SUM- AND DIFFERENCE-FREQUENCY-GENERATION FOR BROAD-BAND INPUT FIELDS

We analyze the dynamics of sum-frequency generation (SFG) and differen ce-frequency generation (DFG) for broadband input fields. We demonstra te that amplitude modulation of the input fields significantly affects conversion efficiency of SFG and DFG, but frequency modulation does n ot affect conversion efficiency. Analytic results for SFG and DFG outp ut-field intensities are thereby available for arbitrary fields. Self- and cross-phase modulation can affect the dynamics in the limit of ve ry high field strengths, but these effects are of higher nonlinearity and therefore usually negligible. The quantum efficiency of DFG is sho wn to be generally higher than SFG, but the energy efficiency is much lower if the difference frequency is significantly less than the input frequencies. Optimal SFG;quantum conversion efficiency for such syste ms approaches that of second-harmonic generation only if the. quantum fluence (total number of photons) in the two input beams are equal. Op timal DFG quantum conversion efficiency occurs when the number of phot ons of frequency omega(2) is small-yet sufficient for significant stim ulation. A recently developed method for obtaining efficient SFG for m ultimode input fields is theoretically analyzed. The method involves u sing an arrangement with two or more nonlinear mixing crystals with a time-delay line situated between the crystals that delays one of the f undamental fields relative to the other. The efficiency in the second crystal depends on the cross-correlation function of the two fundament al fields upon leaving the first nonlinear crystal. The time-delay met hod is not effective for multimode DFG.