Abstract
This paper demonstrates the superlensing effect of flexural waves by phononic plates with the negative index of refraction. The phononic plate consists of a square lattice of spring-mass resonators attached to an infinite thin plate. The periodic resonator array induces a resonant band gap between the first and second dispersion curves of band structures calculating by a plane wave expansion method. All-angle negative refraction phenomenon has been found for a propagation mode under specific elastic parameters of spring-mass resonators. Furthermore, a flat lens composed by a finite number of spring-mass resonators is designed to focus elastic fields of a point-like excitation operating at this propagating mode. Multiple scattering simulations show that the image resolution of the designed flat lens is about 0.15λ, overcoming the Rayleigh diffraction limit of traditional imaging systems.
Highlights
Phononic crystals consisting of periodic inhomogeneities made in different materials can offer wave focusing phenomena for phonons waves, acoustic waves and elastic waves
This paper presents a periodic lattice of spring-mass resonators to study the superlensing effect of flexural wave propagation
The location of the point source is (−0.04m, 3m) which has a distance of 0.09m from left interface of the flat lens
Summary
Phononic crystals consisting of periodic inhomogeneities made in different materials can offer wave focusing phenomena for phonons waves, acoustic waves and elastic waves. The significant advances in wave focusing are related to doubly-negative metamaterials which have the potential to greatly enhance the resolution of imaging.. Different methods have been reported to achieve super resolution focusing of acoustic waves propagating in phononic crystals. For double negative metamaterials formed by tuning local Helmholtz resonators, the maximum resolution of imaging has been reported to be 0.33λ.16. The method of AANR phenomenon usually requires an additional condition to obtain the superlensing effect in phononic crystals at a certain frequency. This paper presents a periodic lattice of spring-mass resonators to study the superlensing effect of flexural wave propagation. Spring-mass resonators can regulate dispersion curves of phononic thin plates to obtain the AANR phenomenon in the lowest dispersion curve. The superlensing effect is further investigated by assigning suitable parameters of spring-mass resonators
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