Improving the performance of structure-embedded acoustic lenses via gradient-index local inhomogeneities

We investigate the use of graded inhomogeneities in order to enhance the focusing and collimation performance of structure-embedded acoustic metamaterial lenses. The type of inhomogeneity exploited in this study consists in axial symmetric exponential-like gradients of either material or geometric properties that create gradient-index inclusions able to bend and redirect propagating waves. In particular, we exploit the concept of gradient index inclusions to achieve focusing and collimation of ultrasonic beams created by embedded drop-channel lenses in both bulk and thin-walled structures. In the latter, the implementation is possible thanks to geometric exponential tapers known as Acoustic Black Holes (ABH). ABH tapers allow accurate control of the characteristics of the acoustic beam emanating from the lens channel which in the conventional design is severely affected by diffraction. The concept of beam control via graded inclusions is numerically illustrated and validated by using a combination of methodologies including geometric acoustics, finite difference time domain, and finite element methods.