Boundary Effects of Weak Nonlocality in Multilayered Dielectric Metamaterials

TL;DR

This paper investigates how weak nonlocal effects in multilayered dielectric metamaterials can lead to significant boundary phenomena under certain conditions, which are not predicted by standard local effective-medium theories.

Contribution

It introduces a novel approach using error propagation in transfer matrix maps to analyze and identify critical parameters for boundary effects caused by weak nonlocality.

Findings

Weak nonlocality can cause strong boundary effects under specific conditions.

Simple closed-form expressions effectively describe these boundary effects.

Nonlocal corrections can accurately capture the boundary phenomena.

Abstract

Nonlocal (spatial-dispersion) effects in multilayered metamaterials composed of periodic stacks of alternating, deeply subwavelength dielectric layers are known to be negligibly weak. Counterintuitively, under certain critical conditions, weak nonlocality may build up strong boundary effects that are not captured by conventional (local) effective-medium models based on simple mixing formulas. Here, we show that this phenomenon can be fruitfully studied and understood in terms of error propagation in the iterated maps of the trace and anti-trace of the optical transfer matrix of the multilayer. Our approach effectively parameterizes these peculiar effects via remarkably simple and insightful closed-form expressions, which enable direct identification of the critical parameters and regimes. We also show how these boundary effects can be captured by suitable nonlocal corrections.