Calculations, using the Maxwell equations, are presented of nonlinear effects on the carrier-envelope phase for pulse durations in the two-optical-cycle range for pulses propagating in sapphire. Initially, with increasing pulse intensity the carrier-envelope phase increases monotonically. However, at higher intensities there is a turnabout in the direction of the phase change and a large change in the phase that is caused by a warping of the envelope from strong nonlinear effects. The Kerr nonlinear response occurs on a time scale of ~1fs and gives significantly different results from those obtained by assuming an instantaneous response.
Peter M. Goorjian and Steven T. Cundiff, "Nonlinear effects on the carrier-envelope phase," Opt. Lett. 29, 1363-1365 (2004)