# ProfessorRichardCraster

Faculty of Natural Sciences

Dean of the Faculty of Natural Sciences

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### Contact

+44 (0)20 7594 8554r.craster

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### Assistant

Ms Mary Scott +44 (0)20 7594 5477

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### Location

3.05Faculty BuildingSouth Kensington Campus

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## Publications

Publication Type
Year
to

317 results found

Putley HJ, Chaplain GJ, Rakotoarimanga-Andrianjaka H, Maling B, Craster RVet al., 2021, Whispering-Bloch elastic circuits, Wave Motion, Vol: 105, Pages: 1-19, ISSN: 0165-2125

We investigate structured arrays and rings in elasticity to design elastic platonic circuitsthat utilise resonant phenomena. Creating ring resonators, and understanding theircoupling to input and output arrays, allows for the development of platonic circuitsincluding add–drop filters (ADFs) and coupled resonator elastic arrays (CREAs), andhence we envisage integrated platonic devices. Structured rings of point-masses placedatop a thin elastic plate lead to highly confined quasi-modes that leak energy; theleakage being quantified by the limiting quality factor Q. The conditions of resonanceare deduced using highly accurate numerical simulations based on a Green’s functionapproach to solve the dispersion relation associated with the structured ring resonators.The sharp resonances that emerge are then used to filter and direct wave energy basedon input frequency, and this is illustrated through analogy with devices used in optics,e.g. integrated photonic circuits. The potential applications of the elastic devices includeelastic delay lines and passive energy harvesters.

Journal article

Balmforth NJ, Craster R, Hewitt DR, 2021, Building on Oldroyd's viscoplastic legacy: Perspectives and new developments, Journal of Non-Newtonian Fluid Mechanics, Vol: 294, ISSN: 0377-0257

The decade following the second world war heralded the publication of a collection of important papers on non-Newtonian fluid mechanics; Oldroyd’s work featured heavily in this collection. Not only did these articles establish important results, but Oldroyd’s style and methods set the scene for subsequent work in the area, exploiting mathematical analysis to formulate problems, establish results and guide further research. While Oldroyd’s name will forever be linked with the study of elastic fluids, the purpose of the present paper is to offer a modern perspective on a number of Oldroyd’s papers on viscoplastic fluids from 1947–1951 [1], [2], [3], [4], [5], [6], [7], [8]. Along the way, we sprinkle in a brief review of some of the subsequent developments stemming from Oldroyd’s advances, together with a few new results guided by his work. Following the approach of most of Oldroyd’s original papers, we focus on unidirectional flow down conduits. In an Appendix, we complement this discussion with a lubrication analysis, extending, clarifying and correcting the important original analysis of Walton and Bittleston (1991) [9]; although lubrication theory was not directly utilized by Oldroyd, the methodology aligns with his philosophy of using asymptotic and analytical approaches.

Journal article

Laforge N, Wiltshaw R, Craster RV, Laude V, Martínez JAI, Dupont G, Guenneau S, Kadic M, Makwana MPet al., 2021, Acoustic topological circuitry in square and rectangular phononic crystals, Physical Review Applied, Vol: 15, Pages: 1-13, ISSN: 2331-7019

We systematically engineer a series of square and rectangular phononiccrystals to create experimental realisations of complex topological phononiccircuits. The exotic topological transport observed is wholly reliant upon theunderlying structure which must belong to either a square or rectangularlattice system and not to any hexagonal-based structure. The phononic systemchosen consists of a periodic array of square steel bars which partitionsacoustic waves in water over a broadband range of frequencies (~0.5 MHz). Anultrasonic transducer launches an acoustic pulse which propagates along adomain wall, before encountering a nodal point, from which the acoustic signalpartitions towards three exit ports. Numerical simulations are performed toclearly illustrate the highly resolved edge states as well as corroborate ourexperimental findings. To achieve complete control over the flow of energy,power division and redirection devices are required. The tunability afforded byour designs, in conjunction with the topological robustness of the modes, willresult in their assimilation into acoustical devices.

Journal article

Quadrelli DE, Craster R, Kadic M, Braghin Fet al., 2021, Elastic wave near-cloaking, Extreme Mechanics Letters, Vol: 44, Pages: 1-8, ISSN: 2352-4316

Cloaking elastic waves has, in contrast to the cloaking of electromagnetic waves, remained a fundamental challenge: the latter successfully uses the invariance of Maxwell’s equations, from which the field of transformational optics has emerged, whereas the elastic Navier equations are not invariant under coordinate transformations. Our aim is to overcome this challenge, at least in practical terms, and thereby unlock applications in mechanics, ultrasound, vibration mitigation, non-destructive evaluation and elastic wave control. We achieve near-cloaking by recognizing that, despite the lack of invariance, a decoupling into a system of form invariant potential equations together with a quantifiable approximation, can be used effectively in many cases to control the flow of elastodynamic waves. Here, in particular we focus on the efficiency and practicability of the proposed near-cloaking which is illustrated using carpet cloaks to hide surface defects from incoming compressional and shear in-plane waves and from surface elastic Rayleigh waves.

Journal article

Chaplain GJ, Craster RV, 2021, Surface corrugated laminates as elastic grating couplers: Splitting of SV- and P-waves by selective diffraction, Journal of Applied Physics, Vol: 129, Pages: 1-10, ISSN: 0021-8979

The phenomenon of selective diffraction is extended to in-plane elastic waves, and we design surface corrugated periodic laminates that incorporate crystal momentum transfer, which, due to the rich physics embedded within the vector elastic system, results in frequency, angle, and wave-type selective diffraction. The resulting devices are elastic grating couplers, with additional capabilities as compared to analogous scalar electromagnetic couplers, in that the elastic couplers possess the ability to split and independently redirect, through selective negative refraction, the two body waves present in the vector elastic system: P- (compressional) and SV- (shear-vertical) elastic waves. The design paradigm, and interpretation, is aided by obtaining isofrequency contours via a non-dimensionalized transfer matrix method.

Journal article

Batchvarov A, Kahouadji L, Constante-Amores CR, Norões Gonçalves GF, Shin S, Chergui J, Juric D, Craster RV, Matar OKet al., 2021, Three-dimensional dynamics of falling films in the presence of insoluble surfactants, Journal of Fluid Mechanics, Vol: 906, Pages: A16-1-A16-13, ISSN: 0022-1120

We study the effect of insoluble surfactants on the wave dynamics of vertically falling liquid films. We use three-dimensional numerical simulations and employ a hybrid interface-tracking/level-set method, taking into account Marangoni stresses induced by gradients of interfacial surfactant concentration. Our numerical predictions for the evolution of the surfactant-free, three-dimensional wave topology are validated against the experimental work of Park & Nosoko (AIChE J., vol. 49, 2003, pp. 2715–2727). The addition of surfactants is found to influence significantly the development of horseshoe-shaped waves. At low Marangoni numbers, we show that the wave fronts exhibit spanwise oscillations before eventually acquiring a quasi-two-dimensional shape. In addition, the presence of Marangoni stresses is found to suppress the peaks of the travelling waves and preceding capillary wave structures. At high Marangoni numbers, a near-complete rigidification of the interface is observed.

Journal article

Haslinger SG, Lowe MJS, Craster R, Huthwaite P, Shi Fet al., 2021, Prediction of reflection amplitudes for ultrasonic inspection of rough planar defects, Insight, Vol: 63, Pages: 28-36, ISSN: 2156-485X

The characteristics of planar defects (no loss of material volume) that arise during industrial plant operation are difficult to predict in detail, yet these can affect the performance of non-destructive testing (NDT) used to manage plant structural integrity. Inspection modelling is increasingly used to design and assess ultrasonic inspections of such plant items. While modelling of smooth planar defects is relatively mature and validated, issues have remained in the treatment of rough planar defect species. The qualification of ultrasonic inspections for such defects is presently very conservative, owing to the uncertainty of the amplitudes of rough surface reflections. Pragmatic solutions include the addition of large sensitivity thresholds and more frequent inspection intervals, which require more plant downtime. In this article, an alternative approach has been developed by the authors to predict the expected surface reflection from a rough defect using a theoretical statistical model. Given only the frequency, angle of incidence and two statistical parameter values used to characterise the defects, the expected reflection amplitude is obtained rapidly for any scattering angle and size of defect, for both compression and shear waves. The method is applicable for inspections of isotropic media that feature surface reflections such as pulse-echo or pitch-catch, rather than for tip signal-dependent techniques such as time-of-flight diffraction. The potential impact for inspection qualification is significant, with the new model predicting increases of up to 20 dB in signal amplitude in comparison with models presently used in industry. All mode conversions are included and rigorous validations using numerical and experimental methods have been performed. The model has been instrumental in obtaining new statistically significant results related to the effect of tilt; the expected pulse-echo backscattered amplitude for very rough planar defects is independent of til

Journal article

Craster R, Diatta A, Guenneau S, Hutridurga Het al., 2021, On near-cloaking for linear elasticity, Multiscale Modeling & Simulation, Vol: 19, Pages: 633-664, ISSN: 1540-3459

We make precise some results on the cloaking of displacement fields in linear elasticity. In the spirit of transformation media theory, the transformed governing equations in Cosseratand Willis frameworks are shown to be equivalent to certain high-contrast small defect problems forthe usual Navier equations. We discuss near-cloaking for elasticity systems via a regularized transform and perform numerical experiments to illustrate our near-cloaking results. We also study thesharpness of the estimates from [H. Ammari, H. Kang, K. Kim, and H. Lee, J. Differential Equations,254 (2013), pp. 4446--4464], wherein the convergence of the solutions to the transmission problems isinvestigated, when the Lam\'e parameters in the inclusion tend to extreme values. Both soft and hardinclusion limits are studied and we also touch upon the finite frequency case. Finally, we propose anapproximate isotropic cloak algorithm for a symmetrized Cosserat cloak.

Journal article

Wiltshaw R, Craster R, Makwana M, 2020, Asymptotic approximations for Bloch waves and topological mode steering in a planar array of Neumann scatterers, Wave Motion, Vol: 99, ISSN: 0165-2125

We study the canonical problem of wave scattering by periodic arrays, either of infinite or finite extent, of Neumann scatterers in the plane; the characteristic lengthscale of the scatterers is considered small relative to the lattice period. We utilise the method of matched asymptotic expansions, together with Fourier series representations, to create an efficient and accurate numerical approach for finding the dispersion curves associated with Floquet-Bloch waves through an infinite array of scatterers. The approach also lends itself to direct scattering problems for finite arrays and we illustrate the flexibility of these asymptotic representations on some topical examples from topological wave physics.

Journal article

Tang K, Makwana MP, Craster RV, Sebbah Pet al., 2020, Observations of symmetry induced topological mode steering in a reconfigurable elastic plate, Physical Review B, Vol: 102, ISSN: 2469-9969

We experimentally investigate the valley-Hall effect for interfacial edge states, highlighting the importance of the modal patterns between geometrically distinct regions within a structured elastic plate. These experiments, for vibration, are at a scale where detailed measurements are taken throughout the system and not just at the input/output ports; this exposes the coupling between geometrically distinct modes that underlie the differences between wave transport around gentle and sharp bends.

Journal article

Chaplain GJ, Ponti JMD, Aguzzi G, Colombi A, Craster RVet al., 2020, Topological rainbow trapping for elastic energy harvesting in graded Su-Schrieffer-Heeger systems, Applied Physics Letters, Vol: 14, Pages: 054035 – 1-054035 – 15, ISSN: 0003-6951

We amalgamate two fundamental designs from distinct areas of wave control in physics, and place them in the setting of elasticity. Graded elastic metasurfaces, so-called metawedges, are combined with the now classical Su-Schrieffer-Heeger (SSH) model from the field of topological insulators. The resulting structures form one-dimensional graded-SSH-metawedges that support multiple, simultaneous, topologically protected edge states. These robust, enhanced localised modes are leveraged for applications in elastic energy harvesting using the piezoelectric effect. The designs we develop are first motivated by applying the SSH model to mass-loaded Kirchhoff-Love thin elastic plates. We then extend these ideas to using graded resonant rods, and create SSH models, coupled to elastic beams and full elastic half-spaces.

Journal article

De Ponti JM, Colombi A, Riva E, Ardito R, Braghin F, Corigliano A, Craster RVet al., 2020, Experimental investigation of amplification, via a mechanical delay-line, in a rainbow-based metamaterial for energy harvesting, Applied Physics Letters, Vol: 117, Pages: 143902-1-143902-6, ISSN: 0003-6951

We experimentally demonstrate that a rainbow-based metamaterial, created by a graded array of resonant rods attached to an elastic beam, operates as a mechanical delay-line by slowing down surface elastic waves to take advantage of wave interaction with resonance. Experiments demonstrate that the rainbow effect reduces the amplitude of the propagating wave in the host structure. At the same time, it dramatically increases both the period of interaction between the waves and the resonators and the wavefield amplitude in the rod endowed with the harvester. Increased energy is thus fed into the resonators over time: we show the enhanced energy harvesting capabilities of this system.

Journal article

Makwana M, Wiltshaw R, Guenneau S, Craster Ret al., 2020, Hybrid topological guiding mechanisms for photonic crystal fibers, Optics Express, Vol: 28, Pages: 30871-30888, ISSN: 1094-4087

We create hybrid topological-photonic localisation of light by introducing concepts from the field of topological matter to that of photonic crystal fiber arrays. S-polarized obliquely propagating electromagnetic waves are guided by hexagonal, and square, lattice topological systems along an array of infinitely conducting fibers. The theory utilises perfectly periodic arrays that, in frequency space, have gapped Dirac cones producing band gaps demarcated by pronounced valleys locally imbued with a nonzero local topological quantity. These broken symmetry-induced stop-bands allow for localised guidance of electromagnetic edge-waves along the crystal fiber axis. Finite element simulations, complemented by asymptotic techniques, demonstrate the effectiveness of the proposed designs for localising energy in finite arrays in a robust manner.

Journal article

Proctor M, Xiao X, Craster RV, Maier SA, Giannini V, Arroyo Huidobro Pet al., 2020, Near- and far-field excitation of topological plasmonic metasurfaces, Photonics, Vol: 7, ISSN: 2304-6732

The breathing honeycomb lattice hosts a topologically non-trivial bulk phase due to the crystalline-symmetry of the system. Pseudospin-dependent edge states, which emerge at the interface between trivial and non-trivial regions, can be used for the directional propagation of energy. Using the plasmonic metasurface as an example system, we probe these states in the near- and far-field using a semi-analytical model. We provide the conditions under which directionality was observed and show that it is source position dependent. By probing with circularly-polarised magnetic dipoles out of the plane, we first characterise modes along the interface in terms of the enhancement of source emissions due to the metasurface. We then excite from the far-field with non-zero orbital angular momentum beams. The position-dependent directionality holds true for all classical wave systems with a breathing honeycomb lattice. Our results show that a metasurfac,e in combination with a chiral two-dimensional material, could be used to guide light effectively on the nanoscale.

Journal article

Batchvarov A, Kahouadji L, Magnini M, Constante-Amores CR, Shin S, Chergui J, Juric D, Craster RV, Matar OKet al., 2020, Effect of surfactant on elongated bubbles in capillary tubes at high Reynolds number, Physical Review Fluids, Vol: 5, Pages: 093605 – 1-093605 – 21, ISSN: 2469-990X

The effect of surfactants on the tail and film dynamics of elongated gas bubbles propagating through circular capillary tubes is investigated by means of an extensive three-dimensional numerical study using a hybrid front-tracking/level-set method. The focus is on the visco-inertial regime, which occurs when the Reynolds number of the flow is much larger than unity. Under these conditions, “clean” bubbles exhibit interface undulations in the proximity of the tail, with an amplitude that increases with the Reynolds number. We perform a systematic analysis of the impact of a wide range of surfactant properties, including elasticity, bulk surfactant concentration, solubility, and diffusivity, on the bubble and flow dynamics in the presence of inertial effects. The results show that the introduction of surfactants is effective in suppressing the tail undulations as they tend to accumulate near the bubble tail. Here large Marangoni stresses are generated, which lead to a local “rigidification” of the bubble. This effect becomes more pronounced for larger surfactant elasticities and adsorption depths. At reduced surfactant solubility, a thicker rigid film region forms at the bubble rear, where a Couette film flow is established, while undulations still appear at the trailing edge of the downstream “clean” film region. In such conditions, the bubble length becomes an influential parameter, with short bubbles becoming completely rigid.

Journal article

Varma TV, Ungureanu B, Sarkar S, Craster R, Guenneau S, Brule Set al., 2020, The influence of structure geometry and material on seismic metamaterial performance, Publisher: arXiv

Diverting, and controlling, elastic vibrations impacting upon infrastructureis a major challenge for seismic hazard mitigation, and for the reduction ofmachine noise and vehicle vibration in the urban environment. Seismicmetamaterials (SMs), with their inherent ability to manipulate wavepropagation, provide a key route for overcoming the technological hurdlesinvolved in this challenge. Engineering the structure of the SM serves as abasis to tune and enhance its functionality, and inspired by split rings,swiss-rolls, notch-shaped and labyrinthine designs of elementary cells inelectromagnetic and mechanical metamaterials, we investigate altering thestructure geometries of SMs with the aim of creating large bandgaps\textcolor{black}{in a subwavelength regime}. We show that square stiffinclusions, perform better in comparison to circular ones, whilst keeping thesame filling fraction. En route to enhancing the bandgap, we have also studiedthe performance of SMs with different constituent materials; we find that steelcolumns, as inclusions, show large bandgaps, however, the columns are too largefor steel to be a feasible material in practical or financial terms.Non-reinforced concrete would be preferable for industry level scaling up ofthe technology because, concrete is cost-effective, easy to cast directly atthe construction site and easy to provide arbitrary geometry of the structure.As a part of this study, we show that concrete columns can also be designed toexhibit bandgaps if we cast them within a soft soil coating surrounding theprotected area for various civil structures like a bridge, building, oilpipelines etc.

Working paper

Wang Y-T, Craster R, 2020, Designing hyper-thin acoustic metasurfaces with membrane resonators, Publisher: arXiv

We design extremely-thin acoustic metasurfaces, providing a versatileplatform for the manipulation of reflected pressure fields, that areconstructed from mass loads and stretched membranes fixed to a periodic rigidframework. These metasurfaces demonstrate deeply subwavelength control and canhave thicknesses an order of magnitude less than those based around Helmholtzresonators. Each sub-unit of the metasurface is resonant at a frequency tunedgeometrically, this tunability provides phase control and using a set of finelytuned membrane resonators we create a phase-grating metasurface. This surfaceis designed to exhibit all-angle negative reflections with the ratio ofwavelength, $\lambda$, to thickness, $h$, of $\lambda/h\approx 23.1$, and tocreate a flat mirror using the phase profile of an elliptic reflecting mirror.A further important acoustic application is to sound diffusers and we proceedto design a deeply subwavelength membrane-based meta-diffuser that can be twoorders of magnitude thinner than the operating wavelength, i.e. thickness$\approx\lambda/102$. This paves the way for developing advanced acousticmetasurfaces with applicability to functional acoustic devices in sound-relatedindustries.

Working paper

Chaplain GJ, Ponti JMD, Colombi A, Fuentes-Dominguez R, Dryburg P, Pieris D, Smith RJ, Clare A, Clark M, Craster RVet al., 2020, Tailored elastic surface to body wave Umklapp conversion, Nature Communications, Vol: 11, ISSN: 2041-1723

Elastic waves guided along surfaces dominate applications in geophysics, ultrasonic inspection, mechanical vibration, and surface acoustic wave devices; precise manipulation of surface Rayleigh waves and their coupling with polarised body waves presents a challenge that offers to unlock the flexibility in wave transport required for efficient energy harvesting and vibration mitigation devices. We design elastic metasurfaces, consisting of a graded array of rod resonators attached to an elastic substrate that, together with critical insight from Umklapp scattering in phonon-electron systems, allow us to leverage the transfer of crystal momentum; we mode-convert Rayleigh surface waves into bulk waves that form tunable beams. Experiments, theory and simulation verify that these tailored Umklapp mechanisms play a key role in coupling surface Rayleigh waves to reversed bulk shear and compressional waves independently, thereby creating passive self-phased arrays allowing for tunable redirection and wave focusing within the bulk medium.

Journal article

Archer AJ, Wolgamot HA, Orszaghova J, Bennetts LG, Peter MA, Craster RVet al., 2020, Experimental realization of broadband control of water-wave-energy amplification in chirped arrays, Physical Review Fluids, Vol: 5, Pages: 62801(R) – 1-62801(R) – 8, ISSN: 2469-990X

Water waves in natural environments are typically broadband, nonlinear anddynamic phenomena. Taking concepts developed for slow light in optics, weaddress the challenge of designing arrays to control the spatial distributionof wave energy, and amplify target frequencies at specified locations.Experiments on incident waves interacting with a chirped array of eightvertical cylinders demonstrate significant amplifications as predictednumerically, and provide motivation for application to energy harvesting.

Journal article

Chaplain GJ, Pajer D, De Ponti JM, Craster RVet al., 2020, Delineating rainbow reflection and trapping with applications for energy harvesting, New Journal of Physics, Vol: 22, Pages: 1-12, ISSN: 1367-2630

Important distinctions are made between two related wave control mechanisms that act to spatially separate frequency components; these so-called rainbow mechanisms either slow or reverse guided waves propagating along a graded line array. We demonstrate an important nuance distinguishing rainbow reflection from genuine rainbow trapping and show the implications of this distinction for energy harvesting designs, through inspection of the interaction time between slowed zero group velocity waves and the array. The difference between these related mechanisms is highlighted using a design methodology, applied to flexural waves on mass loaded thin Kirchhoff-Love elastic plates, and emphasised through simulations for energy harvesting in the setting of elasticity, by elastic metasurfaces of graded line arrays of resonant rods atop a beam. The delineation of these two effects, reflection and trapping, allows us to characterise the behaviour of forced line array systems and predict their capabilities for trapping, conversion and focusing of energy.

Journal article

Chaplain GJ, Craster R, 2020, Ultrathin entirely flat Umklapp lenses, Physical Review B: Condensed Matter and Materials Physics, Vol: 101, Pages: 155430 – 1-155430 – 9, ISSN: 1098-0121

We design ultra-thin, entirely flat, dielectric lenses using crystal momentum transfer, so-called Umklapp processes, achieving the required wave control for a new mechanism of flat lensing; physically, these lenses take advantage of abrupt changes in the periodicity of a structured line array so there is an overlap between the first Brillouin zone of one medium with the second Brillouin zone of the other. At the interface between regions of different periodicity, surface, array guided waves hybridize into reversed propagating beams directed into the material exterior to the array. This control, and redirection, of waves then enables the device to emulate a Pendry-Veselago lens that is one unit cell in width, with no need for an explicit negative refractive index. Simulations using an array embedded in an idealized slab of silicon nitride (Si3N4) in air, operating at visible wavelengths between 420–500THz demonstrate the effect.

Journal article

Makwana M, Laforge N, Craster R, Dupont G, Guenneau S, Laude V, Kadic Met al., 2020, Experimental observations of topologically guided water waves within non-hexagonal structures, Applied Physics Letters, Vol: 116, Pages: 131603-1-131603-5, ISSN: 0003-6951

We investigate symmetry-protected topological water waves within a strategically engineered square lattice system. Thus far, symmetry-protected topological modes in hexagonal systems have primarily been studied in electromagnetism and acoustics, i.e. dispersionless media. Herein, we show experimentally how crucial geometrical properties of square structures allow for topological transport that is ordinarily forbidden within conventional hexagonal structures. We perform numerical simulations that take into account the inherent dispersion within water waves and devise a topological insulator that supports symmetry-protected transport along the domain walls. Our measurements, viewed with a high-speed camera under stroboscopic illumination, unambiguously demonstrate the valley-locked transport of water waves within a non-hexagonal structure. Due to the tunability of the energy's directionality by geometry, our results could be used for developing highly-efficient energy harvesters, filters and beam-splitters within dispersive media.

Journal article

Haslinger SG, Lowe MJS, Huthwaite P, Craster RV, Shi Fet al., 2020, Elastic shear wave scattering by randomly rough surfaces, Journal of the Mechanics and Physics of Solids, Vol: 137, Pages: 1-20, ISSN: 0022-5096

Characterizing cracks within elastic media forms an important aspect of ultrasonic non-destructive evaluation (NDE) where techniques such as time-of-flight diffraction and pulse-echo are often used with the presumption of scattering from smooth, straight cracks. However, cracks are rarely straight, or smooth, and recent attention has focussed upon rough surface scattering primarily by longitudinal wave excitations.We provide a comprehensive study of scattering by incident shear waves, thus far neglected in models of rough surface scattering despite their practical importance in the detection of surface-breaking defects, using modelling, simulation and supporting experiments. The scattering of incident shear waves introduces challenges, largely absent in the longitudinal case, related to surface wave mode-conversion, the reduced range of validity of the Kirchhoff approximation (KA) as compared with longitudinal incidence, and an increased importance of correlation length.The expected reflection from a rough defect is predicted using a statistical model from which, given the angle of incidence and two statistical parameters, the expected reflection amplitude is obtained instantaneously for any scattering angle and length of defect. If the ratio of correlation length to defect length exceeds a critical value, which we determine, there is an explicit dependence of the scattering results on correlation length, and we modify the modelling to find this dependence. The modelling is cross-correlated against Monte Carlo simulations of many different surface profiles, sharing the same statistical parameter values, using numerical simulation via ray models (KA) and finite element (FE) methods accelerated with a GPU implementation. Additionally we provide experimental validations that demonstrate the accuracy of our predictions.

Journal article

Ungureanu B, Makwana M, Craster R, Guenneau Set al., 2020, Localising symmetry protected edge waves via the topological rainbow effect, Publisher: arXiv

We combine two different fields, topological physics and metamaterials to design a topological metasurface tocontrol and redirect elastic waves. We strategically design a two-dimensional crystalline perforated elastic platethat hosts symmetry-induced topological edge states. By concurrently allowing the elastic substrate to spatiallyvary in depth, we are able to convert the incident slow wave into a series of robust modes, with differing envelopemodulations. This adiabatic transition localises the incoming energy into a concentrated region where it can thenbe damped or extracted. For larger transitions, different behaviour is observed; the incoming energy propagatesalong the interface before being partitioned into two disparate chiral beams. This “topological rainbow” effectleverages two main concepts, namely the quantum valley-Hall effect and the rainbow effect usually associatedwith electromagnetic metamaterials. The topological rainbow effect transcends specific physical systems, hence,the phenomena we describe can be transposed to other wave physics. Due to the directional tunability of theelastic energy by geometry our results have far-reaching implications for applications such as switches, filtersand energy-harvesters.

Working paper

Proctor M, Huidobro PA, Maier SA, Craster RV, Makwana MPet al., 2020, Manipulating topological valley modes in plasmonic metasurfaces, Nanophotonics, Vol: 9, Pages: 657-665, ISSN: 2192-8606

The coupled light-matter modes supported by plasmonic metasurfaces can be combined with topological principles to yield subwavelength topological valley states of light. We give a systematic presentation of the topological valley states available for lattices of metallic nanoparticles: All possible lattices with hexagonal symmetry are considered, as well as valley states emerging on a square lattice. Several unique effects which have yet to be explored in plasmonics are identified, such as robust guiding, filtering and splitting of modes, as well as dual-band effects. We demonstrate these by means of scattering computations based on the coupled dipole method that encompass the full electromagnetic interactions between nanoparticles.

Journal article

Craster R, Maria de Ponti J, Colombi A, ardito R, braghin F, corigliano Aet al., 2020, Graded elastic metasurface for enhanced energy harvesting, New Journal of Physics, Vol: 22, Pages: 1-11, ISSN: 1367-2630

Journal article

Haslinger SG, Lowe MJS, Huthwaite P, Craster R, Shi Fet al., 2019, Appraising Kirchhoff approximation theory for the scattering of elastic shear waves by randomly rough defects, Journal of Sound and Vibration, Vol: 460, Pages: 1-16, ISSN: 0022-460X

Rapid and accurate methods, based on the Kirchhoff approximation (KA), are developed to evaluate the scattering of shear waves by rough defects and quantify the accuracy of this approximation. Defect roughness has a strong effect on the reflection of ultrasound, and every rough defect has a different surface, so standard methods of assessing the sensitivity of inspection based on smooth defects are necessarily limited. Accurately resolving rough cracks in non-destructive evaluation (NDE) inspections often requires shear waves since they have higher sensitivity to surface roughness than longitudinal waves. KA models are attractive, since they are rapid to deploy, however they are an approximation and it is important to determine the range of validity for the scattering of ultrasonic shear waves; this range is found here. Good agreement between KA and high fidelity finite element simulations is obtained for a range of incident/scattering angles, and the limits of validity for KA are found to be much stricter than for longitudinal wave incidence; as the correlation length of rough surfaces is reduced to the order of the incident shear wavelength, a combination of multiple scattering and surface wave mode conversion leads to KA predictions diverging from those of the true diffuse scattered fields.

Journal article

Proctor M, Craster RV, Maier SA, Giannini V, Huidobro PAet al., 2019, Exciting pseudospin-dependent edge states in plasmonic metasurfaces, ACS Photonics, Vol: 6, Pages: 2985-2995, ISSN: 2330-4022

We study a plasmonic metasurface that supports pseudospin-dependent edge states confined at a subwavelength scale, considering full electrodynamic interactions including retardation and radiative effects. The spatial symmetry of the lattice of plasmonic nanoparticles gives rise to edge states with properties reminiscent of the quantum spin Hall effect in topological insulators. However, unlike the spin-momentum locking characteristic of topological insulators, these modes are not purely unidirectional and their propagation properties can be understood by analyzing the spin angular momentum of the electromagnetic field, which is inhomogeneous in the plane of the lattice. The local sign of the spin angular momentum determines the propagation direction of the mode under a near-field excitation source. We also study the optical response under far-field excitation and discuss in detail the effects of radiation and retardation.

Journal article

Bennetts LG, Peter MA, Craster RV, 2019, Low-frequency wave-energy amplification in graded two-dimensional resonator arrays, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 377, ISSN: 1364-503X

Energy amplification in square-lattice arrays of C-shaped low-frequency resonators, where the resonator radii are graded with distance, is investigated in the two-dimensional linear acoustics setting for both infinite (in one dimension) and finite arrays. Large amplifications of the incident energy are shown in certain array locations. The phenomenon is analysed using: (i) band diagrams for doubly-periodic arrays; (ii) numerical simulations for infinite and finite arrays; and (iii) eigenvalue analysis of transfer matrices operating over individual columns of the array. It is shown that the locations of the large amplifications are predicted by propagation cut-offs in the modes associated with the transfer-matrix eigenvalues. For the infinite array, the eigenvalues form a countable set, and for the low frequencies considered, only a single propagating mode exists for a given incident wave, which cuts off within the array, leading to predictive capabilities for the amplification location. For the finite array, it is shown that (in addition to a continuous spectrum of modes) multiple discrete propagating modes can be excited, with the grading generating new modes, as well as cutting others off, leading to complicated amplification patterns. The numerical simulations reveal that the largest amplifications are achieved for a single row array, with amplifications an order of magnitude smaller for the corresponding infinite array.

Journal article

Theodorakis PE, Smith ER, Craster RV, Müller EA, Matar OKet al., 2019, Molecular dynamics simulation of the super spreading of surfactant-laden droplets. A review, Fluids, Vol: 4, Pages: 1-23, ISSN: 2311-5521

Superspreading is the rapid and complete spreading of surfactant-laden droplets on hydrophobic substrates. This phenomenon has been studied for many decades by experiment, theory, and simulation, but it has been only recently that molecular-level simulation has provided significant insights into the underlying mechanisms of superspreading thanks to the development of accurate force-fields and the increase of computational capabilities. Here, we review the main advances in this area that have surfaced from Molecular Dynamics simulation of all-atom and coarse-grained models highlighting and contrasting the main results and discussing various elements of the proposed mechanisms for superspreading. We anticipate that this review will stimulate further research on the interpretation of experimental results and the design of surfactants for applications requiring efficient spreading, such as coating technology.

Journal article

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