Whispering gallery mode single nanoparticle detection and sizing: The validity of the dipole approximation

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.