# Spoof surface plasmons guided by narrow grooves

## TL;DR

This paper develops an approximate analytical model for surface waves on periodically grooved surfaces, revealing resonant behaviors and field localization, with applications to acoustic and electromagnetic waveguides.

## Contribution

It introduces a new simplified dispersion relation for surface waves on narrow-groove gratings, improving accuracy over previous models and covering different propagation regimes.

## Key findings

- Analytical dispersion relation matches well with exact calculations.
- Resonant enhancement of fields within grooves at specific regimes.
- Maximal field localization occurs near groove resonance.

## Abstract

An approximate description of surface waves propagating along periodically grooved surfaces is intuitively developed in the limit where the grooves are narrow relative to the period. Considering acoustic and electromagnetic waves guided by rigid and perfectly conducting gratings, respectively, the wave field is obtained by interrelating elementary approximations obtained in three overlapping spatial domains. Specifically, above the grating and on the scale of the period the grooves are effectively reduced to point resonators characterised by their dimensions as well as the geometry of their apertures. Along with this descriptive physical picture emerges an analytical dispersion relation, which agrees remarkably well with exact calculations and improves on preceding approximations. Scalings and explicit formulae are obtained by simplifying the theory in three distinguished propagation regimes, namely where the Bloch wavenumber is respectively smaller than, close to, or larger than that corresponding to a groove resonance. Of particular interest is the latter regime where the field within the grooves is resonantly enhanced and the field above the grating is maximally localised, attenuating on a length scale comparable with the period.