Spatial offset of excited states in non-Hermitian lattices

We investigate the behavior of light-wave packets injected into non-Hermitian microcavity lattices under highly dissipative conditions. While all eigenstates of the lattice exhibit exponential decay, a specifically excited state maintains coherent propagation. In a one-dimensional lattice, this state undergoes a spatial displacement shift away from the injection position, which is a fundamental property of non-Hermitian systems with a point gap when the spectrum encircles a finite region in the complex plane. Extending such a shift to two-dimensional lattices reveals a geometrically anomalous $\mathsf{V}$-shaped wave-packet formation with orientation-tunable arms. Notably, this geometric control mechanism enables all-optical steering of non-Hermitian photonic states without requiring structural modifications.