Analysis of cross correlation, phase velocity mismatch and group velocity mismatches in sum-frequency generation

Sum-frequency generation obtained by phase-matched optical pulses of different profiles and unequal pulse widths and frequencies is analyzed. Expressions are obtained that indicate the exact dependence of field and intensity upon phase mismatch, crystal thickness, and group velocity mismatches between the fundamental pulses and between fundamental and the sum-frequency pulses. The expressions reduce to known results in the case of replica fundamental pulses, in which case autocorrelation is used. A rigorous model is derived and, in the case where the group velocity mismatch between incident and generated pulses for a specific profile can be neglected, analytical and numerical treatments are given