Acoustic flat lensing using an indefinite medium

Abstract

Acoustic flat lensing is achieved here by tuning a phononic array to have indefinite medium behaviour in a narrow frequency spectral region along the acoustic branch. This is confirmed by the occurrence of a flat band along an unusual path in the Brillouin zone and by interpreting the intersection point of isofrequency contours on the corresponding isofrequency surface; coherent directive beams are formed whose reflection from the array surfaces create lensing. Theoretical predictions are corroborated by time-domain experiments, airborne acoustic waves generated by a source with a frequency centered about 10.6 kHz, placed at three different distances from one side of a finite phononic crystal slab, constructed from polymeric spheres, yield distinctive focal spots on the other side. These experiments evaluate the pressure field using optical feedback interferometry and demonstrate precise control of the three-dimensional wave trajectory through a sonic crystal.The band spectra of photonic [1, 2] and phononic [3] crystals can be interpreted to predict a rich array of interesting physical effects, for instance anomalous refraction [1,4] and all-angle-negative refraction [5] amongst many others; understanding these spectra underpins advances in electronic properties, wave transport in photonics and acoustics, as well as in interference phenomena throughout many fields of physical and engineering sciences.In this Letter we report experimental results where an image of a volumetric source through a three-dimensional phononic crystal (PC) forms according to the physics of indefinite media [6], see Fig. 1. The image is not created by tilting the crystal as in acoustic superlenses [7], or at low frequencies using effective media [8] nor by negative refraction acoustic flat lenses using metamaterials [9,10]. Instead we identify critical points on the isofrequency surfaces, for a simple cubic array of rigid spheres, where beam-like trajectories are formed and use these beams, and their reflections, to create lensing; this is using the properties of indefinite media [6].The first experimental demonstration of a threedimensional flat acoustic lens in 2004 [7] used 0.8-mm tungsten carbide beads surrounded by water, with the beads closely packed in a face-centered cubic crystal structure along the body diagonal (ΓR crystal direction); the lensing function was above the phononic band gap of the PC and at 1.57 MHz with the pressure waves focused into a tight spot (about 5 mm). We give an alternative design to this well-known phononic lens, based upon a different physical mechanism, also exhibiting focusing reminiscent of the Veselago-Pendry convergent flat lens [11,12], see Fig. 1. Negative refraction and superlensing of underwater pressure waves has been theorized with an anisotropic acoustic metamaterial formed by layers of perforated rigid plates [13], that is analogous to a hyperbolic medium in electromagnetism [14].As in [7] we use an array of sound-hard spheres, although now in air, take a primitive cubic array, and take ad...

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“…Interestingly, anomalous refraction, and notably a negative one, had actually been observed earlier in another kind of artificial medium, namely the photonic/phononic crystal [11][12][13][14][15] . a) Electronic mail: maxime.lanoy@gmail.com.…”

“…a) Electronic mail: maxime.lanoy@gmail.com. b) Electronic mail: John.Page@UManitoba.ca Note that these media can be either two- 11,12 or three- [13][14][15] dimensional. The refraction in this case is actually due to the intrinsic periodic nature of these media, and can be seen as a generalization of the diffraction orders of periodic gratings.…”

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