Algebraic skin effect in two-dimensional non-Hermitian metamaterials

TL;DR

This paper explores the algebraic skin effect in two-dimensional non-Hermitian metamaterials, establishing criteria for its realization, demonstrating it through simulations, and proposing a practical photonic crystal design for experimental observation.

Contribution

It introduces the concept of algebraic skin effect in 2D non-Hermitian metamaterials, providing theoretical criteria, numerical validation, and a feasible design for experimental implementation.

Findings

ASE exhibits power-law decay instead of exponential localization.

ASE is governed by a generalized Fermi surface with higher dimensionality.

A realistic photonic crystal design for observing ASE is proposed and validated.

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.