Abstract Luneburg lens is a symmetric gradient-index lens with a refractive index that increases from the outer surface to the center in a radial manner. It has the ability to focus and collimate waves, which makes it useful for energy harvesting, waveguiding and as a component in transducers. An ideal Luneburg lens should be easy to fabricate, has broadband and omnidirectional characteristics, as well as a focal length that can be easily tuned. However, existing structural Luneburg lenses based on phononic crystals can hardly achieve these requirements. Here, we propose an alternative structural Luneburg lens which has a refractive index that varies smoothly with its radial distance as a result of a changing thickness. Theoretical calculations, numerical simulations and experimental measurements of flexural wave propagation through the lens showed that flexural wave focusing can be obtained inside, at the edge and outside of the variable thickness lens for different frequencies and propagation directions. Flexural wave collimation was also demonstrated when a point source was placed at the respective focal points for each lens. Furthermore, it was shown that flexural waves that were focused onto a piezoelectric energy harvester by the Luneburg lens can lead to a significant increase in the harvested voltage compared to that obtained without focusing.

中文翻译：

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用于宽带聚焦和准直的改良结构 Luneburg 透镜

摘要 Luneburg 透镜是一种对称的梯度折射率透镜，其折射率从外表面到中心呈放射状增加。它具有聚焦和准直波的能力，这使其可用于能量收集、波导和作为换能器的组件。理想的 Luneburg 镜头应该易于制造，具有宽带和全向特性，以及可以轻松调整的焦距。然而，现有的基于声子晶体的结构 Luneburg 透镜很难达到这些要求。在这里，我们提出了一种替代结构的 Luneburg 透镜，其折射率随着厚度的变化而随径向距离平滑变化。理论计算，弯曲波通过透镜传播的数值模拟和实验测量表明，对于不同频率和传播方向，可以在可变厚度透镜的内部、边缘和外部获得弯曲波聚焦。当一个点源被放置在每个透镜的各自焦点上时，弯曲波准直也得到了证明。此外，研究表明，与未聚焦时获得的电压相比，由 Luneburg 透镜聚焦到压电能量采集器上的弯曲波可导致采集电压显着增加。当一个点源被放置在每个透镜的各自焦点上时，弯曲波准直也得到了证明。此外，研究表明，与未聚焦时获得的电压相比，由 Luneburg 透镜聚焦到压电能量采集器上的弯曲波可导致采集电压显着增加。当一个点源被放置在每个透镜的各自焦点上时，弯曲波准直也得到了证明。此外，研究表明，与未聚焦时获得的电压相比，由 Luneburg 透镜聚焦到压电能量采集器上的弯曲波可导致采集电压显着增加。