Physics Department, Queens College of CUNY, Flushing, New York 11367, USA.
The Graduate Center of CUNY, New York, New York 10016, USA.
Phys Rev E. 2019 Jan;99(1-1):013310. doi: 10.1103/PhysRevE.99.013310.
An efficient numerical method for determining the spectral characteristics and spatial distribution of the field of a spheroidal whispering-gallery-mode (WGM) resonator interacting with a dielectric nanoparticle is presented. The developed approach is based on a combination of T-matrix formalism applied to a single resonator with a dipole approximation for the field of the nanoparticle. The method is illustrated by computation of the scattered field of the resonator-particle system illuminated by an incident field in the form of a single WGM mode of TE or TM polarization mimicking the excitation of the resonances by a tapered fiber. Our calculations show that even a very small (less than 0.1%) deviation of the resonator's shape from an ideal sphere renders spherical approximation invalid. They also confirm that analytical resonant approximation for spheroidal resonators developed previously gives a reasonable qualitative description of the spectral characteristics of the resonator-particle system. It was found, however, that corrections to the resonant approximation are significant enough for realistic nominally spherical resonators to be taken into account for accurate analysis of the experimental data.
提出了一种用于确定与介电纳米粒子相互作用的椭球 whispering-gallery 模式（WGM）谐振器的光谱特性和场空间分布的有效数值方法。所开发的方法基于应用于单个谐振器的 T 矩阵公式与用于纳米粒子场的偶极子近似的组合。该方法通过计算由以 TE 或 TM 偏振的单个 WGM 模式形式的入射场照明的谐振器-粒子系统的散射场来说明，该入射场模拟由锥形光纤激发的共振。我们的计算表明，即使谐振器的形状相对于理想球体有很小的（小于 0.1%）偏差，球近似也会失效。它们还证实，以前为椭球谐振器开发的分析谐振近似可以合理地定性描述谐振器-粒子系统的光谱特性。然而，发现对于实际的标称球形谐振器，谐振近似的修正非常重要，需要考虑这些修正才能对实验数据进行准确分析。
