Theory of resonance shifts of whispering gallery modes by arbitrary plasmonic nanoparticles

Shifts of the resonance frequency of high Q whispering gallery modes (WGMs) in spherical dielectric microresonators by plasmonic nanoparticles can be greater than the WGM line width, such that the perturbation theory commonly used for describing resonance shifts by dielectric nanoparticles (Teraoka and Arnold 2006 J. Opt. Soc. Am. B 23 1381) is no longer applicable. This paper therefore reports on an analytic framework, based on generalized Lorenz-Mie theory, capable of describing resonance shifts by metallic nanoparticles supporting plasmon oscillations. Generalization to nanoparticles of arbitrary geometry is presented by employing the extended boundary condition method. Within this framework, hybrid resonance conditions for coupled spherical photonic and plasmonic resonators are established and shown to simplify for small plasmonic nanoparticles. Approximate analytic formulae are derived for the shift and broadening of the isolated WGM and plasmon resonances, from which either apparent resonance shifts or mode splitting are shown to follow. Tuning of plasmon resonances using, for example, core-shell nanoparticles to attain a large spectral overlap between WGM and plasmon resonances is demonstrated to significantly enhance the magnitude of resonance shifts, with a 60-fold enhancement achieved without any optimization. Hybridization of photonic-plasmonic resonances is furthermore demonstrated (in addition to hybridization of transverse electric-transverse magnetic WGMs) and the associated level repulsion illustrated. Finally, the dependence of WGM resonance shifts on the orientation of silver nanorods is theoretically investigated and found to be strong by virtue of the asymmetry of the nanorod.