Algebraic skin effect in two-dimensional non-Hermitian metamaterials

Abstract: Metamaterials have unlocked unprecedented control over light by leveraging novel mechanisms to expand their functionality. Non-Hermitian physics further enhances the tunability of non-Hermitian metamaterials (NHMs) through phenomena such as the non-Hermitian skin effect (NHSE), enabling applications like directional amplification. The higher-dimensional NHSE manifests unique effects, including the algebraic skin effect (ASE), which features power-law decay instead of exponential localization, allowing for quasi-long-range interactions. In this work, we establish apparent criteria for achieving ASE in two-dimensional reciprocal NHMs with anisotropic and complex dielectric tensors. By numerically and theoretically demonstrating ASE through mismatched optical axes and geometric structures, we reveal that ASE is governed by a generalized Fermi surface whose dimensionality exceeds that of the Fermi surface. We further propose and validate a realistic photonic crystal design for ASE, which is experimentally accessible. Our recipe for ASE provides a versatile pathway for broader generalizations, including three-dimensional structures, synthetic dimensions, and other classical wave systems, paving the way for advancements in non-Hermitian photonics.