title: Rayleigh-Bloch waves along elastic diffraction gratings.
abstract: Rayleigh-Bloch (RB) waves in elasticity, in contrast to those in scalar wave systems, appear to have had little attention. Despite the importance of RB waves in applications, their connections to trapped modes and the ubiquitous nature of diffraction gratings, there has been no investigation of whether such waves occur within elastic diffraction gratings for the in-plane vector elastic system. We identify boundary conditions that support such waves and numerical simulations confirm their presence. An asymptotic technique is also developed to generate effective medium homogenized equations for the grating that allows us to replace the detailed microstructure by a continuum representation. Further numerical simulations confirm that the asymptotic scheme captures the essential features of these waves.
authors.affiliation: Department of Mathematics , Imperial College London , London SW7 2AZ, UK.
authors.forename: D J
authors.identifier: 0000-0001-5637-1626
authors.initials: DJ
authors.lastname: Colquitt
authors.affiliation: Department of Mathematics , Imperial College London , London SW7 2AZ, UK.
authors.forename: R V
authors.initials: RV
authors.lastname: Craster
authors.affiliation: Department of Mathematics , Imperial College London , London SW7 2AZ, UK ; 80 Capital LLP, London W1S 4JJ, UK.
authors.forename: T
authors.initials: T
authors.lastname: Antonakakis
authors.affiliation: Institut Fresnel, UMR CNRS 7249, University of Aix-Marseille, Marseille, France.
authors.forename: S
authors.initials: S
authors.lastname: Guenneau
keywords: elastic waves; homogenization; plasmonics