Modification of the saddle-point equation for strong-field ionization from atomic p orbitals

The saddle-point approximation (SPA) within the framework of strong-field approximation is extensively applied in strong-field physics because it offers clear physical insight into intense light-matter interactions. In this study, we introduce an m-resolved saddle-point approximation (m-SPA), where m is the magnetic quantum number, to analyze the ionization dynamics of atoms initially in p orbitals subjected to an intense laser field. Our results reveal that m influences not only the prefactor of the ionization rate but also the saddle-point equation itself, an effect overlooked in prior studies. The accuracy of the m-SPA method is validated through comparisons with the backpropagation method and the strong-field approximation, showing its superiority over the conventional SPA approach. By employing the m-SPA approach, we are able to extract more accurate distributions of the initial tunneling exit energy and position, thereby allowing for a more precise determination of the asymptotic photoelectron characteristics. Additionally, we extend the conservation law for angular momentum and energy of photoelectrons from s orbitals to p orbitals and from circularly polarized to elliptically polarized laser fields, both at the tunnel exit and in the asymptotic region. This work facilitates future research on strong-field ionization from arbitrary atomic orbitals.