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Journal of Physics B Atomic Molecular and Optical Physics

A significant enhancement of high-order harmonic generation by using a dipole gas

В. П. Гавриленко, Eugene Oks

Published Apr 7, 2000• 12 citations
Publisher

Abstract

This paper presents an analytical study of high-order harmonic generation (HHG) by quantum systems possessing permanent dipole moments (PDMs), such as atoms/molecules placed in a static electric field or polar molecules. HHG by conventional, non-PDM systems typically demonstrated a plateau in the envelope of harmonics followed by a steep fall in harmonic intensities when the harmonic number exceeds a certain threshold. This paper shows that the HHG by PDM systems results in a significant extension of the plateau to higher frequencies and a slower decline of intensities at frequencies higher than the end of the plateau . Moreover, there occurs a substantial growth of the total, summed intensity of all components of the scattering spectrum . Other physically interesting distinctive features of the HHG by PDM systems are: the presence of both odd and even harmonics of the laser frequency in the scattering spectrum; a triplet structure of both odd and even harmonics; and the appearance of a component at the doubled Rabi frequency (i.e. at a frequency much lower than the laser frequency). The results are obtained by using the adiabatic basis for the analysis of a multi-quantum resonance in a two-level system possessing PDMs.

DOI
10.1088/0953-4075/33/8/312

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This paper presents an analytical study of high-order harmonic generation (HHG) by quantum systems possessing permanent dipole moments (PDMs), such as atoms/molecules placed in a static electric field or polar molecules. HHG by conventional, non-PDM systems typically demonstrated a plateau in the envelope of harmonics followed by a steep fall in harmonic intensities when the harmonic number exceeds a certain threshold. This paper shows that the HHG by PDM systems results in a significant extension of the plateau to higher frequencies and a slower decline of intensities at frequencies higher than the end of the plateau . Moreover, there occurs a substantial growth of the total, summed intensity of all components of the scattering spectrum . Other physically interesting distinctive features of the HHG by PDM systems are: the presence of both odd and even harmonics of the laser frequency in the scattering spectrum; a triplet structure of both odd and even harmonics; and the appearance of a component at the doubled Rabi frequency (i.e. at a frequency much lower than the laser frequency). The results are obtained by using the adiabatic basis for the analysis of a multi-quantum resonance in a two-level system possessing PDMs.
An analysis is made of the collective resonant generation of higher harmonics by a spatially extended system of two-level molecules possessing an intrinsic electron dipole moment in the excited state. Frequency and angular dependences of the scattered radiation are studied. It is shown that for moderately small numbers of harmonics their intensity depends comparatively weakly on the number (plateau) and the intensity of the emitted harmonics then falls sharply as the number increases. The angular distribution of the harmonics is strongly anisotropic. It is also shown that collective effects significantly change the time profile of the generated harmonic pulse. In addition, as a result of cooperative effects harmonics of a certain parity are suppressed in the low-frequency part of the radiation spectrum.
We show that a simple nonperturbative two-level model of an atom driven by a very strong periodic field, results in a rich picture of very high harmonic generation and related phenomena. It reproduces experimentally observed plateau, yields for the first time simple analytic formulas for the plateau cutoff frequency, critical driving intensity, and saturation, and predicts intensity-induced multi-resonances. One of the most fascinating phenomenon discovered recently in nonlinear interaction of light with atoms and ions, is very high-order (up to 135) odd harmonic generation (HHG) by intense (∼ 1013 W/cm2 and higher) optical laser radiation in rare gasses and some ions [1], The spectra of generated harmonics drasticly deviate from the perturbation theory predictions [2], In particular, intensity of harmonics, falling monotonically with their orders only up to a certain point, levels off forming a so-called “plateau", and falls monotonically again beyond it. Generally, harmonte generation depends on phase-matching conditions and nonlinear response of individual atoms. It has recently become clear however [3,4] that the major features of HHG, in particular the plateau, result mainly from general properties of atomic nonlinear response. The most direct and apparently successful way so far to approach the problem theoretically has been numerical simulation of the Schrödinger [2,5-7] (including an empiric rule [6]) for many-electron atoms using Hartry-Slater approximation. This approach requires, however, tremendous amount of calculations and involves many processes, making it difficult to gain simple insights. An interesting simplified model [8] based on 3-D delta-potential with a single (ground) level [9] produces results in integration form. The idea of retaining a single energy scale (ionization energy) brings one close to an even simpler system: a two-level model atom. A two-level model of HHG [10], however, due to various complications introduced into it, failed to generate simple results, whereas an analytic solution [11] holds for a virtually degenerate two-level model only (see below) which is unapplicable to the experimental conditions [1-4,7,9]; besides, no relaxation was considered in [10,11].
The interaction between radiation and a two-level molecular system in the presence of permanent dipole moments is analyzed. It is found that the nonzero difference between permanent dipoles induces a polarization that oscillates at frequencies /spl omega/, 2/spl omega/, 3/spl omega/, etc., where /spl omega/ is the frequency of the electromagnetic field resonant with the two-level system. An analysis of the propagation equation of the harmonics shows that even harmonics are amplified while odd harmonics are absorbed.
The phase relationship between an induced atomic dipole moment and a driving laser field is an essential aspect of high harmonic generation (HHG) in a dense medium. A ``phase-matching'' criterion must be fulfilled to obtain coherent amplification of harmonic radiation, which is critical for practical HHG. We have performed numerical calculations on model atoms to survey the intensity dependence of the phase in the case of strong one- or two-frequency laser fields. The calculations show that multiphoton resonances significantly affect the yield of harmonic generation and that in the ``plateau'' regime, the phases exhibit only weak dependence upon the intensity of the driving field. \textcopyright{}1996 The American Physical Society.
We present a theoretical study of the high-order-harmonic generation (HHG) from coherent superposition states of a three-level system driven by monochromatic cw laser fields. The HHG spectrum can be enhanced by about 105{10}^{5}105 times via tuning the relative phase between the states which are initially prepared. Even if the ionization effects are taken into account, the enhancement factors are still up to about 102{10}^{2}102 times. The enhancement is interpreted as the quantum constructive interference of different dipole transitions between quasienergy states. To realize the interference, the intensity of the driving laser field is chosen such that frequencies of the harmonics generated from the different dipole-transition paths, which are dependent on the ac Stark shifted energy separation of quasienergy states, are equal to each other. Moreover, the case studies of HHG spectra from a coherent superposition state of a three-level system show that the enhancement of harmonics is closely related to the harmonic strengths of the dipole transitions, as well as the parity of quasienergy states which are involved in the dipole-transition paths. The reduction of enhancement factors due to ionization effects is also qualitatively analyzed.