Multinanoparticle scattering in a multimode microspheroid resonator

We theoretically investigate the scattering of multiple Rayleigh nanoparticles in a microspheroid resonator which supports multiple polar whispering gallery modes. Different from a standard microsphere resonator in which polar modes with the same radial and angular mode numbers are degenerate, a spheroid resonator supports spectrally nondegenerate polar modes. The mode splitting, mode shift, and linewidth broadening of polar modes are deduced at the presence of multiple Rayleigh scatterers following the Weisskopf-Wigner semi-QED treatment. It is found that the radial, polar, and azimuthal coordinates of the nanoparticle can be inferred from the transmission spectra of the polar modes. In particular, the changes of both the mode shift and linewidth broadening show cosinoidal dependence on the azimuthal angle. Our scheme provides an efficient platform to locate the three-dimensional positions of multiple nanoparticles in a microcavity, which may push the microcavity sensing to sizing and further quantitative measurements.