Two-dimensional flat-band solitons in superhoneycomb lattices

TL;DR

This paper demonstrates the existence and stability of various flat-band solitons in a continuous superhoneycomb lattice, revealing new light localization phenomena in nonlinear flat-band systems.

Contribution

It introduces stable flat-band solitons in a continuous superhoneycomb lattice, expanding understanding of flat-band physics beyond discrete models.

Findings

Stable fundamental, dipole, multi-peak, and vortex solitons identified.

Solitons are stable over a broad power range.

Solitons do not bifurcate from the flat band and are described as Wannier solitons.

Abstract

Flat-band periodic materials are characterized by a linear spectrum containing at least one band where the propagation constant remains nearly constant irrespective of the Bloch momentum across the Brillouin zone. These materials provide a unique platform for investigating phenomena related to light localization. Meantime, the interaction between flat-band physics and nonlinearity in continuous systems remains largely unexplored, particularly in continuous systems where the band flatness deviates slightly from zero, in contrast to simplified discrete systems with exactly flat bands. Here, we use a continuous superhoneycomb lattice featuring a flat band in its spectrum to theoretically and numerically introduce a range of stable flatband solitons. These solutions encompass fundamental, dipole, multi-peak, and even vortex solitons. Numerical analysis demonstrates that these solitons are stable in a broad range of powers. They do not bifurcate from the flat band and can be analyzed using Wannier function expansion leading to their designation as Wannier solitons. These solitons showcase novel possibilities for light localization and transmission within nonlinear flat-band systems.