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Optics Letters

Stochastic field effects and transform-limited laser pulses

James C. Camparo, P. Lambropoulos

Published Oct 1, 1994• 2 citations
Publisher

Abstract

In many ultrashort-laser-pulse experiments the field is transform limited, and under these conditions it is usually assumed that the stochastic nature of the field can be ignored in the interpretation of experimental data. We theoretically consider the 3 + 2 photoionization of xenon, using a pulsed stochastic field. Our results show that the field's stochastic nature always has an effect on the ac Stark shift modification factor Re(M), no matter what the pulse width, and that a short-pulse approximation to Re(M) can require a Fourier-transform bandwidth 1000 times larger than the laser's intrinsic (cw) spectral width.

DOI
10.1364/ol.19.001562

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In many ultrashort-laser-pulse experiments the field is transform limited, and under these conditions it is usually assumed that the stochastic nature of the field can be ignored in the interpretation of experimental data. We theoretically consider the 3 + 2 photoionization of xenon, using a pulsed stochastic field. Our results show that the field's stochastic nature always has an effect on the ac Stark shift modification factor Re(M), no matter what the pulse width, and that a short-pulse approximation to Re(M) can require a Fourier-transform bandwidth 1000 times larger than the laser's intrinsic (cw) spectral width.
We have developed a computational framework for the study of the effects of field fluctuations on strongly driven nonlinear transitions. Nonlinearity may stem from cither the strong coupling (saturation) of a resonant transition or its multiphoton character, or it may stem from both in the most general case. Our approach is based on a Monte Carlo simulation of stochastic field fluctuations, which allows maximum flexibility in the stochastic nature of the field and in the type of process that is studied. Here, we report on a more general problem than has previously been considered in the interaction of atoms with stochastic fields, namely, the three-photon resonant five- photon ionization of xenon, 3 + 2 photoionization of xenon has been the subject of a fair number of experimental investigations. It involves nonlinearity in with a bound-bound and a bound-free transition as well as an ac-Stark shift. Consequently, there are correlations among three fluctuating parameters: the three-photon Rabi frequency, the two-photon ionization rate, and the intensity-dependent ac-Stark shift, and it is these correlations that make the stochastic-field problem almost intractable to traditional methods of analysis.
An ultrashort weak pulse that propagates resonantly on the $\ensuremath{\mid}a⟩\ensuremath{\rightarrow}\ensuremath{\mid}b⟩$ transition of a three-level system $(\ensuremath{\mid}a⟩,\ensuremath{\mid}b⟩,\ensuremath{\mid}c⟩)$ experiences reshaping effects on a time scale longer than its duration. When a strong field is applied (nonresonantly) on the $\ensuremath{\mid}b⟩\ensuremath{\rightarrow}\ensuremath{\mid}c⟩$ transition, important light shifts are induced. We have theoretically studied the novel behavior of both the medium and weak propagating laser pulses in such conditions. For the transmitted field profile, drastic changes occur: at long times, efficient reduction of the distortion is obtained, while strong oscillations appear for short times, mapping out the dynamical light shift. These shaping effects, which are accompanied by new features in the spectrum for the propagating pulse, are interpreted as the result of the interference between incident field and induced dipole radiated field, whose frequency sweeps in time because of the induced light shift.
We have investigated the ac Stark shift of a two-photon transition induced by a model stochastic field by using a Monte Carlo technique. The model field has a stochastic single mode, which can possess both colored amplitude and colored frequency fluctuations. The stochastic field’s modification of the ac Stark shift is quantified by a parameter M, which is the ratio of the Stark shift in the model stochastic field to the Stark shift that would be obtained in a phase-diffusion field of equivalent linewidth (i.e., a field with frequency fluctuations but no amplitude fluctuations). In the regime of weak fields, below saturation of the bound-bound transition, we find that M is greater than unity: the Stark shift is enhanced by the stochastic field. Moreover, in this regime M is an increasing function of the field’s degree of photon bunching. In strong fields, where the bound–bound transition is nearly saturated, the enhancement of the Stark shift is diminished, so much so that in extremely strong fields M is actually less than unity. Our calculations indicate that the ac Stark shift’s modification occurs through two distinct processes, depending on the strength of the field. In weak fields enhancement of a multiphoton transition’s Stark shift is influenced primarily by the intrinsic correlation between ac-Stark-shift fluctuations and Rabi-frequency fluctuations. In strong fields the fluctuating Stark shifts give rise to an asymmetric resonance line shape in a fashion analogous to inhomogeneous broadening. The line shape’s peak position then has a sublinear dependence on the stochastic field’s intensity, and this yields a diminished value of M.
We investigate AC Stark-shifted resonances in argon with ultrashort near-infrared pulses. Using 30 fs pulses, we observe periodic enhancements of the excitation yield in the intensity regions corresponding to the absorption of 13 and 14 photons. By reducing the pulse duration to 6 fs with only a few optical cycles, we also demonstrate that the enhancements are significantly reduced beyond what is measurable in the experiment. Comparing these to numerical predictions, which are in quantitative agreement with experimental results, we find that even though the quantum state distribution can be broad, the enhancements are largely due to the efficient population of a select few AC Stark-shifted resonant states rather than the closing of an ionization channel. Because these resonances are dependent on the frequency and intensity of the laser field, the broad bandwidth of the 6 fs pulses means that the resonance condition is fulfilled across a large range of intensities. This is further exaggerated by volume-averaging effects, resulting in excitation of the 5g5g5g state at almost all intensities and reducing the apparent magnitude of the enhancements. For 30 fs pulses, volume averaging also broadens the quantum state distribution, but the enhancements are still large enough to survive. In this case, selectivity of excitation to a single state is reduced below 25% of the relative population. However, an analysis of time-dependent Schr\"odinger equation simulations indicates that excitation of up to 60% into a single state is possible if volume averaging can be eliminated and the intensity can be precisely controlled.
The influence of ac Stark shifts on the three-photon ionization of cesium in a moderate-intensity laser beam is investigated. The ionization process involves a two-photon resonance with the 8d8d8d fine-structure levels. The work consists of two related parts. In the first part, atomic parameters, such as the two-photon Rabi rate and the ac Stark shift, are calculated in the nonrelativistic Hartree-Fock approximation. In the second part, the atomic parameters thus obtained are used as coefficients in a system of coupled differential equations representing the time evolution of the density matrix. Ionization line shapes are generated for a transform-limited pulsed laser of moderate intensity with a single-mode transverse structure. As the time history of the intensity profile is varied from square to smooth, the ionization line shape becomes asymmetric due to the time dependence of the ac Stark shift. The effects of varying the spatial intensity distribution of the laser light to include transverse centering and longitudinal focusing are also studied.