Cross-phase modulation caused by cascading of third-order processes

The evolution of the phase of a weak signal wave (omega(2)) copropagating w ith a strong gate wave (omega(1)) in a centrosymmetric medium is studied an alytically and numerically for the case when the two waves are involved in a nearly phase-matched third-order process that generates a third wave (ome ga(3) = 2 omega(1) + omega(2)) It is shown that the signal wave collects, i n addition to the phase shift that is due to the omega(2) = omega(1) + omeg a(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) a nd omega(2) = omega(3) - 2 omega(1). The attractive feature of this new typ e 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 p rocess and the gate intensity. (C) 1999 Optical Society of America [S0740-3 224(99)01702-6].