Effect of group velocity mismatch on the measurement of ultrashort optical pulses via second harmonic generation

The use of second harmonic generation as a technique for optical pulse width measurements is analyzed to determine the effects of both phase velocity and group velocity mismatch between fundamental and second harmonic fields. An expression for the time average second harmonic energy, which except for special cases differs from the intensity autocorrelation function, is derived. For Type I phase matching, the measurement yields an apparent correlation width which can be either shorter or longer than the actual intensity correlation width, depending on the specific pulse shape. When the group velocity mismatch is nonzero, the measurement becomes sensitive to the phase matching condition. Two special pulse shapes for which the measurement is independent of group and phase velocity mismatch are the Gaussian and the single-sided exponential.