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Significance Statement
We show in this work that one can accurately determine the focal length, the size of the focal spot, and the displacement distribution within a phononic crystal-based gradient index acoustic lens, when accounting for the local anisotropy if any, within a row of inclusions. Being based on a geometrical approach, the ray analysis we present here remains valid whatever the polarization of the waves is. Whereas the paraxial ray equation is well suited to accurately determine the focusing properties of a gradient index lens only when the equi-frequency contours are circular, this ray analysis is more general and allows accounting for both the position of the focus on the x-axis and for the extension along the y-axis.
From the experimental side, we demonstrate in this article the focusing of zero-order Lamb mode in the MHz range, in gradient index lenses featuring two different designs: square and rectangular symmetries. These heterostructures are free from curved surfaces, compact, and therefore they can easily be integrated with other phononic devices. In both systems, we found very good agreement between the numerical simulations and the experimental results. In particular, we have shown that the focusing over a spot with the lateral dimension close to the Abbé limit are easily obtained with the acoustic lens with the rectangular symmetry.
New Journal of Physics, Volume 16 June 2014, J Zhao et al 2014 New J. Phys. 16 063031.
J Zhao1, B Bonello2, R Marchal1 and O Boyko1
1 UPMC Univ Paris 06, UMR 7588, Institut des NanoSciences de Paris, F-75005, Paris, France and
2 CNRS, UMR 7588, Institut des NanoSciences de Paris, F-75005, Paris, France.
Abstract
We describe an analytical approach that allows calculating the trajectories of an elastic beam within a two-dimensional phononic crystal-based gradient index medium. The formalism takes into account the anisotropy along the lines of inclusions where the equi-frequency contours may depart from a circle. We then report on a numerical and experimental study of the focusing of flexural Lamb waves in gradient-indexed phononic crystals. The silicon/air heterostructures that we considered for this work features an index that is obtained through the modulation along one axis of either the diameter of the air inclusions or their spacing. In both cases, numerical and experimental results agree very well. The formalism that we have developed explains well the location, shape and size of the focus in either system.
