Analytic formulae for high harmonic generation

Abstract

Analytic formulae describing harmonic generation by a weakly bound electron are derived quantum mechanically in the tunnelling limit. The formulae confirm the classical three-step model and provide an analytic explanation for oscillatory structures on the harmonic generation plateau.

Bicircular High-Harmonic Spectroscopy Reveals Dynamical Symmetries of Atoms and Molecules

“…Following the reasoning behind the three-step model [48] and the factorization of the high-harmonic-generation (HHG) process [49][50][51], we treat the HHG process as a chronological sequence of ionization, propagation, and recombination steps. We first study the ionization yields from the three p orbitals.…”

Analytic Description of the High-Energy Plateau in Harmonic Generation by Atoms: Can the Harmonic Power Increase with Increasing Laser Wavelengths?

“…are the field amplitude and frequency), we discuss first our recent analytic result for HHG rates, RðE Þ (E ¼ @ ¼ n@! ), for the case of an electron bound by a short-range potential in the state c lm ðrÞ, with energy E 0 ¼ À@ 2 2 =ð2m e Þ and angular momentum l [15]. This latter result was derived quantum mechanically [in the tunneling limit, ( 1, where ¼ @!=ðeF À1 Þ is the Keldysh parameter] based on a general, ab initio formulation for the HHG amplitude [16] that was applied to the case of HHG by an electron in a short-range potential using time-dependent effective range (TDER) theory [17].…”

“…(28) for RðE Þ in Ref. [15] as a product of three factors, R ðE Þ ¼ IðF; !ÞW ðEÞ ðrÞ ðEÞ; E¼ E À jE 0 j;…”

Harmonic generation spectroscopy with a two-colour laser field having orthogonal linear polarizations

“…It can be shown that the dipole moments d 0,0 and d 1,−1 given by equation (12) for F 2 = 0 coincide with those in [24] for a monochromatic field, while d 1,+1 = 0. Since each of the three factors in the parametrization (12) has a clear physical meaning in terms of the three-step HHG scenario [25,26] and since the propagation factor χ (l,q) is insensitive to the atomic dynamics, one can extend the parametrization (12) to the case of a neutral atom by replacing the tunnelling rate st (F ) and the matrix elements D ll [or σ (E, α)] by their counterparts for a given atom, as is done in [16].…”