Analytic Formulas for High-Order Harmonic Generation

Synopsis We present closed-form analytic formulas for high-order harmonic generation (HHG) rates for both negative ions and neutral atoms. These formulas provide a fully quantum justification for the famous classical three-step scenario (TSS) of HHG as well as a correction to the well-known classical law for the HHG plateau cutoff energy. For the case of an electron bound in a short-range potential, we present a closed-form an-alytic formula for high-order harmonic genera-tion (HHG) rates (obtained in the quasiclassical limit [1]) that shows excellent agreement with ex-act time-dependent effective range results over the high energy part of the HHG plateau (and beyond). It justifies the empirical parametriza-tion of HHG rates suggested in Refs. [2]. Our analytic results allow one to describe the depen-dence of the oscillatory patterns of HHG rates o