arXiv subjects

Richard V. Craster

Publications and source records attributed to Richard V. Craster.

53 records · Page 3Linked to original sources

arXiv2019

Graded metasurface for enhanced sensing and energy harvesting

In elastic wave systems, combining the powerful concepts of resonance and spatial grading within structured surface arrays enable resonant metasurfaces to exhibit broadband wave focusing, mode conversion from surface (Rayleigh) waves to bulk (shear) waves, and spatial frequency selection. Devices built around these concepts allow for precise control of surface waves, often with structures that are subwavelength, and utilise rainbow trapping that separates the signal spatially by frequency. Rainbow trapping yields large amplifications of displacement at the resonator positions where each frequency component accumulates. We investigate whether this amplification, and the associated control, can be used to create energy harvesting devices; the potential advantages and disadvantages of using graded resonant devices as energy harvesters is considered. We concentrate upon elastic plate models for which the A0 mode dominates, and take advantage of the large displacement amplitudes in graded resonant arrays of rods, to design innovative metasurfaces that focus waves for enhanced piezoelectric sensing and energy harvesting. Numerical simulation allows us to identify the advantages of such graded metasurface devices and quantify its efficiency, we also develop accurate models of the phenomena and extend our analysis to that of an elastic half-space and Rayleigh surface waves.

physics.class-ph↗

arXiv2019

Flat Lensing by Graded Line Meta-arrays

Motivated by flat lensing effects, now commonplace utilising negative refraction with finite slabs, we create negative refraction upon a graded line-array. We do so in the setting of flexural waves on a structured Kirchhoff--Love elastic plate, as a paradigm in wave physics, that has direct extensions to electromagnetic and acoustic wave systems. These graded line arrays are geometrically simple and provide strong coupling from the array into the bulk. Thorough analysis of the dispersion curves, and associated mode structure, of these meta--arrays, supported by mode coupling theory, creates array guided wave (AGW) reversal and hybridisation into the bulk that leads to striking wave control via generalised flat lensing.

physics.class-ph↗

arXiv2018

Extraordinarily transparent compact metallic metamaterials

Metals are highly opaque, yet we show that densely packed arrays of metallic nanoparticles can be more transparent to infrared radiation than dielectrics such as germanium, even for arrays that are over 75% metal by volume. Despite strong interactions between the metallic particles, these arrays form effective dielectrics that are virtually dispersion-free, making possible the design of optical components that are achromatic over ultra-broadband ranges of wavelengths from a few microns up to millimetres or more. Furthermore, the local refractive indices may be tuned by altering the size, shape, and spacing of the nanoparticles, allowing the design of gradient-index lenses that guide and focus light on the microscale. The electric field is also strongly concentrated in the gaps between the metallic nanoparticles, and the simultaneous focusing and squeezing of the electric field produces strong `doubly-enhanced' hotspots which could boost measurements made using infrared spectroscopy and other non-linear processes over a broad range of frequencies, with minimal heat production.

physics.optics↗

arXiv2018

Spectral algorithms for reaction-diffusion equations

A collection of codes (in MATLAB & Fortran 77), and examples, for solving reaction-diffusion equations in one and two space dimensions is presented. In areas of the mathematical community spectral methods are used to remove the stiffness associated with the diffusive terms in a reaction-diffusion model allowing explicit high order timestepping to be used. This is particularly valuable for two (and higher) space dimension problems. Our aim here is to provide codes, together with examples, to allow practioners to easily utilize, understand and implement these ideas; we incorporate recent theoretical advances such as exponential time differencing methods and provide timings and error comparisons with other more standard approaches. The examples are chosen from the literature to illustrate points and queries that naturally arise.

math.NA↗

arXiv2018

Asymptotic modelling of phononic box crystals

We introduce phononic box crystals, namely arrays of adjoined perforated boxes, as a three-dimensional prototype for an unusual class of subwavelength metamaterials based on directly coupling resonating elements. In this case, when the holes coupling the boxes are small, we create networks of Helmholtz resonators with nearest-neighbour interactions. We use matched asymptotic expansions, in the small hole limit, to derive simple, yet asymptotically accurate, discrete wave equations governing the pressure field. These network equations readily furnish analytical dispersion relations for box arrays, slabs and crystals, that agree favourably with finite-element simulations of the physical problem. Our results reveal that the entire acoustic branch is uniformly squeezed into a subwavelength regime; consequently, phononic box crystals exhibit nonlinear-dispersion effects (such as dynamic anisotropy) in a relatively wide band, as well as a high effective refractive index in the long-wavelength limit. We also study the sound field produced by sources placed within one of the boxes by comparing and contrasting monopole- with dipole-type forcing; for the former the pressure field is asymptotically enhanced whilst for the latter there is no asymptotic enhancement and the translation from the microscale to the discrete description entails evaluating singular limits, using a regularized and efficient scheme, of the Neumann's Green's function for a cube. We conclude with an example of using our asymptotic framework to calculate localized modes trapped within a defected box array.

physics.app-ph↗

arXiv2017

Asymptotic network models of subwavelength metamaterials formed by closely packed photonic and phononic crystals

We demonstrate that photonic and phononic crystals consisting of closely spaced inclusions constitute a versatile class of subwavelength metamaterials. Intuitively, the voids and narrow gaps that characterise the crystal form an interconnected network of Helmholtz-like resonators. We use this intuition to argue that these continuous photonic (phononic) crystals are in fact asymptotically equivalent, at low frequencies, to discrete capacitor-inductor (mass-spring) networks whose lumped parameters we derive explicitly. The crystals are tantamount to metamaterials as their entire acoustic branch, or branches when the discrete analogue is polyatomic, is squeezed into a subwavelength regime where the ratio of wavelength to period scales like the ratio of period to gap width raised to the power 1/4; at yet larger wavelengths we accordingly find a comparably large effective refractive index. The fully analytical dispersion relations predicted by the discrete models yield dispersion curves that agree with those from finite-element simulations of the continuous crystals. The insight gained from the network approach is used to show that, surprisingly, the continuum created by a closely packed hexagonal lattice of cylinders is represented by a discrete honeycomb lattice. The analogy is utilised to show that the hexagonal continuum lattice has a Dirac-point degeneracy that is lifted in a controlled manner by specifying the area of a symmetry-breaking defect.

physics.optics↗

arXiv2017

Enhanced sensing and conversion of ultrasonic Rayleigh waves by elastic metasurfaces

Recent years have heralded the introduction of metasurfaces that advantageously combine the vision of sub- wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. An important topic within metasurfaces is the tailored rainbow trapping and selective spatial frequency separation of electromagnetic and acoustic waves using graded metasurfaces. This frequency dependent trapping and spatial frequency segregation has implications for energy concentrators and associated energy harvesting, sensing and wave filtering techniques. Different demonstrations of acoustic and electromagnetic rainbow devices have been performed, however not for deep elastic substrates that support both shear and compressional waves, together with surface Rayleigh waves; these allow not only for Rayleigh wave rainbow effects to exist but also for mode conversion from surface into bulk waves. We design, and test experimentally, a device creating not only elastic Rayleigh wave rainbow trapping, but also selective mode conversion of surface Rayleigh waves to shear waves.

physics.class-ph↗

arXiv2017

An Interface-Tracking Technique for Multiphase Flow with Soluble Surfactant

We adapt and extend a formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu & Tryggvason (JCP 274 (2014) 737-757) to the context of the Level Contour Reconstruction Method (Shin et al. IJNMF 60 (2009) 753-778) which is a hybrid method that combines the advantages of the Front-tracking and Level Set methods. Particularly close attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with experiments and results from previous simulations. All benchmarking tests compare well with existing data thus providing confidence that our adapted LCRM formulation for surfactant advection and diffusion is accurate and effective in three-dimensional multiphase flows. We also demonstrate that this approach applies easily to massively parallel simulations.

cs.CE↗

arXiv2016

Van der Waals force assisted heat transfer for vacuum gap spacings

Phonons (collective atomic vibrations in solids) are more effective in transporting heat than photons. This is the reason why the conduction mode of heat transport in nonmetals (mediated by phonons) is dominant compared to the radiation mode of heat transport (mediated by photons). However, since phonons are unable to traverse a vacuum gap (unlike photons) it is commonly believed that two bodies separated by a gap cannot exchange heat via phonons. Recently, a mechanism was proposed by which phonons can transport heat across a vacuum gap - through Van der Waals interaction between two bodies with gap less than wavelength of light. Such heat transfer mechanisms are highly relevant for heating (and cooling) of nanostructures; the heating of the flying heads in magnetic storage disks is a case in point. Here, the theoretical derivation for modeling phonon transmission is revisited and extended to the case of two bodies made of different materials separated by a vacuum gap. Magnitudes of phonon transmission, and hence the heat transfer, for commonly used materials in the micro and nano-electromechanical industry are calculated and compared with the calculation of conduction heat transfer through air for small gaps.

cond-mat.mes-hall↗

arXiv2016

Controlling flexural waves in semi-infinite platonic crystals

We address the problem of scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several classes of point defects, including mass-spring resonators attached to the top surface of the flexural plate and their limiting case of concentrated point masses. We also analyse the special case of resonators attached to opposite faces of the plate. The problem is reduced to a functional equation of the Wiener-Hopf type, whose kernel varies with the type of scatterer considered. A novel approach, which stems from the direct connection between the kernel function of the semi-infinite system and the quasi-periodic Green's functions for corresponding infinite systems, is used to identify special frequency regimes. We thereby demonstrate dynamically anisotropic wave effects in semi-infinite platonic crystals, with particular attention paid to designing systems to exhibit dynamic neutrality (perfect transmission) and localisation close to the structured interface.

physics.class-ph↗

arXiv2016

High frequency homogenization for travelling waves in periodic media

We consider high frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schr{ö}dinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wave vector $\Bk$ and frequency $ω_1$ plus a modulated Bloch carrier wave having crystal wave vector $\Bm$ and frequency $ω_2$. We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless $ω_1=ω_2$ and $(\Bk-\Bm)\odotΛ\in 2π\mathbb Z^d,$ where $Λ=(λ_1λ_2\dotsλ_d)$ is the periodicity cell of the medium and for any two vectors $a=(a_1,a_2,\dots,a_d), b=(b_1,b_2,\dots,b_d)\in\mathbb R^d,$ the product $a\odot b$ is defined to be the vector $(a_1b_1,a_2b_2,\dots,a_db_d).$ This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigor as that of Allaire and coworkers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.

math.AP↗

arXiv2016

Surface-plasmon resonances of arbitrarily shaped nanometallic structures in the small-screening-length limit

According to the hydrodynamic Drude model, surface-plasmon resonances of metallic nanostructures blueshift owing to the nonlocal response of the metal's electron gas. The screening length characterising the nonlocal effect is often small relative to the overall dimensions of the metallic structure, which enables us to derive a coarse-grained nonlocal description using matched asymptotic expansions; a perturbation theory for the blueshifts of arbitrary shaped nanometallic structures is then developed. The effect of nonlocality is not always a perturbation and we present a detailed analysis of the "bonding" modes of a dimer of nearly touching nanowires where the leading-order eigenfrequencies and eigenmode distributions are shown to be a renormalisation of those predicted assuming a local metal permittivity.

physics.optics↗

arXiv2016

Bloch waves in an arbitrary two-dimensional lattice of subwavelength Dirichlet scatterers

We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions, the scatterers are effectively replaced by asymptotic point constraints. The resulting coarse-grained Bloch-wave dispersion problem is solved by a generalised Fourier series, whose singular asymptotics in the vicinities of scatterers yield the dispersion relation governing modes that are strongly perturbed from plane-wave solutions existing in the absence of the scatterers; there are also empty-lattice waves that are only weakly perturbed. Characterising the latter is useful in interpreting and potentially designing the dispersion diagrams of such lattices. The method presented, that simplifies and expands on Krynkin & McIver [Waves Random Complex, 19 347 2009], could be applied in the future to study more sophisticated designs entailing resonant subwavelength elements distributed over a lattice with periodicity on the order of the operating wavelength.

physics.class-ph↗

arXiv2015

Asymptotics of surface-plasmon redshift saturation at sub-nanometric separations

Many promising nanophotonics endeavours hinge upon the unique plasmonic properties of nanometallic structures with narrow non-metallic gaps, which support super-concentrated bonding modes that singularly redshift with decreasing separations. In this letter, we present a descriptive physical picture, complemented by elementary asymptotic formulae, of a nonlocal mechanism for plasmon-redshift saturation at subnanometric gap widths. Thus, by considering the electron-charge and field distributions in the close vicinity of the metal-vacuum interface, we show that nonlocality is asymptotically manifested as an effective potential discontinuity. For bonding modes in the near-contact limit, the latter discontinuity is shown to be effectively equivalent to a widening of the gap. As a consequence, the resonance-frequency near-contact asymptotics are a renormalisation of the corresponding local ones. Specifically, the renormalisation furnishes an asymptotic plasmon-frequency lower bound that scales with the $1/4$-power of the Fermi wavelength. We demonstrate these remarkable features in the prototypical cases of nanowire and nanosphere dimers, showing agreement between our elementary expressions and previously reported numerical computations.

physics.optics↗

arXiv2015

Dynamic interfacial trapping of flexural waves in structured plates

The paper presents new results on localisation and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, surface waves are identified and studied at the interface boundary between the homogeneous part of the flexural plate and the part occupied by rigid pins. A formal connection has been made with the dispersion properties of flexural Bloch waves in an infinite doubly periodic array of rigid pins. Special attention is given to regimes corresponding to standing waves of different types as well as Dirac-like points, that may occur on the dispersion surfaces. A single half-grating problem, hitherto unreported in the literature, is also shown to bring interesting solutions.

math.AP↗

arXiv2013

Asymptotic theory of microstructured surfaces: 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 such as Spoof Surface Plasmon Polaritons in photonics. Several illustrative examples are considered and it is shown that the theory extends to similar waves that propagate along gratings. Line source excitation is considered and an implicit long-scale wavelength is identified and compared to full numerical simulations. We also investigate non-periodic situations where a long-scale geometric variation in the structure is introduced and show that localised defect states emerge which the asymptotic theory explains.

physics.optics↗

arXiv2011

On a class of three-phase checkerboards with unusual effective properties

We examine the band spectrum, and associated Floquet-Bloch eigensolutions, arising in a class of three-phase periodic checkerboards. On a periodic cell $[-1,1[^2$, the refractive index is defined by $n^2= 1+ g_1(x_1)+g_2(x_2)$ with $g_i(x_i)= r^2\quad {\rm for} \quad 0\leq x_i<1, \hbox{and} g_i(x_i)= 0\quad {\rm for} \quad -1\leq x_i\leq 0$ where $r^2$ is constant. We find that for $r^2>-1$ the lowest frequency branch goes through origin with linear behaviour, which leads to effective properties encountered in most periodic structures. However, the case whereby $r^2=-1$ is very unusual, as the frequency $λ$ behaves like $\sqrt{k}$ near the origin, where $k$ is the wavenumber. Finally, when $r^2<-1$, the lowest branch does not pass through the origin and a zero-frequency band gap opens up. In the last two cases, effective medium theory breaks down even in the quasi-static limit, while the high-frequency homogenization [Craster et al., Proc. Roy. Soc. Lond. A 466, 2341-2362, 2010] neatly captures the detailed features of band diagrams.

physics.optics↗