Mode splitting induced by an arbitrarily shaped Rayleigh scatterer in a whispering-gallery microcavity

Abstract

We investigate theoretically the mode splitting induced by an arbitrarily shaped Rayleigh scatterer attached to a whispering-gallery microcavity. The information including polar position, orientation, and polarizability tensor of the nanoparticle can be obtained through the mode-splitting signal. It is found that when the electric field of a pair of counterpropagating modes have different orientations and are not linearly polarized, both of the split modes experience frequency shift and linewidth broadening. The polar angle, at which a nanoparticle binds on the microsphere cavity, can be extracted by comparing frequency splittings of two fundamental TE modes. Moreover, the orientation and polarizability of the particle can be acquired by combining frequency splittings and linewidth broadenings of three modes which polarize the particle in different orientations. This work provides a comprehensive theory base for microcavity sensing of nanoparticles of arbitrary shape instead of nanospheres and could push nanoparticle detection towards quantitative characterization.