Group velocity difference effect on incoherent sum-frequency generation spectrum

The spectral distribution of optical sum-frequency generation (SFG) by incoherent non-linear mixing of two chaotic beams with identical spectral width is calculated theoretically in the first approximation of the iterative method including dispersion of the non-linear medium and the difference between the group velocity of the input beams. It is shown that for the same group velocities (=0) of the input beams in non-linear medium the resultant field has a spectral width narrower than , and if a phase mismatch is present the spectral maximum of the resultant field is shifted towards lower or higher frequencies according to the sign of the phase mismatch. If the input beams have different group velocities (0) in the non-linear medium, then the spectral distribution of SFG is strongly dependent on . For small the spectral distribution of SFG is the same irrespective of . For large the difference in group velocities broadens the spectrum of SFG and for very large differences in group velocity the SFG has a spectral width identical to that of the input beams.