Fig. 7: Propagation dynamics in a 2D Hatano–Nelson lattice for the focusing and defocusing Kerr-nonlinear cases.
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 \({\psi }_{{n}_{x},{n}_{y}}(z=0)=A{e}^{-[{({n}_{x}-{x}_{c})}^{2}+{({n}_{y}-{y}_{c})}^{2}]}/2{w}^{2}\), with xc = yc = 13, w = 2, where the excitation amplitude A is such that the optical power is \({{{{\mathcal{P}}}}}_{{{{\rm{HN}}}}}(z=0)=20\). Normalized amplitude \(| {\psi }_{{n}_{x},{n}_{y}}(z)|\) (color map) for the focusing case at propagation distances a z = 0, b z = 1.5, c z = 3, and d z = 6. e–h Normalized amplitude \(| {\psi }_{{n}_{x},{n}_{y}}(z)|\) for the defocusing case at the same propagation distances. In all color maps, the wavefunctions are normalized such that their maximum amplitude equals unity.
