Ionization by a strong orthogonal two-color laser field: a quantum-orbit-theory approach

theory of high-order above-threshold ionization (HATI) of atoms is presented and applied to the ionization of inert gases by an orthogonal two-color (OTC) field. The transition matrix element is derived within the strong-field approximation and calculated by numerical integration and the saddle-point method. The atomic bound state is expressed as an expansion in terms of the Slater-type orbitals as well as an asymptotic wave function. The energy and momentum distributions of the HATI electrons are calculated for the ω – 2ω and ω – 3ω OTC fields. A detailed analysis of the saddle-point solutions and their contribution to the overall differential ionization rate for these two cases is presented. Optimal values of the OTC field parameters for which the ionization rate is maximal in the high-energy region of the photoelectron spectra are found. Special attention is devoted to the symmetry consideration of the photoelectron momentum distributions. All these results are analyzed in detail using the quantum-orbit formalism, which gives a better physical insight into the HATI process. Graphic abstract