Generalized phase-matching condition for nondegenerate four-wave mixing
Phillip R. Peterson, A. Gavrielides, David A. Cardimona
The coupled-probe, conjugate, and pump differential equations are solved in the undepleted pump approximation when the pumps are of unequal frequencies. In the usual analysis the two pump wave vectors satisfy k1 + k2 = 0, so that the conjugate and probe wave vectors satisfy kp + kc = 0. The vector phase matching then consists of two one-dimensional problems. However, the unequal pump frequencies require a true two-dimensional analysis, since the pump wave vectors do not sum to zero separately from the probe/conjugate fields. This then requires the inclusion of a transverse dimension in the differential equations. The net result is that the direction of the maximum conjugate intensity, usually determined by the phase-match condition Δk = 0, is instead determined by the generalized condition kc · Δk = 0, where Δk = k1 + k2 − kp − kc. This new phase-matching condition is quadratic in kc, leading to two peaks in the conjugate reflection coefficient.
Journal of the Optical Society of America B•Mar 1, 1987•3 citations