Rayleigh–Bloch waves along elastic diffraction gratings

Rayleigh–Bloch waves along elastic diffraction gratings

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. ...

Scattering of plane elastic waves by three-dimensional diffraction gratings

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

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 il...

Elastic interface waves along a fracture

Non-welded interfaces can be treated as a displacement discontinuity characterized by elastic stiffnesses. Applying this boundary condition to a generalized Rayleigh wave, it is shown that a fast and a slow dispersive wave can propagate along the fracture, even when the seismic properties of the rock on each side are identical.

Direct and Inverse Elastic Scattering Problems for Diffraction Gratings

This paper is concerned with the direct and inverse scattering of time-harmonic plane elastic waves by unbounded periodic structures (diffraction gratings). We present a variational approach to the forward scattering problems with Lipschitz grating profiles and give a survey of recent uniqueness and existence results. Concerning the inverse problem, global uniqueness results within the class of...