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

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.

X-ray dynamical diffraction analogues of the integer and fractional Talbot effects

The X-ray integer and fractional Talbot effect is studied under two-wave dynamical diffraction conditions in a perfect crystal, for the symmetrical Laue case of diffraction. The fractional dynamical diffraction Talbot effect is studied for the first time. A theory of the dynamical diffraction integer and fractional Talbot effect is given, introducing the dynamical diffraction comb function. An expression for the dynamical diffraction polarization-sensitive Talbot distance is established. At the rational multiple depths of the Talbot depth the wavefield amplitude for each dispersion branch is a coherent sum of the initial distributions, shifted by rational multiples of the object period and having its own phases. The simulated dynamical diffraction Talbot carpet for the Ronchi grating is presented.