Foreman Matthew R, Keng David, Treasurer Eshan, Lopez Jehovani R, Arnold Stephen
Opt Lett. 2017 Mar 1;42(5):963-966. doi: 10.1364/OL.42.000963.
Interactions between whispering gallery modes (WGMs) and small nanoparticles are commonly modeled by treating the particle as a point dipole scatterer. This approach is assumed to be accurate as long as the nanoparticle radius, a, is small compared to the WGM wavelength λ. In this Letter, however, we show that the large field gradients associated with the evanescent decay of a WGM causes the dipole theory to significantly underestimate the interaction strength and, hence, the induced WGM resonance shift, even for particles as small as a∼λ/10. To mitigate this issue, we employ a renormalized Born approximation to more accurately determine nanoparticle-induced resonance shifts and, hence, enable improved particle sizing. The domain of validity of this approximation is investigated, and supporting experimental results are presented.
回音壁模式（WGMs）与小纳米粒子之间的相互作用通常通过将粒子视为点偶极散射体来建模。只要纳米粒子半径a与WGM波长λ相比很小，就假定这种方法是准确的。然而，在本信函中，我们表明，与WGM的倏逝衰减相关的大场梯度会导致偶极理论显著低估相互作用强度，进而低估诱导的WGM共振位移，即使对于小至a ∼ λ/10的粒子也是如此。为了缓解这个问题，我们采用重正化玻恩近似来更准确地确定纳米粒子诱导的共振位移，从而实现更精确的粒子尺寸测量。研究了这种近似的有效范围，并给出了支持性的实验结果。
