The above-threshold ionization spectrum in a strong linearly polarized laser field

We use the saddle-point method to derive analytical expressions for the spectral-angular probability distributions of the ionization by a strong linearly polarized laser field in Keldysh’s model that are valid for an arbitrary electron energy and adiabaticity parameter. We obtain asymptotic expansions of the general formulas in the multiphoton and tunneling regimes, analyze their accuracy, and formulate the validity conditions. We provide literal estimates of the parameters that characterize the properties and evolution of the distributions.