arXiv subjects

M. J. A. Smith

Publications and source records attributed to M. J. A. Smith.

12 recordsLinked to original sources

arXiv2022

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

Using a combination of multipole methods and the method of matched asymptotics, 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 very thick-walled limits. Additionally, we examine the impact of dissipation for very 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 crucially, connect these findings to earlier works by the authors on two-dimensional arrays of resonators, deducing that depolarisability effects (off-diagonal terms) for a single resonator do not ensure the existence of Willis coupling effects (bianisotropy) in bulk.

physics.flu-dyn↗

arXiv2022

Two-dimensional Helmholtz resonator arrays. Part I. Matched asymptotic expansions for thick- and thin-walled resonators

We present a novel multipole formulation for computing the band structures of two-dimensional arrays of cylindrical Helmholtz resonators. This formulation is derived by combining existing multipole methods for arrays of ideal cylinders with the method of matched asymptotic expansions. We construct asymptotically close representations for the dispersion equations of the first band surface, correcting and extending an established lowest-order (isotropic) result in the literature for thin-walled resonator arrays. The descriptions we obtain for the first band are accurate over a relatively broad frequency and Bloch vector range and not simply in the long-wavelength and low-frequency regime, as is the case in many classical treatments. Crucially, we are able to capture features of the first band, such as low-frequency anisotropy, over a broad range of filling fractions, wall thicknesses, and aperture angles. In addition to describing the first band we use our formulation to compute the first band gap for both thick- and thin-walled resonators, and find that thicker resonator walls correspond to both a narrowing of the first band gap and an increase in the central band gap frequency.

physics.flu-dyn↗

arXiv2022

Two-dimensional Helmholtz resonator arrays. Part II. Matched asymptotic expansions for specially-scaled resonators

We present a solution method which combines the method of matched asymptotics with the method of multipole expansions to determine the band structure of cylindrical Helmholtz resonators arrays in two dimensions. The resonator geometry is considered in the limit as the wall thickness becomes very large compared with the aperture width (the specially-scaled limit). In this regime, the existing treatment in Part I, with updated parameters, is found to return spurious spectral behaviour. We derive a regularised system which overcomes this issue and also derive compact asymptotic descriptions for the low-frequency dispersion equation in this setting. In the specially-scaled limit, our asymptotic dispersion equation not only recovers the first band surface but also extends to high, but still subwavelength, frequencies. A homogenisation treatment is outlined for describing the effective bulk modulus and effective density tensor of the resonator array for all wall thicknesses. We demonstrate that specially-scaled resonators are able to achieve exceptionally low Helmholtz resonant frequencies, and present closed-form expressions for determining these explicitly. We anticipate that the analytical expressions and the formulation outlined here may prove useful in industrial and other applications.

physics.flu-dyn↗

arXiv2020

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.

physics.flu-dyn↗

arXiv2019

Compression properties of polymeric syntactic foam composites under cyclic loading

Syntactic foams are composite materials frequently used in applications requiring the properties of low density and high damage tolerance. In the present work, polymer-based syntactic foams were studied under cyclic compression in order to investigate their compressibility, recoverability, energy dissipation and damage tolerance. These syntactic foams were manufactured by adding hollow polymer microspheres of various sizes and wall thicknesses into a polyurethane matrix. The associated loading and unloading curves during cyclic testing were recorded, revealing the viscoelastic nature of the materials. SEM images of the samples were obtained in order to study potential damage mechanisms during compression. It was observed that these syntactic foams exhibit high elastic recovery and energy dissipation over a wide range of compressional strains and the addition of polymer microspheres mitigate the damage under compressional loading.

cond-mat.mtrl-sci↗

arXiv2018

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 in all calculations. 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 theoretically predict that a layered medium comprising nanometre-thin layers of silicon and As$_2$S$_3$ glass possesses a bulk SBS gain of $1.28 \times 10^{-9} \, \mathrm{W}^{-1} \, \mathrm{m}$. This is more than 500 times larger than the gain coefficient of silicon, and substantially larger than the gain of As$_2$S$_3$. The enhancement is due to a combination of roto-optic, photoelastic, and artificial photoelastic contributions in the composite structure.

physics.optics↗

arXiv2017

Enhanced acousto-optic properties in layered media

We present a rigorous procedure for evaluating the photoelastic coefficients of a layered medium where the periodicity is smaller than the wavelengths of all optical and acoustic fields. Analytical expressions are given for the coefficients of a composite material comprising thin layers of optically isotropic materials. These coefficients include artificial contributions that are unique to structured media and arise from the optical and mechanical contrast between the constituents. Using numerical examples, we demonstrate that the acousto-optic properties of layered structures can be enhanced beyond those of the constituent materials. Furthermore, we show that the acousto-optic response can be tuned as desired.

physics.optics↗

arXiv2016

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.

physics.optics↗

arXiv2016

Stimulated Brillouin scattering in metamaterials

We compute the SBS gain for a metamaterial comprising a cubic lattice of dielectric spheres suspended in a background dielectric material. Theoretical methods are presented to calculate the optical, acoustic, and opto-acoustic parameters that describe the SBS properties of the material at long wavelengths. Using the electromagnetic and strain energy densities we accurately characterise the optical and acoustic properties of the metamaterial. From a combination of energy density methods and perturbation theory, we recover the appropriate terms of the photoelastic tensor for the metamaterial. We demonstrate that electrostriction is not necessarily the dominant mechanism in the enhancement and suppression of the SBS gain coefficient in a metamaterial, and that other parameters, such as the Brillouin linewidth, can dominate instead. Examples are presented that exhibit an order of magnitude enhancement in the SBS gain as well as perfect suppression.

physics.optics↗

arXiv2016

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 As$_2$S$_3$ 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 As$_2$S$_3$ 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.

physics.optics↗

arXiv2015

Electrostriction enhancement in metamaterials

We demonstrate a controllable enhancement in the electrostrictive properties of a medium using dilute composite artificial materials. Analytical expressions for the composite electrostriction are derived and used to show that enhancement, tunability and suppression can be achieved through a careful choice of constituent materials. Numerical examples with Ag, As$_2$S$_3$, Si and SiO$_2$ demonstrate that even in a non-resonant regime, artificial materials can bring more than a threefold enhancement in the electrostriction.

physics.optics↗

arXiv2014

Trapped Modes and Steered Dirac Cones in Platonic Crystals

This paper discusses the properties of flexural waves obeying the biharmonic equation, propagating in a thin plate pinned at doubly-periodic sets of points. The emphases are on the properties of dispersion surfaces having the Dirac cone topology, and on the related topic of trapped modes in plates with 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 the 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.

math-ph↗