The design of two-dimensional elastic diffusers

Abstract

The ability to design surfaces with specific scattering properties has widespread applicability. In this article, we leverage a stochastic method for designing randomly rough, two-dimensional surfaces with a prescribed mean angular intensity distribution. Analytical and numerical techniques are implemented for a linearly elastic medium-vacuum interface, to generate band-limited diffusers with square and elliptical domains of scattering. Longitudinal incidence is assumed, and the theory allows for bulk wave mode conversions. Multivalued, discontinuous surfaces are formulated, and it is shown that the theoretical model may be satisfied independently of the facet shape utilised, with square and hexagonal discretisations given as examples. In the context of elastic wave scattering, the surfaces presented in this article may have applications in the calibration of scatterometers for wave manipulation as well as for crack detection using ultrasound.