The evolution of the phase of a weak signal wave (ω<sub>2</sub>) copropagating with a strong gate wave (ω<sub>1</sub>) 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 (ω<sub>3</sub>=2ω<sub>1</sub>+ω<sub>2</sub>). It is shown that the signal wave collects, in addition to the phase shift that is due to the ω<sub>2</sub>=ω<sub>1</sub>+ω<sub>2</sub>−ω<sub>1</sub> process, an extra nonlinear phase shift caused by cascading of two third-order nonlinear processes, ω<sub>3</sub>=2ω<sub>1</sub>+ω<sub>2</sub> and ω<sub>2</sub>= ω<sub>3</sub>−2ω<sub>1</sub>. 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
S. Saltiel, K. Koynov, K. Kirov, and K. Petrova, "Cross-phase modulation caused by cascading of third-order processes," J. Opt. Soc. Am. B 16, 262-266 (1999)