Finite-size effects in wave transmission through plasmonic crystals: A tale of two scales

TL;DR

This paper investigates how finite-sized layered plasmonic structures influence wave transmission, comparing detailed models with homogenized approximations, and highlights the importance of geometry-dependent effects and resonances.

Contribution

It introduces a combined analytical and numerical approach to model wave transmission in layered plasmonic crystals, emphasizing the role of a geometry-dependent corrector field.

Findings

Homogenized models accurately predict transmission for small layer numbers.

The corrector field captures surface plasmon effects and lateral resonances.

Finite-size effects significantly influence wave transmission properties.

Abstract

We study optical coefficients that characterize wave propagation through layered structures called plasmonic crystals. These consist of a finite number of stacked metallic sheets embedded in dielectric hosts with a subwavelength spacing. By adjustment of the frequency, spacing, number as well as geometry of the layers, these structures may exhibit appealing transmission properties in a range of frequencies from the terahertz to the mid-infrared regime. Our approach uses a blend of analytical and numerical methods for the distinct geometries with infinite, translation invariant, flat sheets and nanoribbons. We describe the transmission of plane waves through a plasmonic crystal in comparison to an effective dielectric slab of equal total thickness that emerges from homogenization, in the limit of zero interlayer spacing. We demonstrate numerically that the replacement of the discrete plasmonic crystal by its homogenized counterpart can accurately capture a transmission coefficient akin to the extinction spectrum, even for a relatively small number of layers. We point out the role of a geometry-dependent corrector field, which expresses the effect of subwavelength surface plasmons. In particular, by use of the corrector we describe lateral resonances inherent to the nanoribbon geometry.