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In an approach based on the nonlinear Riccati-type differential equation for the ratio of the level population amplitudes, rather than on the optical Bloch equations, we describe the response of a two-level system to a few--cycle light pulse of intensity from the regime of extreme nonlinear optics, i.e., when the Rabi and transition frequencies are comparable. Emphasis is put on the dependence of the spectra of the scattered light on the carrier--envelope phase, duration and strength of both resonant and off-resonant pulses.

Abstract.The density of a d-dimensional polynomial-Gaussian distribution (PGDj)is the product of a non-negative polynomial and a Gaussian density. The density of a (PGDd) has many properties similar to a d-dimensional Gaussian distribution (GDj), but one-dimensional marginal distributions of (PGDj) are (PGDi). Analogously onedimensional densities of a polynomial-Gaussian process (PGP) are (PGD\). We investigate the differences and similarities between the Gaussian and non-Gaussian cases.