Statistics of multiple-scatterer-induced frequency splitting in whispering gallery microresonators and microlasers

We investigate numerically and experimentally the statistics of the changes in the amount of frequency splitting upon adsorption of particles one by one into the mode volume of a whispering gallery mode (WGM) microresonator. This multiple-particle-induced frequency splitting (MPIFS) statistics carries information on the size and number of particles adsorbed into the mode volume, and is strongly affected by two experimental parameters: the WGM field distribution and the positions of particles within the mode volume. We show that the standard deviation and maximum value of the MPIFS are proportional to the polarizability of the particles, and propose a method to estimate particle size from the MPIFS if the only available data from experiments are frequency splitting.