A formula for the photoelectron-counting distribution for a two-photon detector is derived quantum mechanically assuming that the ionising transitions in the atoms of the detector take place through the simultaneous absorption of two photons. It is assumed that the incident light is quasimonochromatic. It is shown that the distribution of the photoelectrons is given by the average of a Poisson distribution, the parameter of the distribution being proportional to the time integral of the square of the instantaneous light intensity. Counting distributions for the thermal (gaussian) light and for some models of laser light are obtained for the limiting case when the counting-time interval T is short compared to the coherence time Tc of the light. An approximate formula for arbitrary time intervals for the counting distribution of thermal light is also proposed.
A. K. JAISWAL and G. S. AGARWAL, "Photoelectric Detection with Two-Photon Absorption," J. Opt. Soc. Am. 59, 1446-1452 (1969)