Design and simulation of acoustic metamaterial luneburg lenses for predetermined focal points

This paper presents the design and simulation of acoustic metamaterial lenses that focus elastic waves at predetermined focal points. The modified Luneburg refractive index profile is used in the design process to define focal point locations, a capability not previously explored in elastic wave research. This new approach is important because it enables more precise spatial control of waves, resulting in enhanced resolution for elastic wave focusing applications. Three lenses, each targeting specific focal points, are designed by proposing hexagonal unit cells containing blind holes with varying diameters. Dispersion curves are calculated by finite element simulations to determine wave properties of unit cells, including refractive indices. These unit cells provide a wide range of refractive indices (۱.۰۳۱۴-۱.۴۹۵۹) at the design frequency of ۵۰ kHz, which is suitable for constructing Luneburg lenses. Unit cells are then arranged according to the discretized refractive index profiles to form the lenses. Numerical simulations validate effective wave focusing at the intended focal points (F=R, ۱.۵R, ۲R) with three lenses. The highest amplification of waves and the narrowest focal zone are for the lens with F=R. As the focal point shifts toward ۲R, wave distribution becomes scattered along the focal axis. Decay length analysis of F=۱.۵R and ۲R lenses indicates their suitability for long distribution of high-velocity regions. Frequency-dependent simulations across ۴۶–۵۲ kHz reveal that all lenses maintain efficient focusing between ۴۹–۵۱ kHz. At more distant off-design frequencies, amplifications result from refractive index shifts that misalign the focal point.

کلیدواژه ها:

Acoustic Metamaterials ، Luneburg lens ، Predetermined Focal Points ، Elastic Waves