Designing multidirectional energy splitters and topological valley supernetworks

Makwana, Mehul P.; Craster, Richard V.

doi:10.1103/physrevb.98.235125

Cited by 70 publications

(88 citation statements)

References 60 publications

(113 reference statements)

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“…In order to differentiate between the two effects, the symmetry of the inclusions within the unit cell is of paramount importance; rainbow reflection effects can be achieved with any inclusion geometry, since ultimately they leverage only the Bragg condition by virtue of the periodicity. For true rainbow trapping effects, trapping must be located at wavevectors within the first Brillouin Zone (BZ), and hence rely on the decoupling of orthogonal eigensolutions, or symmetry breaking of the array geometry [26,27] so to lift accidental degeneracies within the first BZ.…”

Section: Graded Line Arraysmentioning

confidence: 99%

“…Degenerate eigensolutions of the dispersion relation, or accidental degeneracies (band crossings) within the Brillouin Zone ( Fig. 3(a)) correspond to orthogonal modes and can exist if there is reflectional symmetry of the inclusion geometry about the array axis [26]. These more complex geometries are not normally analysed in graded systems, but the extension to such geometries is trivial.…”

Section: Graded Line Arraysmentioning

confidence: 99%

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Delineating rainbow reflection and trapping with applications for energy harvesting

et al. 2020

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Important distinctions are made between two related wave control mechanisms that act to spatially separate frequency components; these socalled 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. 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.

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Section: Graded Line Arraysmentioning

confidence: 99%

Section: Graded Line Arraysmentioning

confidence: 99%

Delineating rainbow reflection and trapping with applications for energy harvesting

et al. 2020

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“…Replacing velocities with the corresponding pressures, and reproducing the process at junction A, we can obtain the governing equations (1). The corresponding energy terms ε A,B are given by equation (6). And the function G α ( f, f α ) is given by…”

Section: ( )mentioning

confidence: 99%

“…Over the last years, in the context of metamaterials, a plethora of sophisticated acoustic structures exhibiting unusual wave properties have been theoretically proposed and also experimentally studied. Examples include Dirac cones [1], unidirectional propagation [2][3][4], topological interface waves [5][6][7], robust localized modes [8], etc. Recently periodic acoustic/elastic media have been proven to be an excellent platform for studying various wave phenomena [9].…”

Section: Introductionmentioning

confidence: 99%

Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves

et al. 2020

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In this work, we study the propagation of sound waves in a honeycomb waveguide network loaded with Helmholtz resonators (HRs). By using a plane wave approximation in each waveguide we obtain a first-principle modeling of the network, which is an exact mapping to the graphene tight-binding Hamiltonian. We show that additional Dirac points appear in the band diagram when HRs are introduced at the network nodes. It allows to break the inversion (sub-lattice) symmetry by tuning the resonators, leading to the appearence of edge modes that reflect the configuration of the zigzag boundaries. Besides, the dimerization of the resonators also permits the formation of interface modes located in the band gap, and these modes are found to be robust against symmetry preserving defects. Our results and the proposed networks reveal the additional degree of freedom bestowed by the local resonance in tuning the properties of not only acoustical graphene-like structures but also of more complex systems.

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“…This relationship between the two interfaces allows for propagation, within our square structure, that is ordinarily forbidden within graphene-like struc- tures. Coupling between modes, that are hosted along different interfaces, is crucial for energy navigation around sharp corners 17 and within complex topological domains 9,13,14,16 .…”

mentioning

confidence: 99%

Experimental observations of topologically guided water waves within non-hexagonal structures

Makwana

Laforge

Dupont

et al. 2020

Applied Physics Letters

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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.Considerable recent activity in wave phenomena is motivated through topological effects and focused on identifying situations where topological protection occurs that can enhance, or create, robust wave guidance along edges or interfaces. Remarkably, the core concepts that gave rise to topological insulators, originating within quantum mechanics 2 carry across, in part, to classical wave systems 3,4 . Topological insulators can be divided into two broad categories: those that preserve time-reversal symmetry (TRS), and those which break it. We concentrate upon the former due to the simplicity of their construction that solely requires passive elements. By leveraging the discrete valley degrees of freedom, arising from degenerate extrema in Fourier space, we are able to create robust symmetry-protected waveguides. These valley states are connected to the quantum valley-Hall effect and hence this research area has been named valleytronics 5,6 .Hexagonal structures are the prime candidates for valleytronic devices as they exhibit symmetry induced Dirac cones at the high-symmetry points of the Brillouin zone (BZ); when perturbed these Dirac points can be gapped, leading to well-defined KK valleys distinguished, from each other, by their opposite chirality or pseudospin.This pseudospin has been used in a wide variety of dispersionless wave settings to design valleytronic devices 7,8 . Here we extend the earlier research by examining a highlydispersive physical system, i.e. water waves (Fig. 1), and move away from hexagonal structures. The topological proa) Electronic tection afforded by these valley states is attributed to, both, the orthogonality of the pseudospins as well as the Fourier separation between the two valleys 9 . The vast majority of the valleytronics literature, inspired by graphene, opts to use hexagonal structures [10][11][12][13][14][15][16][17][18][19] . However a negative that emerges with these, especially when dealing with complex topological domains 9 , is that certain prop...

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Designing multidirectional energy splitters and topological valley supernetworks

Cited by 70 publications

References 60 publications

Delineating rainbow reflection and trapping with applications for energy harvesting

Delineating rainbow reflection and trapping with applications for energy harvesting

Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves

Experimental observations of topologically guided water waves within non-hexagonal structures

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