Two-dimensional intra-band solitons in lattice potentials with local defects and self-focusing nonlinearity

TL;DR

This paper demonstrates the existence of stable two-dimensional embedded defect solitons in lattice potentials with local defects and self-focusing nonlinearity, forming a continuous superfamily across the spectral bands.

Contribution

It introduces the concept of embedded defect solitons in 2D lattices with defects, linking them to gap and regular solitons, and explores their stability and existence conditions.

Findings

Embedded defect solitons exist in the first two Bloch bands.

Stable dipole-mode solitons and vortices are supported by multi-defect structures.

A continuous chain of solitons links the entire bandgap spectrum.

Abstract

It is commonly known that stable bright solitons in periodic potentials, which represent gratings in photonics/plasmonics, or optical lattices in quantum gases, exist either in the spectral semi-infinite gap (SIG) or in finite bandgaps. Using numerical methods, we demonstrate that, under the action of the cubic self-focusing nonlinearity, defects in the form of "holes" in two-dimensional (2D) lattices support continuous families of 2D solitons \textit{embedded} into the first two Bloch bands of the respective linear spectrum, where solitons normally do not exist. The two families of the \textit{embedded defect solitons} (EDSs) are found to be continuously linked by the branch of \textit{gap defect solitons} (GDSs) populating the first finite bandgap. Further, the EDS branch traversing the first band links the GDS family with the branch of regular defect-supported solitons populating the SIG. Thus, we construct a continuous chain of regular, embedded, and gap-mode solitons ("superfamily") threading the entire bandgap structure considered here. The EDSs are stable in the first Bloch band, and partly stable in the second. They exist with the norm exceeding a minimum value, hence they do not originate from linear defect modes. Further, we demonstrate that double, triple and quadruple lattice defects support stable dipole-mode solitons and vortices.