Integrated acoustic multilayer metasurfaces for high degree of diffractive functionality

Abstract

Phase-gradient metasurfaces exhibit diverse extraordinary diffractive behaviors. These range from reflective or transmissive scattering of an incident wave toward any targeted direction to temporal trapping of waves inside structures. The behaviors are determined by the design parameters, phase gradient and number of discrete unit cells within a supercell. In this study, we propose a higher-level design scheme by integrating a stack of multiple metasurfaces. We focus on a case with negligible separation in which the constituent metasurfaces perfectly interact with each other. A significantly higher degree of diffractive behavior compared with that of a conventional single layer is observed for multilayer metasurfaces specifically in the regime above the critical angle. The scattering angular characteristics can be enriched remarkably in multilayers because, unlike in a single layer, the transformation of the incident tangential wavenumber is not restricted by the number of integer multiples of the phase gradient. The wavenumber transform is available for the entire range of incident angles in multilayers, whereas it is available only for half of this range in a single layer. The temporal duration of internal wave trapping can also be enhanced dramatically in multilayers because the supercell periodicity can be effectively lengthened from those of the constituents by combining different phase gradients. To our knowledge, this is the first report of the distinctive diffractive behaviors of multilayer metasurfaces, particularly for an incident angle above the critical angle. To fully describe the underlying physics, we derive a generalized diffraction law that robustly addresses the multilayers by proposing a novel physical concept to straightforwardly connect repetitive phase accumulations inside metasurface unit cells to diffraction. The reciprocal lattice of a unit cell, rather than that of a supercell, is observed to play an important role in determining dominant scattering. The proposed theories are thoroughly verified by analytical and numerical simulations.