Conformally Mapped Multifunctional Acoustic Metamaterial Lens for Spectral Sound Guiding and Talbot Effect

Abstract

<jats:p>We demonstrate a conformally mapped multifunctional acoustic metamaterial Mikaelian lens. Mikaelian lens is a gradient medium with a hyperbolic secant refractive index profile that can realize functions like beam self-focusing. Unlike the conventional design approaches, with a conformal transformation method, only isotropic material parameters with gradient refractive index profiles are required for the construction of such lens. To realize desired gradient index distribution, we carefully design a new type of cross-channel-shaped acoustic metamaterial, whose refractive index can be effectively modulated by simply changing the slit opening size. The distinct capabilities of the metamaterial Mikaelian lens in manipulating acoustic waves are experimentally verified with the fabricated sample. Simultaneous sound guiding and Talbot effects, which normally require respective geometrical and wave acoustic approximations, are observed in simulations and experiments. Furthermore, those effects of shaping acoustic wave propagations were validated within a relatively wide frequency range. Our study reveals how the conformal transformation method can help to bridge the ray acoustics with wave acoustics. It offers opportunities to the development of novel multifunctional acoustic devices for various applications, such as sound and particle manipulations.</jats:p>

The space-time Talbot effect

“…However, the same basic considerations apply to other physical waves, where it is a universal feature that the decoupled diffraction and dispersion length scales are incommensurate. The spatial Talbot effect has been realized in a variety of physical contexts besides optics, including acoustics [45,46], atom matter waves [47], rogue waves [48], water waves [49], and elastic solid waves [50] (and has been proposed for Bose-Einstein condensates [51,52]), whereas the temporal Talbot effect has been observed thus far in Bose-Einstein condensates [53]. A combined spatio-temporal Talbot effect has not been realized thus far in any physical wave.…”

Metamaterial Acoustics on the (2 + 1)D Einstein Cylinder

“…This is exactly the wave equation which governs acoustic wave propagation on the Einstein cylinder, engineered and enforced by the acoustic parameters determined by Equation (11).…”

“…The constitutive equations, Equation (11), describe the acoustic model at hand and provide the corresponding bulk modulus and the full symmetric matrix of density of the metadevice. As such, they fully encapsulate the structure of the underlying metamaterial for acoustics on the (2 + 1)D Einstein cylinder.…”

“…These metamaterials offer researchers and engineers unique opportunities to design and build novel artificial devices with exceptional characteristics (see, e.g., [7][8][9][10]). For recent remarkable advances in this field of metamaterials acoustic, we refer to [11], where a special type of multifunctional acoustic lens is designed by only using isotropic material parameters. Furthermore, in [12], acoustic metamaterial devices are constructed that are reconfigurable by using untethered physical stimuli, i.e., avoiding mechanisms such as compression or pneumatic actuators.…”

“…Of course, other numerical scenarios are conceivable and may be tackled by diverse numerical integrator software. Alternatively, in a different approach, software such as COMSOL Multiphysics [30] may be used for physically simulating all wave phenomena with finite-element methods in a virtual laboratory by only using the necessary acoustic parameters provided in Equation (11).…”