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Physical Review A

Generation of ultrashort pulses of harmonics

Ph Antoine, B. Piraux, Dejan B. Milošević, Mariusz Gajda

Published Sep 1, 1996• 39 citations
Publisher

Abstract

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)].

DOI
10.1103/physreva.54.r1761

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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 \ensuremathω1{\ensuremath{\omega}}_{1}\ensuremathω1​ and \ensuremathω2{\ensuremath{\omega}}_{2}\ensuremathω2​. 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 \ensuremathω1{\ensuremath{\omega}}_{1}\ensuremathω1​ and \ensuremathω2{\ensuremath{\omega}}_{2}\ensuremathω2​ 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.
The influence of ultrashort low-frequency laser pulses of different intensities and pulse lengths on the dynamics of a resonantly driven atomic system is investigated theoretically. We demonstrate the periodical dependence of the total ionization rate on the appearance time of a strong few-cycle laser pulse. By depleting the excited state, the intense short pulse not only resets the Rabi oscillations, but also introduces a time shift that is proportional to the pulse length. This time shift can be employed to determine the ultrashort pulse length. In the case of ultrashort pulses with lower intensities, we observe side-bands in the two-photon ionization spectrum, whose intensities vary periodically with the appearance time of the pulse. This can be utilized to measure the period of Rabi oscillations. We have developed an S-matrix theory of two-colour ionization which can explain some of the observations of our numerical calculations. Furthermore, we have studied the high harmonic generation spectra as well as the attosecond pulses generated from the high harmonics. We show that the Rabi oscillation can be used to alter the ionization rate within laser sub-cycles and therefore select different quantum trajectories in the high harmonics generation.
We investigate the third order harmonic generation for model atoms interacting with intense short laser pulses. We focus on the cases where the ponderomotive energy is not big enough to generate high-order harmonics, and where resonant transitions between bound states are also as important as multi-photon ionization and low-order harmonic generation. We find that the third order harmonic intensity from a model hydrogen atom can decrease as the laser frequency draws near a resonance between bound states. We explain this result by looking into the ionization and Rabi oscillation from the numerical calculation of the time-dependent 1-D Schrödinger equation. In order to support our explanation we also investigate the populations of bound states that play an important role in this atomic process.
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.
We have investigated the nonlinear susceptibility of atoms induced by high intensity, ultrashort laser pulses using a numerical solution of the time-dependent Schrödinger equation. We found that the instantaneous nonlinear susceptibility becomes saturated at high intensity. We also found that the saturation is closely linked to depletion of the ground state. Based on the numerical results, a simple model that generalizes the nonlinear susceptibility of atoms for high intensity, ultrashort laser pulses is proposed. We also investigated the ionization-induced dipole moment and found that the amplitude of the dipole moment induced by an ionized electron is, in general, smaller than that induced by a free-electron, and is attributable to a residual interaction between the ionized-electron and its parent ion.