Plates with blind holes for harnessing of flexural waves – PLATON

We propose to use a circular partly through-thickness hole, thereafter called “blind hole”, as the building block of 2D complex structures. In contrast to a through hole which does not exhibit low frequency resonant effect, a blind hole is a remarkable resonator despite the simplicity of its geometry. Its resonance frequency decreases with decreasing thickness of the membrane left at the bottom of the hole. It is therefore possible to design holes significantly smaller than the wavelength in the plate, if the thickness of the membrane is small enough. High resonator density is therefore made possible leading to strong coupling and exalted wave-matter interactions. From here, the phononic band structure can be engineered by playing both on the resonator characteristics and the global structure.

1- Demonstration of sub-wavelength focusing of flexural waves on a plate with a 2D-lattice of through holes, the counterpart of the Veselago flat lens for elastic waves;
2- Demonstration of the concept of a flat antenna and achieve far-field (out-of-plane) hyper-resolution and 3D imaging with a single emitter,
3- Role of disorder in these structures and exploration of regimes of extreme scattering where transport is strongly altered and waves may be trapped by disorder.

- Contrl of disorder and localized modes
- Design and structuration of a plte to confine flexuralwaves: the inverse problem
- 3D Imaging system based on Helmholtz resonators
- Maxwell Fisheye

1. M. Dubois, M. Farhat, E. Bossy, S. Enoch, S. Guenneau and P. Sebbah, “Flat lens for pulse focusing of elastic waves in thin plates”, Appl. Phys. Lett. 103, 071915 (2013).
2. N. Etaix, J. Dubois, M.Fink, R. K. Ing, “Increasing the modal density in plates for mono-element focusing in air”, J. Acoust. Soc. Am., 134, 1049 (2013).
3. Marc Dubois, Emmanuel Bossy, Stefan Enoch, Sébastien Guenneau, Patrick Sebbah, “Time Driven Sub-wavelength Focusing with Negative Refraction”, submitted to PRL.
4. N. Bachelard, J. Arlandis, C. Garay, R. Touzani, and P. Sebbah, “Coalescence of Anderson-localized modes at exceptional points in 2D random media”, soumis à Phys. Rev. Lett.

The PLATON project aims at exploring fundamental as well as applied aspects of flexural wave interaction with periodic or random arrays of strongly coupled subwavelength resonators. Of particular interest is the possibility to investigate new wave phenomena by designing artificial meta-structures for elastic waves similar to the ones investigated in optics or electromagnetic waves, such as photonic crystals and metamaterials. Mie scatterers in dielectric optical materials, metallic wires for microwave systems or Helmholtz resonators for scalar acoustic waves are readily available as building blocks of complex structures. Such a strong resonator is yet to be invented for flexural waves. We propose to use a circular partly through-thickness hole, thereafter called “blind hole”, as the building block of 2D complex structures. In contrast to a through hole which does not exhibit low frequency resonant effect, a blind hole is a remarkable resonator despite the simplicity of its geometry. Its resonance frequency decreases with decreasing thickness of the membrane left at the bottom of the hole. It is therefore possible to design holes significantly smaller than the wavelength in the plate, if the thickness of the membrane is small enough. High resonator density is therefore made possible leading to strong coupling and exalted wave-matter interactions. From here, the phononic band structure can be engineered by playing both on the resonator characteristics and the global structure. Very recently, slow modes were observed in a 1D lattice of blind holes. This confirms the potential for new wave physics we foresaw for this simple resonator. In this proposal, this elementary brick will be used - To demonstrate sub-wavelength focusing of flexural waves on a plate with a 2D-lattice of blind holes, the counterpart of the Veselago flat lens for elastic waves; - To demonstrate the concept of a flat antenna and achieve far-field (out-of-plane) hyper-resolution and 3D imaging with a single emitter; - To probe the role of disorder in these structures and explore regimes of extreme scattering where transport is strongly altered and waves may be trapped by disorder. This choice is motivated by the possibility to develop a common theoretical understanding, as well as numerical modeling to address these issues. Moreover, surface elastic-waves offer (1) the priceless ability to access directly and non-invasively the acoustic field within the complex medium itself, (2) to use subwavelength antennas as the excitation source or even laser pulses at distance, (3) to explore time response as well as steady state regime. This project brings together three leading laboratories in wave physics and acoustics, with complementary skills, the Langevin Institute (Paris), the Fresnel Institute (Marseille) and the LAUM (Le Mans). They will join in an effort - To understand the physics of elastic waves in structured thin plates, in interaction with a blind hole or an array of blind holes; - To put forward original properties of the proposed structures, where the strong coupling between small resonators will be the key to the observation new phenomena; - To understand the role of disorder on meta-structures and on the non-trivial character of transport of flexural waves in strongly scattering plates.