Accurate and efficient determination of the radius, refractive index, and dispersion of weakly absorbing spherical particle using whispering gallery modes

Abstract

We present an algorithm that can be used to simultaneously determine the radius and the refractive index (with dispersion) of a spherical, homogeneous particle. This is accomplished by fitting characteristic resonances calculated using Mie scattering coefficients to the measured whispering gallery mode resonances. The advantage of this algorithm over those that have been presented previously is that a large portion of the search can be reduced to two dimensions (a search that includes radius and refractive index with dispersion will always be at least three dimensions). Using this algorithm, we analyze two large sets of cavity-enhanced Raman spectra from optically trapped aerosol particles. The speed of the algorithm allows for best fits to be found in real time. Precision is found to be limited by the resolution of the spectrograph.