Fig. 2: Propagation in a 2D Hatano–Nelson lattice for the linear and Kerr-nonlinear case.
From: Self-trapping and skin solitons in two-dimensional non-Hermitian lattices
For all panels, the non-Hermiticity parameter is h = 0.2 and the initial condition is \({\psi }_{{n}_{x},{n}_{y}}(z=0)=A\,{\delta }_{{n}_{x},13}{\delta }_{{n}_{y},13}\). a–c Normalized amplitude \(| {\psi }_{{n}_{x},{n}_{y}}(z)|\) (color map) for the linear case at propagation distances z = 1, z = 3.5, and z = 6, respectively. e–g Normalized amplitude \(| {\psi }_{{n}_{x},{n}_{y}}(z)|\) (color map) for the nonlinear case with input amplitude A = 4 at the same propagation distances. In all color maps, the wavefunctions are normalized such that their maximum amplitude equals unity. d, h Evolution of the total optical power \({{{{\mathcal{P}}}}}_{{{{\rm{HN}}}}}\) (red) and the on-site intensity at the initially excited site ∣ψ13,13∣2 (blue) for the linear and nonlinear cases, respectively; insets provide zoom-in views of the curves.
