title: An asymptotic theory for waves guided by diffraction gratings or along microstructured surfaces.
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, for example, 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 with full numerical simulations. We also investigate non-periodic situations where a long-scale geometrical variation in the structure is introduced and show that localized defect states emerge which the asymptotic theory explains.
authors.affiliation: Department of Mathematics , Imperial College London , London SW7 2AZ, UK ; European Organization for Nuclear Research, CERN 1211, Geneva 23, Switzerland.
authors.forename: T
authors.initials: T
authors.lastname: Antonakakis
authors.affiliation: Department of Mathematics , Imperial College London , London SW7 2AZ, UK.
authors.forename: R V
authors.initials: RV
authors.lastname: Craster
authors.affiliation: Institut Fresnel , UMR CNRS 7249, Aix-Marseille Université, Ecole Centrale Marseille, 13013 Marseille, France.
authors.forename: S
authors.initials: S
authors.lastname: Guenneau
authors.affiliation: Department of Mathematics , Imperial College London , London SW7 2AZ, UK.
authors.forename: E A
authors.initials: EA
authors.lastname: Skelton
keywords: Rayleigh–Bloch waves; homogenization; plasmonics