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Annual Meeting Optical Society of America

High temporal and spatial resolution via fluctuating pulses

Vladimir Finkelstein, P. R. Berman, A. Bouchene, Anne Débarre, J. Keller, J.-L. Le Gouët, P. Tchénio

Published Jan 1, 1991• 0 citations
Publisher

Abstract

If two strong cross-correlated fluctuating laser pulses having a relative time delay t d interact with a three-level atom, they can modify the atomic response to a third probing pulse in a manner that varies dramatically on a time scale δt d which is much smaller than the correlation time of the pulses τ c . It is found that δt d decreases with increasing strength of the pulses.

DOI
10.1364/oam.1991.wp3

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If two strong cross-correlated fluctuating laser pulses having a relative time delay t d interact with a three-level atom, they can modify the atomic response to a third probing pulse in a manner that varies dramatically on a time scale δt d which is much smaller than the correlation time of the pulses τ c . It is found that δt d decreases with increasing strength of the pulses.
Excitation of a three-level atom irradiated by a sequence of two fluctuating pulses is discussed. The pulses have bandwidth ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{\mathrm{\ensuremath{-}}1}$, relative delay time t12{\mathit{t}}_{12}t12​, and can be correlated with one another. It is shown that, for strong excitation pulses, the level populations and atomic coherence as functions of t12{\mathit{t}}_{12}t12​ can vary on a time scale much smaller than ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$. This effect may lead to a means for obtaining high temporal and spatial resolution.
A theoretical analysis of the optical coherent transients that arise when a sample of two-level atoms is irradiated by a sequence of three broad-bandwidth pulses is presented. The first two pulses have a relative delay time of order of the correlation time of the pulse fluctuations and are sent into an atomic vapor from different directions. These pulses, whose temporal width is much greater than the delay time, can be correlated with one another and can be strong enough to saturate the two-level atomic transition. The third pulse is weak, noncorrelated with the first two, and is delayed in time so that it does not overlap them. We present a detailed examination of the transient signal that is produced when the third pulse is scattered by the spatial gratings in the population difference of atoms created by the first two pulses. Taking into account the effects of inhomogeneous and homogeneous broadening, we calculate the intensity of the transient signal, emitted in different directions, as a function of delay time. The signal is found to depend dramatically on the intensities of the excitation pulses. It is shown that, for strong excitation pulses, there is a direct dependence of the signal on the cross-correlation time of pulses ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$ that does not exist when the pulses are weak. In particular, the strongest signals exhibit a peak of width of order ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$. This peak can have a very narrow dip near its maximum whose width is much smaller than ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$, if the pulses are fully correlated. We develop a representation of the time evolution of the Bloch vector of a two-level atom, driven by time-delayed pulses, that enables us to explain our results. In this representation, the two time-delayed pulses are replaced by two fully overlapping pulses having some effective amplitudes and atomic field detunings.
A theory is developed to describe the optical transient signals that arise when a sample of two-level atoms is irradiated by a sequence of two or three broad-bandwidth pulses is presented. The first two pulses have a relative delay time of order of the correlation time of the pulse fluctuations. These pulses whose temporal width is much greater than the delay time are fully correlated with one another and can be strong enough to saturate the two-level atomic transition. In the case of three-pulse transients the third pulse is weak non-correlated with the first two and is delayed in time so that it does not overlap them. Taking into account the effects ofinhomogeneous and homogeneous broadening we calculate the intensity of the transient signals as a function of delay time. The signals are found to depend dramatically on the intensities of the excitation pulses. It is shown that for strong excitation pulses a direct dependence of the signal on the cross-correlation time of the pulses r occurs that does not exist when the pulses are weak. In particular for saturating pulses the signals exhibit a peak of width of order r . In the case of the two-pulse transient the peak is found to disappear when the Doppler width of the atomic ensemble becomes sufficiently large. This peak can have a very narrow dip near its maximum whose width is much
A theory of atomic transitions in correlated stochastic laser fields is developed for the case in which one pulse is assumed to be arbitrarily strong (beyond the fast fluctuation expansion), while the second, time-delayed, pulse is treated in perturbation theory. The statistics of the driving laser field is assumed to be that of a Markov process. We illustrate the technique by calculating the absorption spectrum of a two-level atom in a pump field and cross-correlated probe laser where the field statistics is described by the phase diffusion model.
Coherent signals produced by time delayed, fluctuating optical pulses interacting with atoms in the vapor phase have attracted much interest recently, due to their potential as a source of sub-picosecond time resolution. The theoretical description of such experiments brings into play many profound questions connected with stochastic Bloch equations. For example, even though the noise properties of a single laser beam may be Markovian in nature, in these experiments the atoms are subjected to at least two time-delayed fields which may be correlated. Because the atoms retain some memory of the first field at the time when the second field acts, the entire process becomes non-Markovian. In principle, the variation of such parameters as the homogeneous and inhomogeneous widths, allows the experimenter some degree of control over this memory time associated with the atomic medium.\n&more...