连接半平面的部分分隔窄缝的声学：连续介质中指数准束缚态及其共振激发的研究
Acoustics of a partially partitioned narrow slit connected to a half-plane: case study for exponential quasi-bound states in the continuum and their resonant excitation
摘要：
开放系统中的局域波振荡不随时间衰减或增长，尽管它们的频率位于携带能量到无穷远或来自无穷远的辐射模式的连续谱内，被称为连续谱中的束缚态（BIC）。BIC的典型微妙条件的小扰动几乎总是导致波与辐射模式弱耦合，导致称为准BIC的泄漏状态，其具有大的品质因数。我们研究了这种弱耦合的渐近性质的情况下，声波相互作用的刚性基板具有部分分区狭缝-设置，支持准BIC指数接近BIC的狭缝越来越窄。在此极限下，我们用匹配渐近展开法结合互易关系研究了这些准BIC及其共振激发。特别是，我们推导出一个领先的近似指数小虚部的每个波数特征值（成反比的品质因数），这是超出了所有的订单的扩展波数特征值本身。此外，我们推导出一个领先的近似的指数大振幅的状态的情况下，它们是共振激发的平面波在斜入射。这些共振发生在指数狭窄的波数间隔，并在物理上表现在圆柱形偶极波从狭缝孔径和狭缝内的指数大的字段增强。数值计算的渐近近似验证。
英文摘要：
Localised wave oscillations in an open system that do not decay or grow in time, despite their frequency lying within a continuous spectrum of radiation modes carrying energy to or from infinity, are known as bound states in the continuum (BIC). Small perturbations from the typically delicate conditions for BIC almost always result in the waves weakly coupling with the radiation modes, leading to leaky states called quasi-BIC that have a large quality factor. We study the asymptotic nature of this weak coupling in the case of acoustic waves interacting with a rigid substrate featuring a partially partitioned slit -- a setup that supports quasi-BIC that exponentially approach BIC as the slit is made increasingly narrow. In that limit, we use the method of matched asymptotic expansions in conjunction with reciprocal relations to study those quasi-BIC and their resonant excitation. In particular, we derive a leading approximation for the exponentially small imaginary part of each wavenumber eigenvalue (inversely proportional to quality factor), which is beyond all orders of the expansion for the wavenumber eigenvalue itself. Furthermore, we derive a leading approximation for the exponentially large amplitudes of the states in the case where they are resonantly excited by a plane wave at oblique incidence. These resonances occur in exponentially narrow wavenumber intervals and are physically manifested in cylindrical-dipolar waves emanating from the slit aperture and exponentially large field enhancements inside the slit. The asymptotic approximations are validated against numerical calculations.
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