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Journal of Modern Optics

Wavelet analysis of short harmonics generated in presence of a two colour laser field

Salvatore De Luca, Emilio Fiordilino

Published Sep 1, 1998• 13 citations
Publisher

Abstract

The Morlet wavelet spectrum of the radiation emitted by a two level atom in presence of two laser pulses with very close frequency is obtained. The wavelet spectrum gives information on the time evolution of the full spectrum and of a particular line. The beating condition stimulates the atom to emit pulses of harmonics with duration of the order of a few optical cycles of the pumping radiation. Pulse trains of 3 optical cycles (FWHM) are observed.

DOI
10.1080/09500349808231701

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The Morlet wavelet spectrum of the radiation emitted by a two level atom in presence of two laser pulses with very close frequency is obtained. The wavelet spectrum gives information on the time evolution of the full spectrum and of a particular line. The beating condition stimulates the atom to emit pulses of harmonics with duration of the order of a few optical cycles of the pumping radiation. Pulse trains of 3 optical cycles (FWHM) are observed.
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.
The spectrum of a two-level atom in the presence of a multimode laser pulse is calculated. The field is allowed to fluctuate in amplitude or in phase; the emitted spectrum has richer emission lines than in the case of the nonfluctuating field and shows peaks shifted toward the blue with respect to the traditional harmonic peaks. The position of the lines is predicted by the formula ω2n+1=(2n+1)(1+Δ)ωL with Δ being a parameter that can be found numerically. In this way the fluctuations seem to result in an effective increase of the laser frequency.
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)].
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.