Acoustic conjugate metamaterials (ACMs), in which the imaginary parts of the effective complex mass density and bulk compressibility are cancelled out in the refractive index, possess the elements of loss and gain simultaneously. Previous works have focused on panel ACMs for plane wave incidence. In this paper, we explore the extraordinary scattering properties, including the acoustic equivalent lasing (AEL) and coherent perfect absorption (CPA) modes, of a three-dimensional ACM sphere, where incident spherical waves with specific topological orders could be extremely scattered and totally absorbed, respectively. Theoretical analysis and numerical simulations show that the AEL or CPA mode with a single order can be realized with a small monolayer ACM sphere with appropriate parameters. A huge (relative to incident wavelength) ACM sphere with pure imaginary parameters could support the even- (or odd-) order AEL and odd- (or even-) order CPA modes simultaneously. In addition, the AEL and/or CPA with multiple orders could be realized based on a small multilayered ACM sphere. The proposed ACM sphere may provide an alternative method to design acoustic functional devices, such as amplifiers and absorbers.

中文翻译：

---

基于共轭超材料球的声等效激光和相干完美吸收

声共轭超材料（Acoustic Conjugate Metamaterials，ACMs），其有效复质量密度和体积压缩率的虚部在折射率中被抵消，同时具有损耗和增益的元素。以前的工作集中在用于平面波入射的面板 ACM。在本文中，我们探索了三维 ACM 球体的非凡散射特性，包括声学等效激光 (AEL) 和相干完美吸收 (CPA) 模式，其中具有特定拓扑阶的入射球面波可以非常分散且完全分别吸收。理论分析和数值模拟表明，采用适当参数的小型单层ACM球可以实现单阶AEL或CPA模式。具有纯虚参数的巨大（相对于入射波长）ACM 球体可以同时支持偶数（或奇数）阶 AEL 和奇数（或偶数）阶 CPA 模式。此外，多阶的 AEL 和/或 CPA 可以基于一个小的多层 ACM 球体来实现。所提出的 ACM 球可以提供一种替代方法来设计声学功能设备，例如放大器和吸收器。