Wavefront Computing in Solids: The Design Parameters and the Ideal Lens

This paper presents a theoretical derivation for the design parameters of wavefront computing (WFC) system in solids including the aperture/transducer sizes, focal length, and the ideal lens. To achieve Fourier transform at the expected focal plane based on the wavefront computing system with ideal lens, the design parameters are derived for various transducers arrays from 4 by 4 to 32 by 32. Based on the theory in geometrical optics, the equations of ideal thick plano-concave lens are derived in solids for a given focal length and material properties. To validate the derived design parameters and the ideal lens, time domain simulation is used to show the propagation of the elastic waves in fused silica block. It can be observed that the waves excited by four piezoelectric transducers will get focused at the expected focal plane after the ideal lens.