Space-time description of strong-field ionization and high-order-harmonic generation

Abstract

We develop the spatiotemporal description of matter-field interaction within the strong-field approximation. We show that the space-time form of the ionized wave function has analogies with the diffraction phenomenon, allowing for the definition of two different regimes: Fresnel and Fraunhofer. We demonstrate that the standard saddle-point analysis corresponds to the paraxial approximation of the Fraunhofer case. The Fresnel number therefore appears as a useful parameter to characterize the validity of the saddle-point approach. We give a closed formula for the ionized wave function beyond the standard saddle-point analysis that takes the form of a chirped Volkov wave. We apply our results to the study of high-order-harmonic generation, demonstrating that the saddle-point approximation breaks down for extended systems, i.e., when the Fresnel number approaches or is above the unity. As a simple example, we analyze the harmonic generation of dissociating ${H}_{2}^{+}$ and demonstrate the Fresnel number as a useful parameter to determine the accuracy of the semiclassical saddle-point approach.