Non-Hermitian impurity problem
In this article, Emmanouil Kokkinakis (Ph.D. Student), Ioannis Komis (Postdoctoral Researcher) and Prof. Konstantinos G. Makris, investigate wave dynamics in two-dimensional nonlinear non-Hermitian photonic lattices. Their work, recently published in Communications Physics, explores how nonlinearity and non-Hermiticity jointly shape light localization and transport in higher-dimensional systems.
Non-Hermitian photonic lattices, characterized by asymmetric couplings, exhibit the so-called non-Hermitian skin effect, where light accumulates at specific edges or corners of the system. While this phenomenon is well understood in linear systems, its interplay with optical nonlinearity, an inherent feature of photonic platforms, remains largely unexplored, especially in two dimensions.
In this work, the authors demonstrate that Kerr nonlinearity introduces a competing mechanism to the skin effect. For localized excitations, sufficiently strong input amplitudes can induce self-trapping, preventing light from drifting toward the preferred lattice corners. Importantly, the threshold for this transition is not universal: it strongly depends on the position of excitation within the lattice and on the degree of coupling asymmetry. Near corners where linear modes are already localized, self-trapping occurs at relatively low powers, while in the lattice bulk it requires significantly higher amplitudes or may even become impossible.
Image: a–c) Bound-state existence maps for infinite one-, two-, and three-dimensional lattices as a function of the real and imaginary parts of the complex impurity strength. Blue regions indicate where bound states exist, while gray regions indicate where bound-state formation is forbidden. d–f) Corresponding trajectories of the bound-state eigenvalue in the complex plane as the impurity strength is varied. These trajectories illustrate the emergence, disappearance, and reappearance of localized bound states in non-Hermitian lattices.
The authors also study finite lattices, which are directly relevant to experimental photonic platforms such as waveguide arrays, optical cavity arrays, and synthetic mesh lattices. In these systems, they find several exotic features, including scale-free localized states, exceptional points, and unusual cross-shaped localized eigenmodes, which differ qualitatively from conventional exponentially localized modes.
These findings deepen the understanding of impurity-induced localization in non-Hermitian systems and may guide future studies of transport, disorder, and localization in photonic and condensed-matter platforms.
Research article: E.T. Kokkinakis, I. Komis, K.G. Makris, & E.N. Economou. Non-Hermitian impurity problem. Commun Phys 9, 152 (2026). https://doi.org/10.1038/s42005-026-02558-y
