Asymptotics of the meta-atom: plane wave scattering by a single Helmholtz resonator.

Using a combination of multipole methods and the method of matched asymptotic expansions, we present a solution procedure for acoustic plane wave scattering by a single Helmholtz resonator in two dimensions. Closed-form representations for the multipole scattering coefficients of the resonator are derived, valid at low frequencies, with three fundamental configurations examined in detail: the thin-walled, moderately thick-walled and extremely thick-walled limits. Additionally, we examine the impact of dissipation for extremely thick-walled resonators, and also numerically evaluate the scattering, absorption and extinction cross-sections (efficiencies) for representative resonators in all three wall thickness regimes. In general, we observe strong enhancement in both the scattered fields and cross-sections at the Helmholtz resonance frequencies. As expected, dissipation is shown to shift the resonance frequency, reduce the amplitude of the field, and reduce the extinction efficiency at the fundamental Helmholtz resonance. Finally, we confirm results in the literature on Willis-like coupling effects for this resonator design, and connect these findings to earlier works by several of the authors on two-dimensional arrays of resonators, deducing that depolarizability effects (off-diagonal terms) for a single resonator do not ensure the existence of Willis coupling effects (bianisotropy) in bulk. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

On the Wiener-Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate.

A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener-Hopf technique. The derivation of the Wiener-Hopf equation is rather different from that which is used traditionally in water-waves problems, and it leads to the required equations directly. It is also shown how the solution can be computed straightforwardly using Cauchy-type integrals, which avoids the need to find the roots of the highly non-trivial dispersion equations. We illustrate the method with some numerical computations, focusing on the evolution of an incident wave pulse which illustrates the existence of two transmitted waves in the submerged plate system. The effect of the porosity is studied, and it is shown to influence the shorter-wavelength pulse much more strongly than the longer-wavelength pulse.

Stimulated Brillouin scattering in layered media: nanoscale enhancement of silicon.

We report a theoretical study of stimulated Brillouin scattering (SBS) in general anisotropic media, incorporating the effects of both acoustic strain and local rotation. We apply our general theoretical framework to compute the SBS gain for layered media with periodic length scales smaller than all optical and acoustic wavelengths, where such composites behave like homogeneous anisotropic media. We predict that a layered medium composing nanometer-thin layers of silicon and As2S3 glass has a bulk SBS gain of 1.28×10-9 W-1 m. This is more than 500 times larger than that of silicon and almost double the gain of As2S3. The enhancement is due to a combination of roto-optic, photoelastic, and artificial photoelastic contributions in the composite structure.

Stimulated Brillouin scattering enhancement in silicon inverse opal waveguides.

Silicon is an ideal material for on-chip applications, however its poor acoustic properties limit its performance for important optoacoustic applications, particularly for stimulated Brillouin scattering (SBS). We theoretically show that silicon inverse opals exhibit a strongly improved acoustic performance that enhances the bulk SBS gain coefficient by more than two orders of magnitude. We also design a waveguide that incorporates silicon inverse opals and which has SBS gain values that are comparable with chalcogenide glass waveguides. This research opens new directions for opto-acoustic applications in on-chip material systems.

Metamaterial control of stimulated Brillouin scattering.

Using full opto-acoustic numerical simulations, we demonstrate enhancement and suppression of the SBS gain in a metamaterial comprising a subwavelength cubic array of dielectric spheres suspended in a dielectric background material. We develop a general theoretical framework and present several numerical examples using technologically important materials. For As2S3 spheres in silicon, we achieve a gain enhancement of more than an order of magnitude compared to pure silicon and for GaAs spheres in silicon, full suppression is obtained. The gain for As2S3 glass can also be strongly suppressed by embedding silica spheres. The constituent terms of the gain coefficient are shown to depend in a complex way on the filling fraction. We find that electrostriction is the dominant effect behind the control of SBS in bulk media.

'Parabolic' trapped modes and steered Dirac cones in platonic crystals.

This paper discusses the properties of flexural waves governed by the biharmonic operator, and propagating in a thin plate pinned at doubly periodic sets of points. The emphases are on the design of dispersion surfaces having the Dirac cone topology, and on the related topic of trapped modes in plates for a finite set (cluster) of pinned points. The Dirac cone topologies we exhibit have at least two cones touching at a point in the reciprocal lattice, augmented by another band passing through the point. We show that these Dirac cones can be steered along symmetry lines in the Brillouin zone by varying the aspect ratio of rectangular lattices of pins, and that, as the cones are moved, the involved band surfaces tilt. We link Dirac points with a parabolic profile in their neighbourhood, and the characteristic of this parabolic profile decides the direction of propagation of the trapped mode in finite clusters.