Source: http://aoot.osa.org/oe/abstract.cfm?uri=oe-27-6-8246
Timestamp: 2019-04-24 04:02:04+00:00

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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 Eat 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/Eat ~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/Eat ~1 and γ ~1 conditions as the limits of perturbative nonlinear optics. We argue that, while the criterion E/Eat << 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/Eat ratio.
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Fig. 1 Nonlinear response of (a) bound-state electrons, (b) recolliding photoelectrons, and (c) photoelectrons in the outgoing wave packet. The perturbative regime: (d) a representative Feynman diagram of the perturbative nonlinear-optical response and (e) a photon diagram of multiphoton ionization. Nonperturbative nonlinear-optical response: (f) tunneling of bound-state electrons, (g) recolliding electron trajectories, and (h) photoelectron trajectories in the outgoing electron wave packet (top) and bursts of photoionization probabilities in the γ < 1 regime.

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