Laser-induced tunneling, the Kapitza effective potential, and the limits of perturbative nonlinear optics

The canonical framework of optical physics connects the validity of perturbative nonlinear optics to the smallness of the optical driver field E compared to a characteristic field E_at that acts on electrons in an atom, a molecule, or a crystal lattice. However, in a vast area of strong-field optical science, the borderline between perturbative and nonperturbative nonlinear optics is defined as γ ~1, where γ is the Keldysh parameter. Not only is this criterion frequency-dependent, in a stark contrast with E/E_at ~1, but it also often dictates much weaker fields at which the perturbative treatment is still valid, leading to a dramatic shrinkage in the convergence radius of perturbation-theory expansions. Here, we identify the physics behind the gap between the E/E_at ~1 and γ ~1 conditions as the limits of perturbative nonlinear optics. We argue that, while the criterion E/E_at << 1 sets a universal upper-bound limit on the validity of perturbative nonlinear optics and its central concept of nonlinear-optical susceptibilities, optical nonlinearities related to photoionization pathways become nonperturbative in much weaker optical fields, with the limits of a perturbative treatment defined by the Keldysh parameter γ rather than the E/E_at ratio.