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

TL;DR

This paper examines the limitations of the dipole approximation in modeling nanoparticle interactions with whispering gallery modes, proposing a renormalized Born approximation for better accuracy in particle sizing.

Contribution

It introduces a renormalized Born approximation to improve the accuracy of nanoparticle size estimation in WGM sensing beyond the traditional dipole model.

Findings

Dipole approximation underestimates interaction strength for particles as small as λ/10.

Renormalized Born approximation provides more accurate resonance shift predictions.

Experimental results support the improved modeling approach.

Abstract

Interactions between whispering gallery modes (WGMs) and small nanoparticles are 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 evanescent decay of a WGM causes the dipole theory to significantly underestimate the interaction strength, and hence induced WGM resonance shift, even for particles as small as $a\sim \lambda/10$. 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.