Abstract Acoustic lenses composed of metamaterials are used as highly anisotropic subwavelength media and have broad applications in a wide range of industrial areas. As reported in recent research, an acoustic lens composed of a cross-shaped structure can achieve high-intensity 3D focusing in an underwater system. However, the operating characteristics of this lens at different frequencies have not been studied in detail until now. In this work, we studied the focusing performance of a particular acoustic lens at different working frequencies, and the band structure, wave intensity distribution, reflection and transmission coefficients, and refractive index of a unit cell were investigated, as well as the characteristics of the acoustic lens through a simulation and experiment. Errors were minimized in the experiments through reasonable design, and we found that although the wave intensity of a single unit cell decreased as the frequency increased, in the acoustic lens, the intensity of the sound field at its focal point increased with the frequency. The present research provides an improved method for designing acoustic lenses with different working frequencies and can guide nondestructive testing (NDT) and biomedical treatment.

中文翻译：

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水声聚焦复合透镜的频率响应

摘要 由超材料构成的声透镜作为高度各向异性的亚波长介质，在广泛的工业领域有着广泛的应用。正如最近的研究报道，由十字形结构组成的声学透镜可以在水下系统中实现高强度的 3D 聚焦。但是，直到现在还没有详细研究这种镜头在不同频率下的工作特性。在这项工作中，我们研究了特定声透镜在不同工作频率下的聚焦性能，研究了晶胞的能带结构、波强分布、反射和透射系数以及折射率，以及其特性。声学透镜通过模拟和实验。通过合理的设计将实验中的误差降到最低，我们发现，虽然单个晶胞的波强度随着频率的增加而降低，但在声透镜中，其焦点处的声场强度随着频率的增加而增加。本研究为设计不同工作频率的声学透镜提供了一种改进方法，可以指导无损检测（NDT）和生物医学治疗。