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

Abstract

We introduce a 2D network built of $\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$-symmetric dual-core waveguides embedded into a photonic crystal. The system supports $\mathcal{P}\mathcal{T}$-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.

11 pages, 9 figures, and 1 table. Optics Express (focus issue on Nonlinear Photonics), in press

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Cited by in corpus (9)

• Multidimensional dissipative solitons and solitary vortices
• Flat band in two-dimensional non-Hermitian optical lattices
• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• Dipolar bright solitons and solitary vortices in a radial lattice
• Staggered $\mathcal{P}\mathcal{T}$-symmetric ladders with cubic nonlinearity
• Cross-symmetry breaking of two-component discrete dipolar matter-wave solitons
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric systems with spin-orbit coupling and critical nonlinearity
• Spatial Control of Localized Oscillations in Arrays of Coupled Laser Dimers