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Journal of Modern Optics

High order harmonic generation: The role of the acceleration matrix elements and of the bound and continuum transitions

Pietro Paolo Corso, ANTONINO DI PIAZZA, Emilio Fiordilino, L. Lo Cascio, Franco Persico

Published Jul 1, 2001• 7 citations
Publisher

Abstract

The electromagnetic spectrum emitted by a one-dimensional atom driven by a strong laser field is obtained by use of the acceleration form and interpreted by means of few general properties of the matrix elements of the acceleration operator. We show that the emission occurs essentially in a region near the atomic core where the acceleration is significant and we investigate the role of the various emission channels arising from interference effects between transitions involving the bare atomic levels.

DOI
10.1080/09500340108232468

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The electromagnetic spectrum emitted by a one-dimensional atom driven by a strong laser field is obtained by use of the acceleration form and interpreted by means of few general properties of the matrix elements of the acceleration operator. We show that the emission occurs essentially in a region near the atomic core where the acceleration is significant and we investigate the role of the various emission channels arising from interference effects between transitions involving the bare atomic levels.
It is well established, both experimentally and theoretically, that atoms exposed to a strong laser pulse emit high order harmonics of the driving field. Although this process has been intensively studied theoretically, the main effort has been focused so far on the study of the harmonic spectrum while no attempt has been made to analyse systematically its time evolution. We show that the time profile of each harmonic may be obtained through a time-frequency analysis of the acceleration of the atomic dipole. We show also that such an analysis, which is very sensitive to the details of the dynamics, provides valuable information about the competition between photon emission and ionization processes.
We present a theory of harmonic generation by a strongly driven atom within the framework of non-relativistic QED. The atom is assumed to possess a finite number N of levels and ionization is neglected. This atom is dressed by the driving field using a unitary time-dependent transformation. Within the quasistatic approximation this transformation is shown to lead from the bare to the Floquet atom. The interaction of the Floquet atom with the vacuum modes is derived and it is shown to give rise both to the high-order harmonic and to the hyper-Raman spectrum. In the case N=2 the spectrum of the light scattered into the vacuum modes can be evaluated analytically and it is shown to consist of two parts. Neglecting interference between these two parts, the first of them is the high-order harmonic spectrum displaying peaks at the odd harmonics of the driving field. The second part is the hyper-Raman spectrum which has finite bandwidth and which displays peaks at the even harmonics of the laser frequency, centred at the Stark-shifted natural atomic frequency. These two spectra partially overlap and they are discussed in various ranges of intensity of the driving field, both in the minimal coupling and in the multipolar scheme. The results support recent suggestions that the presence of the plateau is related to interference between the two spectra. The dependence of the high-order harmonic spectrum from the driving field intensity is found to be related to that of the hyper-Raman spectrum in such a way that when the former increases the latter decreases and vice versa. It is argued that this might help to explain the non-visibility of the hyper-Raman lines when the high-order harmonics are visible.
We present the most prominent features in two-colour coherent control of high-order harmonic generation using a strongly driven two-level atom model, which are known to generate high harmonics as well as hyper-Raman lines with a plateau and a cut-off. Furthermore, for one laser field case, we find, when the hyper-Raman lines are located at the position of the high harmonics, that the high harmonics are strongly enhanced due to the interference effect between the high harmonics and the hyper-Raman lines. Within these conditions, by combining the laser field with another much weaker laser field, we show plentiful and strong high harmonics in the light spectrum of the driven atomic system.
Atomic polarization can have a profound effect on the generation of the high-order harmonics during the interaction of the polarized atom with intense field. In this work, the atomic polarization effect is investigated for the specific case of the 21P2\phantom{\rule{0.2em}{0ex}}^{1}P21P helium subject to infrared radiation. The strong coupling between the 21P2\phantom{\rule{0.2em}{0ex}}^{1}P21P and 21S2\phantom{\rule{0.2em}{0ex}}^{1}S21S states of helium is taken into account using a multichannel version of the strong-field approximation of Lewenstein and co-workers [Lewenstein et al., Phys. Rev. A 49, 2117 (1994); Antoine et al., Phys. Rev. A 53, 1725 (1996)]. The analysis reveals a strong dependence of the high-order harmonic generation efficiency on the atomic polarization. While the occurrence of the predicted effect can be explained in terms of the recollision model, its magnitude is deeply affected by the fast population oscillations between the excited bound states. Moreover, the induced bound-bound transitions bring about the interesting double-maximum structure in the ellipticity dependences of the emitted harmonics, both maxima occurring for nonzero field ellipticities. This unusual structure shows up even for the high-energy harmonics generated solely by the bound-continuum mechanism.