional photonic lattices

“…Defects can be obtained, accidentally or deliberately, by varying the geometry of the lattice or its refractive index. The geometry of the lattice can be changed by adding an interface between two sublattices that form a composite lattice [15][16][17], by changing the width of a waveguide so that it differs from other waveguides in the array or by setting a spacing between two waveguides to be different from the rest of the array [18,19]. These changes enable the occurrence of different types of strongly localized modes.…”

Interface localization of light in disordered photonic lattices

“…In optics, surface waves are known to exist at an interface between continuous and periodic media [19], and also at the interface between a homogeneous lattice and a superlattice [20]. Recently, interface solitons have also been observed at the interfaces separating square and hexagonal photonic lattices with different refractive-index modulation depths [21,22].…”