Single-active-electron analysis of laser-polarization effects on atomic/molecular multiphoton excitation

We theoretically explore the effects of optical ellipticity on single-active-electron multiphoton excitation in atoms and (nearly) spherical molecules irradiated by intense polarized laser fields. This work was motivated by the experimental and theoretical studies of Hertel et al. [Phys. Rev. Lett. 102, 023003 (2009) and Phys. Rev. A 79, 053414 (2009)], who reported pronounced changes in the near-infrared-induced ion yields of xenon and C₆₀ as a function of ellipticity (in particular, yield reduction for circular polarization) at low light intensities and derived a perturbative cross section formula to describe such polarization effects by assuming that the excited-state energies and radial transition electric dipole moments of the system are independent of the azimuthal quantum number l. First, by reformulating the N-photon absorption cross section of a single active electron, we prove that their assumptions reduce the network of optically allowed transition pathways into what we call the "Pascal triangle" consisting of (N + 1) (N + 2)/2 states only. Next, nonperturbative analytical and numerical solutions of the time-dependent Schrödinger equation for a simple model of two-photon excitation are presented not only in the low-intensity regime but also in the high-intensity regime. The results show that the determining factor of ellipticity-dependent multiphoton excitation probability is transition moment magnitudes and that the detailed energetic structure of the system also becomes important at high intensities. The experimentally observed flattening of the ion yields of xenon and C₆₀ with increasing intensity can be explained without a saturation effect, which was previously deemed to be responsible for it. We also argue the applicability range of the cross section formula by Hertel et al. and the identity of the "doorway state" for ionization of C₆₀.