Abstract

The evolution of the phase of a weak signal wave $({\omega }_2)$ copropagating with a strong gate wave $({\omega }_1)$ in a centrosymmetric medium is studied analytically and numerically for the case when the two waves are involved in a nearly phase-matched third-order process that generates a third wave $({\omega }_3=2{\omega }_1+{\omega }_2).$ It is shown that the signal wave collects, in addition to the phase shift that is due to the ${\omega }_2={\omega }_1+{\omega }_2-{\omega }_1$ process, an extra nonlinear phase shift caused by cascading of two third-order nonlinear processes, ${\omega }_3=2{\omega }_1+{\omega }_2$ and ${\omega }_2={\omega }_3-2{\omega }_1.$ The attractive feature of this new type of cross-phase modulation is the fact that one can control its magnitude and sign by changing the wave-vector mismatch of the sum-frequency mixing process and the gate intensity.

© 1999 Optical Society of America

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