Multipole Methods for Periodic Metamaterial Structures
Lead Research Organisation:
Imperial College London
Department Name: Mathematics
Abstract
My research is primarily about the interaction of waves with periodic structures in one-, two- and three-dimensions. The loose objective of this work is to arrive to a mathematical formalism that describes the scattering of waves (be they acoustic, electromagnetic or flexural waves in elasticity) with structures of some long-range order. The scattering of light by photonic crystals, for example, is a well-established area of wave physics, and so the novelty here is the introduction of metamaterials to that photonic structure. The aim is to bring about new effects such as tunability of the crystal or anisotropic scattering by the constituent crystal elements. This certainly aligns with the EPSRC's thematic areas of "advanced materials" and "frontiers in technology", with the field of metamaterials in particular being one of the fastest-growing sectors of the engineering sciences. My project is in collaboration with various experts in the field of wave science from the UK and abroad, and is partly funded by Qinetiq, with whom we have started discussing experimental verification of our mathematical models.
People |
ORCID iD |
| Richard Craster (Primary Supervisor) | |
| Henry Putley (Student) |
| Description | Recent topics in Wave Physics concern the manipulation and control of wave propagation by periodically structured media. By periodically structured, one will conventionally think of crystals; three-dimensional materials harbouring some long-range order that gives rise to characteristic material properties. In my research, I have focused on the design of platonic crystals; structures of long-range order in either one- or two-dimensions embedded in thin-elastic plates. Vibrations, or vibrational waves, are modelled as out-of-plane displacements moving through a thin sheet of elastic material, governed by what is known as Kirchhoff-Love thin-plate theory. These vibrational disturbances can be manipulated and controlled by plate-embedded resonators or masses arranged in periodic geometries. In my most recent work, we have designed "elastic ring resonators" - rings consisting of plate-embedded masses arranged in circular formations that hold intrinsic resonances known as "whispering-gallery modes". Like the whispering galleries of St. Paul's Cathedral in London or Grand Central Station in New York, these modes are characterised by wave propagation around the circumference of a ring, such that when a whisper (or in my case, simply a small out-of-plane vibration) occurs at one point along the ring, it can be heard (seen as an out-of-plane displacement) at another point along the ring. In platonics these are referred to as whispering-Bloch modes due to the periodicity of the geometry, and occur at specific frequencies referred to as resonant frequencies, like the resonances of conventional mass-spring systems. Most recently (in a paper ready to be submitted this week to the journal "Wave Motion") I have combined these elastic ring resonators with periodically arranged line arrays to produce "elastic circuits". These circuits consist of lines and rings of embedded masses, coupled together for the purposes of filtering and directing vibrations through the plate. Together with my supervisor, we have devised plate-bound devices that can direct vibrational energy to a high degree of control and precision. Most notably, we have recreated the add-drop filters commonly found in electrical or optical circuits, and have discovered a Fourier harmonic system in sets of horizontally-conjoined ring resonators. These plate-bound circuits have been modelled non-dimensionally, leaving room for multi-scale fabrication of the resonant devices we have coined CREAs: coupled resonator elastic arrays for the purposes of directing and manipulating wave motion. The conception of these circuits opens exciting new avenues for research in plate-bound energy harvesting networks, or the insulation of a material from vibrational disturbances. If vibrational energy can be manipulated and controlled, there is scope to direct this energy in such a way as to harvest it through the use of piezo-electric devices. These devices turn a mechanical stress or deformation into electrical energy, and such devices already find use in energy harvesting networks designed by other PhD students within my research group. This, in part, will be the subsequent direction of my research funded through this award. |
| Exploitation Route | Plate-bound elastic circuits could find use in passive energy harvesting networks that, placed upon any surface or device that experiences vibrational disturbances, could recycle energy lost through vibrations. If fabrication is successful, they have the potential to make our every-day devices more energy efficient, reducing both power consumption and "vibrational noise". Some examples include bridges, aeroplane wings, hairdryers or fridges; any device that suffers vibrational disturbances through its structure could benefit from these energy harvesters. Fellow researches within the group and collaborators in Spain have already devised energy harvesting networks, and there is scope to combine these elastic circuits with their published findings. Academically, we will be implementing the same model of whispering-Bloch modes into an analysis of photonic crystal fibers for use in communications technologies. This is particularly useful as whispering-Bloch modes can be highly confined, suffering little decay over great distances. This has the potential to vastly improve fiber-based communications technologies, which currently suffer from strong decay at great expense. If our numerical experiments appear promising, there is potential for fabrication of our "Whispering-Bloch Fibers" by several collaborating groups in Marseille, France, and the demonstration of ground-breaking new communications technology. |
| Sectors | Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Electronics,Energy,Other |
| Description | Industrial Partner |
| Organisation | Qinetiq |
| Department | QinetiQ (Farnborough) |
| Country | United Kingdom |
| Sector | Private |
| PI Contribution | We have met with Qinetiq on two occasions, toured their facilities and discussed the current research topics we are pursuing. This has opened the doors for future collaboration with their scientists and potential use of their facilities. I will likely present my findings to those at Qinetiq at some point in the year. |
| Collaborator Contribution | Qinetiq have provided useful advice on the elastic ring resonators, and have offered their expertise in any research conducted on acoustic cloaking devices. |
| Impact | No outcomes directly from this collaboration as of March 2021, but this may change with possible fabrication of the ring resonators, or through our work on Photonic Crystal Fibers. |
| Start Year | 2019 |