Quasi-phase-matching of momentum and energy in nonlinear optical processes

Quasi-phase-matching is an important technique in nonlinear optics and is in widespread use. It not only makes efficient frequency conversion possible, but also enables diverse applications such as beam and pulse shaping, multi-harmonic generation, high harmonic generation, all-optical processing and the generation of entangled photons. However, since its introduction in the early 1960s at the dawn of nonlinear optics, quasi-phase-matching has always been considered a technique in which a purely spatial modulation mitigates the momentum mismatch that dispersion imposes on the interacting photons. Here, we present an important and fundamental generalization of quasi-phase-matching in which spatiotemporal nonlinear optical diffraction allows for correction of both momentum and energy mismatch. This concept provides a powerful tool for manipulating light through nonlinear interactions, and suggests unique applications. Recent experiments provide evidence for the feasibility and importance of spatiotemporal quasi-phase-matching.