Pulse propagation in four-wave mixing process with group index difference of signal and idler waves

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Four-wave mixing process with a large group index difference of the signal and idler pulses in a nonlinear optical fiber is theoretically investigated when the pump is continuous light. We prove that in the four-wave mixing process, the signal and idler waves would finally propagate in a common group velocity in spite of their different group indices. When the effective phase mismatch in four-wave mixing is not zero, their carrier frequencies shift in different directions. The asymptotic result of the signal and idler shape and carrier frequency shift are obtained. The theoretical prediction is validated by the numerical simulation.