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 the adsorption of particles one-by-one into the mode volume of whispering gallery mode (WGM) microresonator and microlasers. This multiple-particle induced frequency splitting (MPIFS) statistics carries information on the size and the number of adsorbed particles into the mode volume, and it is strongly affected by two experimental parameters, namely the WGM field distribution and the positions of the 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 is frequency splitting.