Asymptotic theory of microstructured surfaces: An asymptotic theory for waves guided by diffraction gratings or along microstructured surfaces

TL;DR

This paper develops an asymptotic surface equation to model microstructured surfaces, accurately capturing wave phenomena like Rayleigh-Bloch waves and Spoof Surface Plasmon Polaritons, including effects of defects and non-periodic structures.

Contribution

The paper introduces a new asymptotic theory that effectively models wave behavior on microstructured surfaces, including non-periodic variations and defect states.

Findings

Accurately reproduces Rayleigh-Bloch wave features.

Extends to waves along gratings and non-periodic structures.

Explains localized defect states with asymptotic theory.

Abstract

An effective surface equation, that encapsulates the detail of a microstructure, is developed to model microstructured surfaces. The equations deduced accurately reproduce a key feature of surface wave phenomena, created by periodic geometry, that are commonly called Rayleigh-Bloch waves, but which also go under other names such as Spoof Surface Plasmon Polaritons in photonics. Several illustrative examples are considered and it is shown that the theory extends to similar waves that propagate along gratings. Line source excitation is considered and an implicit long-scale wavelength is identified and compared to full numerical simulations. We also investigate non-periodic situations where a long-scale geometric variation in the structure is introduced and show that localised defect states emerge which the asymptotic theory explains.