Statistics of single-molecule surface enhanced Raman scattering signals: fluctuation analysis with multiple analyte techniques.

The mathematical background, based on a variation of the principal component analysis (PCA) method, is developed for the understanding of fluctuating multiple analyte single-molecule (SM) surface enhanced Raman scattering (SERS) signals; with emphasis on the bianalyte SERS technique developed recently. The method and its significance are presented to provide a systematic framework with which several aspects of the statistics of SM-SERS signals can be analyzed in general. We also apply the method to a concrete example of bianalyte statistics in silver colloidal solutions and discuss related topics around experimental issues and the interpretation of single-molecule SERS data.