Discrete solitons and vortices on two-dimensional lattices of $\mathcal{PT}$-symmetric couplers

TL;DR

This paper explores the existence and stability of discrete solitons and vortices in a 2D lattice of $ ext{PT}$-symmetric couplers with nonlinear interactions, revealing stability regions and unique robustness of certain modes.

Contribution

It introduces a novel 2D $ ext{PT}$-symmetric lattice model supporting various solitons and vortices, analyzing their stability and uncovering the spontaneous transformation of unstable vortices into stable fundamental solitons.

Findings

Symmetric fundamental solitons are stable at low power.

Anti-symmetric solitons and vortices are stable at higher power levels.

Unstable vortices spontaneously rebuild into stable fundamental solitons.

Abstract

We introduce a 2D network built of $\mathcal{PT}$-symmetric dimers with on-site cubic nonlinearity, the gain and loss elements of the dimers being linked by parallel square-shaped lattices. The system may be realized as a set of $\mathcal{PT}$-symmetric dual-core waveguides embedded into a photonic crystal. The system supports $\mathcal{PT}$-symmetric and antisymmetric fundamental solitons (FSs) and on-site-centered solitary vortices (OnVs). Stability of these discrete solitons is the central topic of the consideration. Their stability regions in the underlying parameter space are identified through the computation of stability eigenvalues, and verified by direct simulations. Symmetric FSs represent the system's ground state, being stable at lowest values of the power, while anti-symmetric FSs and OnVs are stable at higher powers. Symmetric OnVs, which are also stable at lower powers, are remarkably robust modes: on the contrary to other PT-symmetric states, unstable OnVs do not blow up, but spontaneously rebuild themselves into stable FSs.