Photon distribution functions of fluorescence photons from single nanoparticles: Three different photon counting methods

Mathematical expressions are derived for three photon distribution functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) corresponding to three different methods for counting fluorescence photons from a single nanoparticle excited by continuous laser radiation. Each of the three functions is expressed in terms of Poisson functions, which makes it possible to pass in the w _N ^M (T), w _N ^Z (T), and w _N ^O functions from N multiple integrals to single or double integrals. This not only eases the numerical calculation of the photon distribution, but it also makes it possible to find that, for each exponential process in the dynamics of a nanoparticle, there is a Poisson function in the photon distribution function. All three photon counting methods yield the same photon distribution for continuous fluorescence and different photon distributions for blinking fluorescence.