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Journal of Experimental and Theoretical Physics

Coherence effects accompanying generation of high-order harmonics

Д.Ф. Зарецкий, É. A. Nersesov

Published Dec 1, 1997• 1 citation
Publisher

Abstract

For phase-locked emitters, provided a certain relation exists between the pump wave and atomic beam parameters, a saturation effect is shown to be possible for which the intensity of the high-order harmonics ceases to depend on the atomic density. By means of a simple model that includes variations in the intensity of the pump wave in the plane transverse to the focal axis, an expression is obtained for the optimum atomic density of the medium corresponding to intensity saturation. The dependence of the optimum atomic density on the laser power and harmonic number obtained is found to be in qualitative agreement with recently published experimental data.

DOI
10.1134/1.558379

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For phase-locked emitters, provided a certain relation exists between the pump wave and atomic beam parameters, a saturation effect is shown to be possible for which the intensity of the high-order harmonics ceases to depend on the atomic density. By means of a simple model that includes variations in the intensity of the pump wave in the plane transverse to the focal axis, an expression is obtained for the optimum atomic density of the medium corresponding to intensity saturation. The dependence of the optimum atomic density on the laser power and harmonic number obtained is found to be in qualitative agreement with recently published experimental data.
Optical harmonic generation and mixing in the gas phase has been proposed as a technique for the generation of coherent radiation in the vacuum ultraviolet and soft x-ray spectral region. At the high field strengths required by these processes the interaction between atoms and the electromagnetic field shows intensity-dependent resonances. In this paper we modify harmonic generation theory to include the effect of these frequency shifts. Closed-form expressions for generated dipole moment, absorption probability, and coherence length are presented. The most important consequences of frequency shifts on resonantly enhanced processes are that the pump laser must be tuned away from the small-field resonance frequency, that the conversion efficiency may saturate, and that the dispersion of the medium may change sign. As an example, the generation of 198-\AA{} radiation by a five-photon mixing process in Li+{\mathrm{Li}}^{+}Li+ is considered.
Expression for the probability of the spontaneous emission of high-order harmonics when the emitter phases are synchronized and are obtained in the region where the multiphoton approximation is applicable to the description of the ionization of an atom (where the adiabaticity parameter satisfies gamma > 1). The dependence of this probability on the main parameters of the pump wave and the atomic medium is established. Criteria for observing emission are formulated with the consideration of phase locking.
The influence of injected atomic coherence on a laser's operation is discussed by analyzing the semiclassical equations of motion of this system. Both stationary-steady-state and time-dependent regimes of operation are investigated. We present the dependence of the stationary laser intensity and phase on the external parameters (population inversion, amplitude of atomic coherence, and detuning). For small cavity-field detuning and large atomic coherence, both frequency and phase locking occurs. The laser frequency is locked to the atomic frequency, and the phase is locked to a value determined primarily by the phase of the atomic coherence. Under certain conditions, in the inverted regime, the output intensity is an ssS-shaped function of the atomic coherence, leading to the possibility of a bistable behavior. However, only a portion of the bistable curve gives stable stationary operation, and in critical points (the location of which depends crucially on the external parameters) time-dependent instabilities branch away. When the detuning is larger than a critical value there is neither phase nor frequency locking. We find that the time-dependent behavior of the laser intensity in this case is oscillatory (quasiperiodic), and show that there is a stable limit cycle in the phase plane of the quadratures. There is a small parameter region where a stationary steady state and an oscillatory state may coexist. We also consider the nonlinear quantum theory of a laser with injected atomic coherence, and include the effect of pumping statistics. We derive the Fokker-Planck equation for the P representation, and express the noise in terms of moments. We find that in the steady state the intensity noise can be suppressed below the shot-noise limit but that the phase fluctuations are not affected by pump regularity. For nonzero detuning, we find that transient squeezing of the phase fluctuations is possible.
Expression for the probability of induced emission of high-order harmonics is obtained in the region where the multiphoton approximation is applicable to the description of the ionization of an atom. The dependence of this probability on the main parameters of the pump wave and the atomic medium is established. Criteria for observing emission are formulated with the consideration of phase locking. The possibility of amplifying a UV probe wave aimed through the region where the atoms interact with the pump wave is considered.
High harmonic generation has been considered for many years to be a coherent source of upconverted laser radiation. We propose a method for the generation of essentially incoherent high harmonic generation with a controlled degree of temporal coherence, obeying random-walk statistics. This is achieved by a unique combination of single-atom and macroscopic effects involving preparation of the medium in an excited state with coordinate-dependent population inversion and using an intense off-resonant and phase-mismatched pumping.
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.