2D Solitons in PT-symmetric photonic lattices

Over the last few years, parity-time ($\mathcal{P}\mathcal{T}$) symmetry has been the focus of considerable attention. Ever since, pseudo-Hermitian notions have permeated a number of fields ranging from optics to atomic and topological physics, as well as optomechanics, to mention a few. Unlike their Hermitian counterparts, nonconservative systems do not exhibit a priori real eigenvalues and hence unitary evolution. However, once $\mathcal{P}\mathcal{T}$ symmetry is introduced, such dissipative systems can surprisingly display a real eigenspectrum, thus ensuring energy conservation during evolution. In optics, $\mathcal{P}\mathcal{T}$ symmetry can be readily established by incorporating, in a balanced way, regions having an equal amount of optical gain and loss. However, thus far, all optical realizations of such $\mathcal{P}\mathcal{T}$ symmetry have been restricted to a single transverse dimension (1D), such as arrays of optical waveguides or active coupled cavity arrangements. In most cases, only the loss function was modulated---a restrictive aspect that is only appropriate for linear systems. Here, we present an experimental platform for investigating the interplay between $\mathcal{P}\mathcal{T}$ symmetry and nonlinearity in two-dimensional (2D) environments, where nonlinear localization and soliton formation can be observed. In contrast to typical dissipative solitons, we demonstrate a one-parameter family of soliton solutions that are capable of displaying attributes similar to those encountered in nonlinear conservative arrangements. For high optical powers, this new family of $\mathcal{P}\mathcal{T}$ solitons tends to collapse on a discrete network---thus giving rise to an amplified, self-accelerating structure.