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  • Journal article
    Makwana M, Craster R, Guenneau S, 2019,

    Topological beam-splitting in photonic crystals

    , Optics Express, Vol: 27, Pages: 16088-16102, ISSN: 1094-4087

    We create a passive wave splitter, created purely by geometry, to engineer three-way beam splitting in electromagnetism in transverse electric and magnetic polarisation. We do so by considering arrangements of Indium Phosphide dielectric pillars in air, in particular we place several inclusions within a cell that is then extended periodically upon a square lattice. Hexagonal lattice structures are more commonly used in topological valleytronics but, as we discuss, three-way splitting is only possible using a square, or rectangular, lattice. To achieve splitting and transport around a sharp bend we use accidental, and not symmetry-induced, Dirac cones. Within each cell pillars are either arranged around a triangle or square; we demonstrate the mechanism of splitting and why it does not occur for one of the cases. The theory is developed and full scattering simulations demonstrate the effectiveness of the proposed designs.

  • Journal article
    Palmer S, Xiao X, Pazos-Perez N, Guerrini L, Correa-Duarte M, Maier S, Craster R, Alvarez-Puebla R, Giannini Vet al., 2019,

    Extraordinarily transparent compact metallic metamaterials

    , Nature Communications, Vol: 10, ISSN: 2041-1723

    The design of achromatic optical components requires materials with high transparency and low dispersion. We show that although metals are highly opaque, densely packed arrays of metallic nanoparticles can be more transparent to infrared radiation than dielectrics such as germanium, even when the arrays are over 75% metal by volume. Such arrays form effective dielectrics that are virtually dispersion-free over ultra-broadband ranges of wavelengths from microns up to millimeters 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.

  • Conference paper
    Mignuzzi S, Cambiasso J, Vezzoli S, Horsley SAR, Barnes WL, Maier SA, Sapienza Ret al., 2019,

    Dielectric nanocavities with enhanced local density of states

    © 2019 The Author(s) 2019 OSA. We present inverse-designed lossless dielectric nanocavities with enhanced local density of optical states. Photon counting statistics from fluorescent molecules allows determining strong field confinement and single-molecule detection at micromolar concentration in liquid.

  • Journal article
    Dubois M, Perchoux J, Vanel AL, Tronche C, Achaoui Y, Dupont G, Bertling K, Rakic AD, Antonakakis T, Enoch S, Abdeddaim R, Craster RV, Guenneau Set al., 2019,

    Acoustic flat lensing using an indefinite medium

    , Physical Review B: Condensed Matter and Materials Physics, Vol: 99, ISSN: 1098-0121

    Acoustic flat lensing is achieved here by tuning a phononic array to have indefinite medium behavior in a narrow frequency spectral region along the acoustic branch in the irreducible Brillouin zone (IBZ). This is confirmed by the occurrence of a flat band along an unusual path in the IBZ and by interpreting the intersection point of isofrequency contours on the corresponding isofrequency surface; coherent directive collimated beams are formed whose reflection from the array surfaces create lensing. Theoretical predictions using a mass-spring lattice approximation of the phononic crystal (PC) are corroborated by time-domain experiments, airborne acoustic waves generated by a source with a frequency centered about 10.6 kHz, placed at three different distances from one side of a finite PC slab, constructed from polymeric spheres, yielding distinctive focal spots on the other side. These experiments evaluate the pressure field using optical feedback interferometry and demonstrate precise control of the three-dimensional wave trajectory through a sonic crystal.

  • Journal article
    Vanel AL, Craster RV, Schnitzer O, 2019,

    Asymptotic modelling of phononic box crystals

    , SIAM Journal on Applied Mathematics, Vol: 79, Pages: 506-524, ISSN: 0036-1399

    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.

  • Journal article
    Chaplain GJ, Makwana MP, Craster R, 2019,

    Rayleigh-Bloch, topological edge and interface waves for structured elastic plates

    , WAVE MOTION, Vol: 86, Pages: 162-174, ISSN: 0165-2125
  • Journal article
    Movchan AB, McPhedran RC, Carta G, Craster RVet al., 2019,

    Platonic localisation: one ring to bind them

    , Archive of Applied Mechanics, Vol: 89, Pages: 521-533, ISSN: 0939-1533

    In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring–mass resonators in an elastic plate. The values for the required masses and stiffnesses of resonators are derived in a closed analytical form. It is shown that spring–mass resonators can be tuned to produce a “negative inertia” input, which is used to enhance localisation of waveforms around the structured ring. Theoretical findings are accompanied by numerical simulations, which show exponentially localised and leaky modes for different frequency regimes.

  • Journal article
    Mignuzzi S, Vezzoli S, Horsley SAR, Barnes WL, Maier SA, Sapienza Ret al., 2019,

    Nanoscale design of the local density of optical states

    , Nano Letters, Vol: 19, Pages: 1613-1617, ISSN: 1530-6984

    We propose a design concept for tailoring the local density of optical states (LDOS) in dielectric nanostructures, based on the phase distribution of the scattered optical fields induced by point-like emitters. First we demonstrate that the LDOS can be expressed in terms of a coherent summation of constructive and destructive contributions. By using an iterative approach, dielectric nanostructures can be designed to effectively remove the destructive terms. In this way, dielectric Mie resonators, featuring low LDOS for electric dipoles, can be reshaped to enable enhancements of 3 orders of magnitude. To demonstrate the generality of the method, we also design nanocavities that enhance the radiated power of a circular dipole, a quadrupole, and an arbitrary collection of coherent dipoles. Our concept provides a powerful tool for high-performance dielectric resonators and affords fundamental insights into lightmatter coupling at the nanoscale.

  • Journal article
    Jacucci G, Onelli OD, De Luca A, Bertolotti J, Sapienza R, Vignolini Set al., 2019,

    Coherent backscattering of light by an anisotropic biological network.

    , Interface Focus, Vol: 9, Pages: 20180050-20180050, ISSN: 2042-8898

    The scattering strength of a random medium relies on the geometry and spatial distribution of its components as well as on their refractive index. Anisotropy can, therefore, play a major role in the optimization of the scattering efficiency in both biological and synthetic materials. In this study, we show that, by exploiting the coherent backscattering phenomenon, it is possible to characterize the optical anisotropy in Cyphochilus beetle scales without the need to change their orientation or their thickness. For this reason, such a static and easily accessible experimental approach is particularly suitable for the study of biological specimens. Moreover, estimation of the anisotropy in Cyphochilus beetle scales might provide inspiration for improving the scattering strength of artificial white materials.

  • Journal article
    Berte R, Della Picca F, Poblet M, Li Y, Cortes E, Craster RV, Maier SA, Bragas AVet al., 2018,

    Acoustic far-field hypersonic surface wave detection with single plasmonic nanoantennas

    , Physical Review Letters, Vol: 121, ISSN: 0031-9007

    The optical properties of small metallic particles allow us to bridge the gap between the myriad of subdiffraction local phenomena and macroscopic optical elements. The optomechanical coupling between mechanical vibrations of Au nanoparticles and their optical response due to collective electronic oscillations leads to the emission and the detection of surface acoustic waves (SAWs) by single metallic nanoantennas. We take two Au nanoparticles, one acting as a source and the other as a receptor of SAWs and, even though these antennas are separated by distances orders of magnitude larger than the characteristic subnanometric displacements of vibrations, we probe the frequency content, wave speed, and amplitude decay of SAWs originating from the damping of coherent mechanical modes of the source. Two-color pump-probe experiments and numerical methods reveal the characteristic Rayleigh wave behavior of emitted SAWs, and show that the SAW-induced optical modulation of the receptor antenna allows us to accurately probe the frequency of the source, even when the eigenmodes of source and receptor are detuned.

  • Journal article
    Makwana MP, Craster R, 2018,

    Designing multidirectional energy splitters and topological valley supernetworks

    , PHYSICAL REVIEW B, Vol: 98, ISSN: 2469-9950
  • Journal article
    Makwana MP, Craster R, 2018,

    Geometrically navigating topological plate modes around gentle and sharp bends

    , PHYSICAL REVIEW B, Vol: 98, ISSN: 2469-9950
  • Journal article
    Bennetts LG, Peter MA, Craster R, 2018,

    Graded resonator arrays for spatial frequency separation and amplification of water waves

    , Journal of Fluid Mechanics, Vol: 854, ISSN: 0022-1120

    A structure capable of substantially amplifying water waves over a broad range of frequencies at selected locations is proposed. The structure consists of a small number of C-shaped cylinders in a line array, with the cylinder properties graded along the array. Using linear potential-flow theory, it is shown that the energy carried by a plane incident wave is amplified within specified cylinders for wavelengths comparable to the array length and for a range of incident directions. Transfer-matrix analysis is used to attribute the large amplifications to excitation of local Rayleigh–Bloch waves and gradual slowing down of their group velocity along the array.

  • Journal article
    Craster R, Guenneau S, Hutridurga Ramaiah H, Pavliotis Get al., 2018,

    Cloaking via mapping for the heat equation

    , Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Vol: 16, Pages: 1146-1174, ISSN: 1540-3459

    This paper explores the concept of near-cloaking in the context of time-dependentheat propagation. We show that after the lapse of a certain threshold time, the boundary measure-ments for the homogeneous heat equation are close to the cloaked heat problem in a certain Sobolevspace norm irrespective of the density-conductivity pair in the cloaked region. A regularised trans-formation media theory is employed to arrive at our results. Our proof relies on the study of the longtime behaviour of solutions to the parabolic problems with high contrast in density and conductivitycoefficients. It further relies on the study of boundary measurement estimates in the presence of smalldefects in the context of steady conduction problem. We then present some numerical examples to illustrate our theoretical results.

  • Journal article
    Skelton E, Craster RV, Colombi A, Colquitt Det al., 2018,

    The multi-physics metawedge: graded arrays on fluid-loaded elastic plates and the mechanical analogues of rainbow trapping and mode conversion

    , New Journal of Physics, Vol: 20, ISSN: 1367-2630

    We consider the propagation and mode conversion of flexural-acoustic waves along a fluid-loaded graded array of elastic resonators, forming a metasurface. The multi-physics nature of the problem, coupling two disparate physical systems, brings both challenges and novel features not previously seen in so-called bifunctional metamaterials. In particular, by using an appropriately designed graded array of resonators, we show that it is possible to employ our metasurface to mode-convert sub-sonic surface flexural waves into bulk acoustic waves and vice-versa; transferring energy between two very different physical systems. Whilst the sub-sonic mechanical surface wave is dispersive, the bulk acoustic wave is dispersionless and radiates energy at infinity. We also show that this bifunctional metasurface is capable of exhibiting the classical effect of rainbow trapping for sub-sonic surface waves.

  • Journal article
    Morozov S, Gaio M, Maier S, Sapienza Ret al., 2018,

    Metal−dielectric parabolic antenna for directing single photons

    , Nano Letters, Vol: 18, Pages: 3060-3065, ISSN: 1530-6984

    Quantum emitters radiate light omni-directionally, making it hard to collect and use the generated photons. Here, we propose a three-dimensional metal–dielectric parabolic antenna surrounding an individual quantum dot as a source of collimated single photons, which can then be easily extracted and manipulated. Our fabrication method relies on a single optically induced polymerization step once the selected emitter has been localized by confocal microscopy. Compared to conventional nanoantennas, our geometry does not require near-field coupling, and it is, therefore, very robust against misalignment issues and minimally affected by absorption in the metal. The parabolic antenna provides one of the largest reported experimental directivities (D = 106) and the lowest beam divergences (Θ1/2 = 13.5°) and a broadband operation over all of the visible and near-infrared range together with extraction efficiency of more than 96%, offering a practical advantage for quantum technological applications.

  • Journal article
    Mignuzzi S, Mota M, Coenen T, Li Y, Mihai A, Petrov PK, Oulton RF, Maier SA, Sapienza Ret al., 2018,

    Energy-momentum cathodoluminescence spectroscopy of dielectric nanostructures

    , ACS Photonics, Vol: 5, Pages: 1381-1387, ISSN: 2330-4022

    Precise knowledge of the local density of optical states (LDOS) is fundamental to understanding nanophotonic systems and devices. Complete LDOS mapping requires resolution in energy, momentum, and space, and hence a versatile measurement approach capable of providing simultaneous access to the LDOS components is highly desirable. Here, we explore a modality of cathodoluminescence spectroscopy able to resolve, in single acquisitions, the dispersion in energy and momentum of the radiative LDOS. We perform measurements on a titanium nitride diffraction grating, bulk molybdenum disulfide, and silicon to demonstrate that the technique can probe and disentangle the dispersion of coherent and incoherent cathodoluminescence signals. The approach presented raises cathodoluminescence spectroscopy to a versatile tool for subwavelength design and optimization of nanophotonic devices in the reciprocal space.

  • Conference paper
    Berte R, Picca FD, Poblet M, Li Y, Cortés E, Craster RV, Maier SA, Bragas AVet al., 2018,

    Generation and detection of surface acoustic waves using single plasmonic nanoresonators

    © 2018 The Author (s). We show in this work that coherent phonons generated after the decay of optically-excited plasmons in isolated metallic nanoantennas, are transmitted through the substrate as surface acoustic waves (SAWs) which can be detected by other nanoantennas used as receptors and positioned at distances up to 3μm away from the source. Two color sub-ps pump-probe technique and numerical methods suggest wave speed and amplitude decay characteristic of Rayleigh waves, the former within 3.2% of the predicted for fused silica. It is also shown that the mechanical excitation of the receptors via SAW modulates the optical response of the probe transmission and that its spectral content shows that the detection is feasible, even when the vibrational modes of the receptor are detuned from those of the source.

  • Conference paper
    Guenneau S, Brule S, Enoch S, Diatta A, Achaoui Y, Ungureanu B, Hutridurga H, Craster RVet al., 2018,

    Some challenges regarding cloaking and earthquake protection

    , 12th International Congress on Artificial Materials for Novel Wave Phenomena (METAMATERIALS), Publisher: IEEE, Pages: 158-160
  • Journal article
    Brule S, Ungureanu B, Achaoui Y, Diatta A, Aznavourian R, Antonakakis T, Craster R, Enoch S, Guenneau Set al., 2017,

    Metamaterial-like transformed urbanism

    , INNOVATIVE INFRASTRUCTURE SOLUTIONS, Vol: 2, ISSN: 2364-4176
  • Journal article
    Schnitzer O, Craster RV, 2017,

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

    , SIAM Journal on Applied Mathematics, Vol: 77, Pages: 2119-2135, ISSN: 0036-1399

    We study waves governed by the planar Helmholtz equation, propagating in aninfinite lattice of subwavelength Dirichlet scatterers, the periodicity beingcomparable to the wavelength. Applying the method of matched asymptoticexpansions, the scatterers are effectively replaced by asymptotic pointconstraints. The resulting coarse-grained Bloch-wave dispersion problem issolved by a generalised Fourier series, whose singular asymptotics in thevicinities of scatterers yield the dispersion relation governing modes that arestrongly perturbed from plane-wave solutions existing in the absence of thescatterers; there are also empty-lattice waves that are only weakly perturbed.Characterising the latter is useful in interpreting and potentially designingthe dispersion diagrams of such lattices. The method presented, that simplifiesand expands on Krynkin & McIver [Waves Random Complex, 19 347 2009], could beapplied in the future to study more sophisticated designs entailing resonantsubwavelength elements distributed over a lattice with periodicity on the orderof the operating wavelength.

  • Journal article
    Vanel AL, Schnitzer O, Craster RV, 2017,

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

    , Europhysics Letters: a letters journal exploring the frontiers of physics, Vol: 119, ISSN: 1286-4854

    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.

  • Journal article
    Pendry JB, Huidobro PA, Luo Y, Galiffi Eet al., 2017,

    Compacted dimensions and singular plasmonic surfaces

    , Science, Vol: 358, Pages: 915-917, ISSN: 0036-8075

    In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer.

  • Conference paper
    Colombi A, Craster R, Clark M, Colquitt Det al., 2017,

    Slow waves, elastic rainbow and dynamic anisotropy with a cluster of resonant rods on an elastic halfspace

    , 2017 11th International Congress on Engineered Material Platforms for Novel Wave Phenomena (METAMATERIALS), Publisher: IEEE, Pages: 409-410
  • Conference paper
    Colombi A, Roux P, Miniaci M, Craster R, Guenneau S, Gueguen Pet al., 2017,

    The role of large scale computing behind the development of seismic (and elastic) metamaterials.

    , 2017 11th International Congress on Engineered Material Platforms for Novel Wave Phenomena (METAMATERIALS), Publisher: IEEE, Pages: 406-408
  • Journal article
    Colombi A, Ageeva V, Smith RJ, Clare A, Patel R, Clark M, Colquitt D, Roux P, Guenneau S, Craster RVet al., 2017,

    Enhanced sensing and conversion of ultrasonic Rayleigh waves by elastic metasurfaces

    , Scientific Reports, Vol: 7, ISSN: 2045-2322

    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 shear waves. Here we demonstrate experimentally not only elastic Rayleigh wave rainbow trapping, by taking advantage of a stop-band for surface waves, but also selective mode conversion of surface Rayleigh waves to shear waves. These experiments performed at ultrasonic frequencies, in the range of 400-600 kHz, are complemented by time domain numerical simulations. The metasurfaces we design are not limited to guided ultrasonic waves and are a general phenomenon in elastic waves that can be translated across scales.

  • Journal article
    O'Neill J, Selsil O, Haslinger SG, Movchan NV, Craster RVet al., 2017,

    ACTIVE CLOAKING FOR FINITE CLUSTERS OF PINS IN KIRCHHOFF PLATES

    , SIAM Journal on Applied Mathematics, Vol: 77, Pages: 1115-1135, ISSN: 0036-1399

    This paper considers active cloaking of a square array of evenly spaced pins in a Kirchhoff plate in the presence of flexural waves. Active sources, modeled as ideal point sources, are represented by the nonsingular Green's function for the two-dimensional biharmonic operator and have an arbitrary complex amplitude. These sources are distributed exterior to the cluster, and their complex amplitudes are found by solving an algebraic system of equations. This procedure ensures that selected multipole orders of the scattered field are successfully annulled. For frequencies in the zero-frequency stop band, we find that a small number of active sources located on a grid is sufficient for cloaking. For higher frequencies, we achieve efficient cloaking with the active sources positioned on a circle surrounding the cluster. We demonstrate the cloaking efficiency with several numerical illustrations, considering key frequencies from band diagrams and dispersion surfaces for a Kirchhoff plate pinned in a doubly periodic fashion.

  • Journal article
    Lefebvre G, Antonakakis T, Achaoui Y, Craster RV, Guenneau S, Sebbah Pet al., 2017,

    Unveiling extreme anisotropy in elastic structured media

    , Physical Review Letters, Vol: 118, ISSN: 0031-9007

    Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones, and saddle points; identifying these and the nature of the associated modes from a direct reading of the dispersion surfaces is not straightforward, especially in three dimensions or at high frequencies when several dispersion surfaces fold back in the Brillouin zone. A recently proposed asymptotic high-frequency homogenization theory is applied to a challenging time-domain experiment with elastic waves in a pinned metallic plate. The prediction of a narrow high-frequency spectral region where the effective medium tensor dramatically switches from positive definite to indefinite is confirmed experimentally; a small frequency shift of the pulse carrier results in two distinct types of highly anisotropic modes. The underlying effective equation mirrors this behavior with a change in form from elliptic to hyperbolic exemplifying the high degree of wave control available and the importance of a simple and effective predictive model.

  • Journal article
    Achaoui Y, Antonakakis T, Brule S, Craster RV, Enoch S, Guenneau Set al., 2017,

    Clamped seismic metamaterials: Ultra-low broad frequency stop-bands

    , New Journal of Physics, Vol: 9, ISSN: 1367-2630

    The regularity of earthquakes, their destructive power, and the nuisance of ground vibration in urbanenvironments, all motivate designs of defence structures to lessen the impact of seismic and groundvibration waves on buildings. Low frequency waves, in the range 1–10 Hz for earthquakes and up to afew tens of Hz for vibrations generated by human activities, cause a large amount of damage, orinconvenience; depending on the geological conditions they can travel considerable distances andmay match the resonant fundamental frequency of buildings. The ultimate aim of any seismicmetamaterial, or any other seismic shield, is to protect over this entire range of frequencies; the longwavelengths involved, and low frequency, have meant this has been unachievable to date. Notably thisis scalable and the effects also hold for smaller devices in ultrasonics. There are three approaches toobtaining shielding effects: bragg scattering, locally resonant sub-wavelength inclusions and zerofrequencystop-band media. The former two have been explored, but the latter has not and isexamined here. Elastic flexural waves, applicable in the mechanical vibrations of thin elastic plates, canbe designed to have a broad zero-frequency stop-band using a periodic array of very small clampedcircles. Inspired by this experimental and theoretical observation, all be it in a situation far removedfrom seismic waves, we demonstrate that it is possible to achieve elastic surface (Rayleigh)wavereflectors at very large wavelengths in structured soils modelled as a fully elastic layer periodicallyclamped to bedrock. We identify zero frequency stop-bands that only exist in the limit of columns ofconcrete clamped at their base to the bedrock. In a realistic configuration of a sedimentary basin 15 mdeep we observe a zero frequency stop-band covering a broad frequency range of 0–30 Hz.

  • Journal article
    Haslinger SG, Movchan NV, Movchan AB, Jones IS, Craster RVet al., 2017,

    Controlling flexural waves in semi-infinite platonic crystals with resonator-type scatterers

    , Quarterly Journal of Mechanics and Applied Mathematics, Vol: 70, Pages: 216-247, ISSN: 1464-3855

    We address the 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 that exhibit dynamic neutrality (perfect transmission) and localisation close to the structured interface.

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