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Interactions between whispering gallery modes (WGMs) and small nanoparticlesare commonly modelled 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 $\lambda$. In this article,however, we show that the large field gradients associated with the evanescentdecay of a WGM causes the dipole theory to significantly underestimate theinteraction strength, and hence induced WGM resonance shift, even for particlesas small as $a\sim \lambda/10$. To mitigate this issue we employ a renormalizedBorn approximation to more accurately determine nanoparticle induced resonanceshifts and hence enable improved particle sizing. The domain of validity ofthis approximation is investigated and supporting experimental results arepresented.

Whispering gallery mode single nano-particle detection and sizing: the validity of the dipole approximation