Theory of two-photon measurement of laser output

Two-photon fluorescence and second-harmonic generation experiments have been used recently to study the picosecond structure of laser signals. A general theory of these measurements is presented in this work, which includes a detailed analysis of the possible responses of the measurement to a mode-locked laser that produces pulses and to a free-running laser that produces a noise-like output. Shapes Of the expected response patterns are calculated; second-order statistics that describe statistical departures from the expected patterns are also determined. Results are given for an arbitrary number of laser modes and general mode spectrum, in computationally useful forms for small and large mode number. Illustrative examples for large mode number are worked out for Gaussian and uniform mode profile curves; in addition, exact results are obtained for the uniform case of any (odd) number of modes. Sample response patterns for the case of a free-running laser are calculated by Monte-Carlo technique for Gaussian and uniform mode spectra. Results that reduce to special cases treated in various prior works are pointed out and new findings are discussed.