AI 中文总结
本文建立单个谐振器声学散射的共振态展开公式，经均匀二维圆柱、扇形扰动圆柱及材料编程硬壁环形超原子验证，可重现相关解、模拟结果与光谱近场，为特定开放谐振器声学散射提供透明模态方法。
AI 中文摘要
我们针对单个谐振器的声学散射问题建立了共振态展开公式。散射压力场和粒子速度场在系统的共振态上展开，激发振幅由入射场与谐振器体积内共振态的重叠积分确定。利用声能通量，我们推导了消光、散射和吸收截面的表达式，并证明消光光谱可分解为各个共振态的贡献。该公式首先针对均匀二维圆柱进行验证，其重现了解析的Mie理论解；接着我们考虑带有耦合角向模式的扇形扰动圆柱，证明其与有限元模拟结果一致；最后，我们结合特征值和散射公式，针对材料编程的硬壁环形超原子，重现了其散射光谱和近场。所建立的框架为具有降低对称性和空间结构化材料参数的开放谐振器的声学散射提供了物理上透明的模态方法。
英文摘要
We develop a resonant-state expansion formulation for acoustic scattering by individual resonators. The scattered pressure and particle-velocity fields are expanded over the resonant states of the system, with excitation amplitudes determined by overlap integrals between the incident field and the resonant states over the resonator volume. Using the acoustic energy flux, we derive expressions for the extinction, scattering, and absorption cross-sections and show that the extinction spectrum can be resolved into contributions from individual resonant states. The formulation is first validated for a homogeneous two-dimensional cylinder, where it reproduces the analytical Mie-theory solution. We then consider a sectorally perturbed cylinder with coupled azimuthal modes and demonstrate agreement with finite-element simulations. Finally, we combine the eigenvalue and scattering formulations for a material-programmed hard-wall annular metaatom and reproduce its scattering spectra and near fields. The developed framework provides a physically transparent modal approach to acoustic scattering by open resonators with reduced symmetry and spatially structured material parameters.
Comments9 pages, 6 figures, Supplemental Material
