Three-dimensional sensing of arbitrarily shaped nanoparticles by whispering gallery mode resonators

Whispering-gallery-mode (WGM) microresonators are a promising platform for highly sensitive, label-free detection and probing of individual nano-objects. Our work expands these capabilities by providing the analysis tools required for three-dimensional (3D) characterization of arbitrarily shaped nanoparticles. Specifically, we introduce a theoretical model that describes interactions between nanoparticles and WGM resonators, taking into account effects that were often not considered, such as the elliptical polarization of the transverse-magnetic (TM) mode, the possible non-spherical shape of the nanoparticle, its finite size, and the open-system nature of the modes. We also introduce a self referencing measurement method that allows the extraction of information from measurements done at arbitrary positions of the nanoparticles within the WGM. We verify our model by experimentally probing a single Tungsten-disulfide (WS2) nanotube with a silica microtoroid resonator inside a scanning electron-microscope (SEM) and perform 3D characterization of the nanotube.