Statistical Fluctuations in Nonlinear Optical Processes

The influence of partial coherence in a laser beam on nonlinear optical interactions is discussed. The presence of several different modes with random amplitude and phases is shown to lead to fluctuations in second-harmonic production and to an error in the measurement of the corresponding nonlinear constant. Experiments have been carried out with a "$Q$-switched" ruby, which demonstrate the role of partial spatial coherence in creating fluctuations in second-harmonic production. Mixing and higher harmonics generation are also considered. Limitations in momentum space necessitate a separate discussion of the creation of light beats at small difference frequencies.