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High Field Interactions and Short Wavelength Generation

Time profile of harmonics generated by a single atom in a strong electromagnetic field

Philippe Antoine, Bernard Piraux, A. Maquet

Published Jan 1, 1994• 6 citations
Publisher

Abstract

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.

DOI
10.1364/hrfts.1994.tub4

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Time profile of harmonics generated by a single atom in a strong electromagnetic field

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We show that the time profile of the harmonics emitted by a single atom exposed to a strong electromagnetic field may be obtained through a wavelet or a Gabor analysis of the acceleration of the atomic dipole. This analysis is extremely sensitive to the details of the dynamics and sheds some light on the competition between the atomic excitation or ionization processes and photon emission. For illustration we study the interaction of atomic hydrogen with an intense laser pulse.

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Singleatomresponse to a Partially Coherent Intense Laser Field

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Highorder optical harmonic emission by a single atom exposed in a partially coherent intense laser field is numerically calculated. We found that all harmonic shift towards highfrequency and the harmonic spectrum is broadened in different degree according to different harmonic order. Comparing with that of monochromatic field atoms are ionized easier by the partially coherent field. It is possible that the wavelength of the harmonic can be tuned by adjusting the coherence of the incident laser field.

中国激光(英文版)•Jan 1, 1997•0 citations
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.
The acceleration of the electron in a two-level atom driven by a short laser pulse of intermediate strength is calculated and therefore analysed through two wavelet transforms in order to obtain the temporal evolution of the spectrum of the emitted radiation. We show (i) the full spectrum at different instants and (ii) the time profile of some representative harmonics. The growth of the harmonics as well as the appearance and erratic behaviour of the hyper-Raman can be followed with the laser intensity.
We study harmonic generation by a single atom exposed to two short perpendicularly polarized laser pulses. The two perpendicular electric fields oscillate at two different frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$. Hence, the resultant field has a polarization which depends on time. Since harmonics are emitted when the resultant oscillating field is linearly polarized, it is expected that a short pulse of harmonics may be emitted if the external field is linearly polarized during a short period of time. We show that, indeed, the atom may emit an ultrashort pulse of a given harmonic. This result has been obtained by time-frequency analyzing the acceleration of the induced dipole moment with a filter whose frequency bandwidth is smaller than twice the frequency of the external field. Our calculation of the dipole acceleration is based on the numerical solution of the time-dependent Schr\"odinger equation. We then address the question of how far it is possible to reduce the duration of the emitted pulse of one given harmonic by adjusting both ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ and keeping the amplitude of this pulse significant. In order to answer to this question, we used the quantum version of the two-step model [M. Lewenstein et al., Phys. Rev. A 49, 2117 (1994)].
We investigate a two-level atom in the field of a strong laser pulse. The resulting time-dependent polarization is the source of a radiation the frequency components of which are essentially harmonics of the driving field's carrier frequency. The time evolution of this secondary radiation is analyzed in terms of the expectation values of the photon-number operators for a large number of electromagnetic modes that are initially in the vacuum state. Our method is based on a multimode version of the Jaynes-Cummings-Paul model and can be generalized to different radiating systems as well. We show that, after the exciting pulse, the final distribution of the photon numbers is close to the conventional (Fourier-transform-based) power spectrum of the secondary radiation. The details of the high-order-harmonic spectra (HHG spectra) are also analyzed; for many-cycle excitations a clear physical interpretation is given in terms of the Floquet quasienergies. A first step towards the determination of the photon statistics of the high-order-harmonic modes reveals states with slightly super-Poissonian distribution.
Abstract A new approach for studying the spontaneous emission of an atomic system in the presence of a high-intensity laser field is used to study the process of harmonic generation. The analysis is based on consideration of quantum system interaction, with the quantized field modes being in the vacuum state, while the intense laser field is considered to be classically beyond perturbation theory. The numerical analysis of the emission from the single one-electron 1D atom irradiated by the femtosecond laser pulse of a Ti:Sa laser is discussed. It is demonstrated that not only odd, but also even harmonics can be emitted if the laser field is strong enough. The origin of the appearance of even harmonics is studied. The obtained results are compared with those found in the framework of the semiclassical approach that is widely used to study harmonic generation. It is found that the semiclassical approach is inapplicable in the strong-field limit.
Highorder optical harmonic emission by a single atom exposed in a partially coherent intense laser field is numerically calculated. We found that all harmonic shift towards highfrequency and the harmonic spectrum is broadened in different degree according to different harmonic order. Comparing with that of monochromatic field atoms are ionized easier by the partially coherent field. It is possible that the wavelength of the harmonic can be tuned by adjusting the coherence of the incident laser field.