Self-phase modulation and frequency generation with few-cycle optical pulses in nonlinear dispersive media

We analyze nonlinear effects associated with the spatiotemporal propagation of few-cycle optical pulses in nonlinear dispersive media, including nonlinearity-induced self-phase modulation, generation of higher harmonics, and the effects of diffraction. First, we discuss the nonlinear equations governing the spatiotemporal propagation of short pulses in dispersive and diffractive nonlinear media and demonstrate a link between the field equation and the cubic nonlinear Schr¨ odinger equation employed for describing the evolution of the pulse envelope. Then, for several different regimes of competitive scales, we study the self-action effects of few-cycle pulses and describe, both analytically and numerically, the pulse self-modulation and self-focusing, including the transformation of the spectral density and harmonic generation in the cases of weak and strong dispersion. Finally, we analyze the effect of the beam diffraction on self-action of the Gaussian few-cycle pulses.