Tunnelling approximation for estimating the amplitude of high harmonic generation in intense laser fields: analysis of ionisation and recombination times

We consider in the low-frequency approximation the quasi-classical equations for the ionisation and recombination times that arise in the analysis of high harmonic generation in the quasi-classical approximation. Based on the assumption that the ratio of the time of the subbarrier motion of an atomic electron, Δt', to the characteristic period of the laser pulse, T, is small, we have constructed a formal perturbation theory with respect to the parameter Δt'/T to calculate the ionisation and recombination times. The accuracy of the constructed perturbation theory is analysed. Using the approach developed, we suggest extending the classical theory of rescattering for linear polarisation to the case of fields with two spatial components.