This paper is concerned with the scattering resonances of open cavities. It is a follow-up of Ammari et al. (ZAMP 71:102, 2020), where the transverse magnetic polarization was assumed. In that case, using the method of matched asymptotic expansions, the leading-order term in the shifts of scattering resonances due to the presence of small particles of arbitrary shapes was derived and the effect of radiation on the perturbations of open cavity modes was characterized. The derivations were formal. In this paper, we consider the transverse electric polarization and prove a small-volume formula for the shifts in the scattering resonances of a radiating dielectric cavity perturbed by small particles. We show a strong enhancement in the frequency shift in the case of subwavelength particles with dipole resonances. We also consider exceptional scattering resonances and perform small-volume asymptotic analysis near them. A significant observation is the large-amplitude splitting of exceptional scattering resonances induced by small particles. Our method in this paper relies on pole-pencil decompositions of volume integral operators.

本文涉及开放腔的散射共振。这是Ammari等的后续研究。（ZAMP 71：102，2020），其中假定了横向磁极化。在那种情况下，使用匹配渐近展开法，推导了由于存在任意形状的小颗粒而引起的散射共振移动的前导项，并表征了辐射对开腔模态扰动的影响。派生是正式的。在本文中，我们考虑了横向极化，并证明了一个小体积公式，用于计算受小颗粒扰动的辐射介质腔的散射共振的位移。在具有偶极子谐振的亚波长粒子的情况下，我们显示出频移方面的增强。我们还考虑了特殊的散射共振，并在它们附近进行小量渐近分析。一个重要的发现是小颗粒引起的特殊散射共振的大幅度分裂。本文中的方法依赖于体积积分算子的极铅笔分解。