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Physical Review A

Amplification of high-order harmonics in a short laser pulse by stimulated interaction

É. A. Nersesov, Sergey V. Popruzhenko, David F. Zaretsky, Wilhelm Becker, Pierre Agostini

Published Jul 17, 2001• 5 citations
Publisher

Abstract

The case is considered of a weak Gaussian harmonic pulse of frquency $(2s+1)\ensuremath{\omega}$ passed through an atomic medium collinearly with an intense Gaussian laser pulse of frequency $\ensuremath{\omega}.$ The harmonic beam may be amplified or deamplified according to the balance between stimulated emission and absorption. A simple analytic expression for the gain is derived in the tunneling limit of ionization. It predicts a positive (negative) gain for positive (negative) delay of the harmonic pulse with respect to the laser pump pulse. The gain may be significant and proportional to the delay for delays of a few laser periods, much shorter than the pulse envelopes. Possibilities for experimental observations are briefly discussed.

DOI
10.1103/physreva.64.023419

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The case is considered of a weak Gaussian harmonic pulse of frquency (2s+1)\ensuremathω(2s+1)\ensuremath{\omega}(2s+1)\ensuremathω passed through an atomic medium collinearly with an intense Gaussian laser pulse of frequency \ensuremathω.\ensuremath{\omega}.\ensuremathω. The harmonic beam may be amplified or deamplified according to the balance between stimulated emission and absorption. A simple analytic expression for the gain is derived in the tunneling limit of ionization. It predicts a positive (negative) gain for positive (negative) delay of the harmonic pulse with respect to the laser pump pulse. The gain may be significant and proportional to the delay for delays of a few laser periods, much shorter than the pulse envelopes. Possibilities for experimental observations are briefly discussed.
Introduction Previous discussions (see Section 10.4) suggested that stimulated emission can be used to generate optical gain, that is, to amplify radiation. The reader certainly has experience in the amplification of electronic signal. For example, radio receivers capture faint radio waves and turn them into a signal that is powerful enough to drive large speakers. This electronic amplification increases the amplitude of the signal while faithfully preserving its acoustic frequencies and modulation characteristics. Similarly, optical amplification is expected to increase the amplitude of an optical signal while preserving its frequency, its modulation characteristics, and its coherence. The latter requirement is of particular significance for optical radiation, where the coherence of naturally occurring radiation rarely exceeds one micrometer. Lasers are the primary source for coherent radiation. They depend on stimulated emission for amplification and for the generation of coherent radiation (the word laser is the acronym of Light Amplification by Stimulated Emission of Radiation). For amplification, an atomic system that is part of the laser medium must be prepared with a sufficiently large number of particles in the excited state. (The term atomic system is used here to describe all microscopic systems including molecules and free electrons.) Radiation passing through that excited medium encounters multiple events of stimulated emission, each event contributing one photon that is added coherently to the propagating beam. When the number of events of stimulated emission exceed all losses by absorption or scattering, the incident radiation is amplified.
The problem of transient four-wave parametric interaction in a two-level medium is solved taking into account the group delay without assuming a weak exciting field. It is found that a high-power narrow peak whose duration τs is considerably shorter than the pump duration τp is observed against the background of a slowly varying envelope of the weak signal during its amplification process. In the case of a high pump intensity (ΩmτP−1) the lowest possible value of τS that can be achieved for a suitable angle of incidence and input signal frequency is governed by τp/Ωm1/2, where Ωm is the peak Stark shift of the resonance frequency.
The amplification of ultrashort extreme-ultraviolet (XUV) pulses in argon in high-order harmonic generation processes is studied by using the time-dependent Schr\"odinger equation in the spin-free one-active-electron and single-atom approximation. We consider a neutral argon atom initially in the valence 3p state and a sufficiently intense two-cycle driving infrared (IR) pulse for the atom to be mainly ionized after the first laser cycle. The correlated dynamics and transitions from the valence 3p to a virtual subvalence 3s state and in the ionized regions are examined by synchronizing a 1.5-fs XUV pulse to the IR pulse. The calculated single-atom gain spectrum (26--45 eV) agrees with recent experimental measurements. We discuss different channels that can be present in the gain process as a function of pulse parameters and through an analysis of the dynamics of the populations in terms of field-free eigenstates. When the XUV pulse is considered at the end of the driving IR field the amplification is due to contributions of stimulated recombination from excited Rydberg and low energy continuum states to the 3s and 3p states of argon. In regions where the IR field is intense, high energy and angular momentum states are populated and the medium can interact with the pulses through bound and continuum states involving parametric transitions, which is further confirmed by studying classical electron trajectories. We discuss how these parametric interactions might be suitable for amplification of photon energies far from the ionization threshold as observed in the experiments.
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We experimentally investigated optical pulse propagation through an amplifying ring resonator, in which a semiconductor optical amplifier was used as a loss or gain medium. Initially, the transmission intensity showed resonance dips as a function of laser frequency. These dips were gradually filled and transformed into resonance peaks as the amplification gain increased. A Gaussian-shaped temporal pulse was either advanced by −7.3 ns at low amplification gain or delayed up to 45 ns at high gain. System operation was classified into a complete set of the four regions depending on the gain parameter, and experimental delay times were analyzed based on relevant system dispersion.
I consider light amplification arising from the competition between absorption and stimulated emission of an excitation, which is induced by a laser field at low intensities interacting with a three-level atom. The lifetime of the induced excitation is 105–106 times longer than those of spontaneously emitted excitations. Conditions are established under which the stimulated emission prevails over the induced absorption, and the net negative intensity is 102–103 times greater than those of spontaneously emitted excitations, indicating that significant amplification occurs near the frequency of the laser field. PACS numbers: 32.80-t, 42.50.-p, 42.50H2