arXiv subjects

Mehul P. Makwana

Publications and source records attributed to Mehul P. Makwana.

10 recordsLinked to original sources

arXiv2026

Reconfigurable topological valley-Hall interfaces: Asymptotics of arrays of Dirichlet and Neumann inclusions for multiple scattering in metamaterials

We study two-dimensional periodic metamaterials in which idealised cylindrical inclusions are modelled by boundary conditions. In the scalar time-harmonic setting, the background field satisfies the Helmholtz equation, and high-contrast inclusion limits reduce to Dirichlet or Neumann conditions, with direct analogues in dielectric and acoustic media. By switching the condition assigned to selected inclusions, we break point-group symmetries of the primitive cell and thereby lift symmetry-induced degeneracies in the Floquet--Bloch spectrum of hexagonal and square lattices, opening valley-type band gaps with Berry curvature localised near opposite valleys. To analyse infinite and finite structures within a unified framework, we derive matched-asymptotic point-scatterer approximations for mixed Dirichlet--Neumann arrays. For doubly periodic systems, this yields a finite-dimensional generalised eigenvalue problem for the Floquet--Bloch spectrum; for finite arrays, it yields a generalised Foldy multiple-scattering system. In both hexagonal and square lattices, geometrically identical crystals can realise distinct valley-Hall phases solely through boundary-condition assignment while retaining an overlapping bulk gap. Spatially varying this assignment therefore creates and relocates internal interfaces without altering the underlying geometry, enabling the associated valley-Hall interfacial modes to be repositioned within the same crystal.

physics.optics↗

arXiv2020

Acoustic topological circuitry in square and rectangular phononic crystals

We systematically engineer a series of square and rectangular phononic crystals to create experimental realisations of complex topological phononic circuits. The exotic topological transport observed is wholly reliant upon the underlying structure which must belong to either a square or rectangular lattice system and not to any hexagonal-based structure. The phononic system chosen consists of a periodic array of square steel bars which partitions acoustic waves in water over a broadband range of frequencies (~0.5 MHz). An ultrasonic transducer launches an acoustic pulse which propagates along a domain wall, before encountering a nodal point, from which the acoustic signal partitions towards three exit ports. Numerical simulations are performed to clearly illustrate the highly resolved edge states as well as corroborate our experimental findings. To achieve complete control over the flow of energy, power division and redirection devices are required. The tunability afforded by our designs, in conjunction with the topological robustness of the modes, will result in their assimilation into acoustical devices.

cond-mat.mes-hall↗

arXiv2020

Localising elastic edge waves via the topological rainbow effect

We combine two different fields, topological physics and graded metamaterials to design a topological metasurface to control and redirect elastic waves. We strategically design a two-dimensional crystalline perforated elastic plate, using a square lattice, %consisting of bore holes, that hosts symmetry-induced topological edge states. By concurrently allowing the elastic substrate to spatially vary in depth, we are able to convert the incident slow wave into a series of robust modes, with differing envelope modulations. This adiabatic transition localises the incoming energy into a concentrated region where it can then be damped or extracted. For larger transitions, different behaviour is observed; the incoming energy propagates along the interface before being partitioned into two disparate chiral beams. This "topological rainbow" effect leverages two main concepts, namely the quantum valley-Hall effect and the rainbow effect usually associated with 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 the elastic energy by geometry our results have far-reaching implications for applications such as switches, filters and energy-harvesters.

physics.app-ph↗

arXiv2020

Asymptotic approximations for Bloch waves and topological mode steering in a planar array of Neumann scatterers

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 lends itself to direct scattering problems for finite arrays and we illustrate the flexibility of these asymptotic representations on topical examples from topological wave physics.

physics.comp-ph↗

arXiv2020

Hybrid topological guiding mechanisms for photonic crystal fibers

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.

physics.optics↗

arXiv2020

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

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.

physics.flu-dyn↗

arXiv2020

Observations of symmetry induced topological mode steering in a reconfigurable elastic plate

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.

physics.app-ph↗

arXiv2019

Manipulating Topological Valley Modes in Plasmonic Metasurfaces

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.

cond-mat.mes-hall↗

arXiv2019

Tunable three-way valley Hall energy-splitter: venturing beyond graphene-like structures

Strategically combining four structured domains creates the first ever three-way topological energy-splitter; remarkably, this is only possible using a square, or rectangular, lattice, and not the graphene-like structures more commonly used in valleytronics. To achieve this effect, the two mirror symmetries, present within all fully-symmetric square structures, are broken; this leads to two nondistinct interfaces upon which valley-Hall states reside. These interfaces are related to each other via the time-reversal operator and it is this subtlety that allows us to ignite the third outgoing lead. The geometrical construction of our structured medium allows for the three-way splitter to be adiabatically converted into a wave steerer around sharp bends. Due to the tunability of the energies directionality by geometry, our results have far-reaching implications for applications such as beam-splitters, switches and filters across wave physics.

cond-mat.mes-hall↗

arXiv2019

Novel topological beam-splitting in photonic crystals

We create a passive wave splitter, created purely by geometry, to engineer three-way beam splitting in electromagnetism in transverse electric 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 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.

physics.optics↗