Theory and experiments for multiple four-wave-mixing processes with multifrequency pumps in optical fibers

Multiple four-wave-mixing (FWM) processes with multifrequency pumps in optical fibers are investigated theoretically and experimentally. The propagation equations describing the FWM nonlinear interactions between pump waves and first-order sideband waves are derived. Based on our theoretical model, the rigorous nonlinear equations governing arbitrary pumps can be developed when the pump waves have equal frequency spacing. The proposed theory can generalize the traditional theory of FWM processes. The rigorous nonlinear equations governing three pumps and three cases of simplified equations governing three, four, and five pumps are achieved. Numerical simulations for three, four, and five pumps are experimentally tested by using a piece of highly nonlinear photonic-crystal fiber, and the experimental observations confirmed our theoretical predictions. The stabilization of waves by multiple FWM processes is proved theoretically and confirmed experimentally.