Analytic confirmation that the factorized formula for harmonic generation involves the exact photorecombination cross section

Abstract

High-order harmonic generation (HHG) by atoms in a strong laser field is analyzed theoretically, taking into account atomic potential effects beyond the strong field approximation (SFA). Our analytical derivation extends the time-dependent effective range (TDER) theory, developed previously for a short-range potential supporting only a single bound state, to the case of a potential supporting two bound states having different angular momenta and dynamically interacting with the continuum. In contrast to the SFA and the single-state TDER model, in both of which the HHG rates in the region of the high-energy plateau cutoff involve only the plane-wave (first Born) approximation for the photorecombination cross section, our analytic expression for the HHG rates in the two-state TDER model involves the exact photorecombination cross section for this model. These results justify the factorization of HHG rates in the high-energy plateau region in terms of the electron wave packet and the exact (non-Born) photorecombination cross section, which was suggested previously using only phenomenological arguments.

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

“…which has a positive imaginary part and the smallest real part [6]. Note that the momentum K i (t ) lies in the XY -plane, so that f 1,0 (K i (t )) = 0 and HHG for the substate ψ 0 (r) is strongly suppressed and vanishes in the approximation (5).…”

“…For a linearly polarized field, this factorization was proposed phenomenologically, based on numerical solutions of the time-dependent Schrödinger equation [3,4]. It has now been justified theoretically for a monochromatic field [5,6], for a short laser pulse [7][8][9], and for a two-colour field with collinearly polarized components [10].…”

“…Its matrix elements do not depend on the laser parameters and involve only radial matrix elements D ll = ϕ κl |r|ψ El , where ψ El (r) is the radial part of the l -wave (including the phase factor exp[iδ l (E )]) of the TDER scattering state ψ P (r) (E = P 2 /(2m)) [6]. The matrix elements ofŜ l,q are related to the PRCS σ (E, α).…”

“…, where K(t ; t, t i ) is the instantaneous (at time t ) classical momentum of an electron that moves along a closed trajectory in the field F(t ) starting at the time of ionization t i and returning at time t. The wave function ψ K(t ) (r) is a field-free scattering state of an electron with 'momentum' K(t ) in the TDER theory [6]. For a given time t, the time t i = t i (t ) in (5) is determined as that root of the energy conservation equation applicable at the moment of ionization,…”

High-order-harmonic generation from molecular isomers with midinfrared intense laser pulses

“…The origin of the differences in HHG spectra is traced as due to the interplay in the angular dependence of the photoionization (or photorecombination) cross section and ionization rate. High-order-harmonic generation (HHG) has been shown both experimentally and theoretically to contain information about the target molecular structure and dynamics, which are encoded in the amplitude and phase of the emitted high-order harmonics [1][2][3][4][5][6][7][8][9][10][11][12]. HHG spectroscopy for simple molecules has been greatly benefited from the ability to align molecules [13].…”