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Bulletin of the Russian Academy of Sciences Physics

Structure of photon echo signals under excitation of a medium by few-cycle optical pulses

N. V. Znamenskiı̆, С. В. Сазонов

Published May 1, 2008• 0 citations
Publisher

Abstract

The results of original theoretical investigations of the primary and long-lived photon echo, generated by sequences of broadband and quasi-monochromatic pulses, are reported. Both echo responses and the effect of correlation of their profiles with the profiles of excitation pulses have a two-frequency character.
DOI
10.3103/s1062873808050274

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Echo responses of a three-level medium formed by the λ-scheme of quantum transitions under exposure to optical pulses consisting of an arbitrary number of oscillations have been studied theoretically. The cases of pulses consisting of few optical oscillations (for which the concept of an envelope cannot be used) and combinations of such pulses and quasi-monochromatic resonance signals have been considered. The approach used can be reduced to the renormalization of dipole moments of allowed quantum transitions through their multiplication by coefficients depending on the shape and duration of pump pulses and having absolute values in the range from zero (for nonresonance pulses) to unity (for resonance quasi-monochromatic pulses and broadband pulses consisting of few oscillations, whose spectrum covers the quantum transitions). A general equation has been proposed for the pulse area. In the limit of a large number of oscillations, it transforms into the well-known definition of the area of a quasi-monochromatic signal. The characteristics of primary and longlived photon echoes have been analyzed in detail. It has been shown that, when a medium is exposed to only pulses consisting of a few oscillations, three echo responses of both types can be principally generated at each frequency of the λ-scheme. Introduction of quasi-monochromatic pulses in pump pulse series decreases the number of echoes, and their qualitative character has a non-commutative property with respect to pulse permutation in a series. The extension of the proposed approach to more complex schemes of quantum transitions with the large number of quantum levels faces no principal difficulties.
It is theoretically established that multiple photon-echo signals reflect the oscillatory structure of the primary echo signal, which arises under the conditions of collinear excitation of two-level active centers by laser pulses having the same width but different amplitudes. It is shown that the oscillatory structure of the primary photon echo exists within the intervals (−t 1, t 1) and (−2t 1, 2t 1), where t 1 is the pulse width. It is found that, when the pulse width is of the same order of magnitude as the delay between the pulses and the amplitudes of the excitation pulses obey certain relations, the oscillatory structure of the primary photon-echo signal becomes asymmetric. In the mode of quadratic detection of the primary photon-echo signal, the asymmetric oscillatory structure of the primary echo manifests itself as a manifold of isolated signals (multiple photon echoes), with the time intervals between these signals being equal to the pulse width.
A photon echo in a multilevel quantum medium excited by two extremely short pulses with durations of less than one period of oscillation of the light is investigated theoretically. It is shown thatQ echo signals (Q is the number of allowed transitions) can form at each frequency of the allowed transitions, and the number of echo responses for all the allowed transitions equalsQ 2. Of these,Q(Q−1) signals are separated in both time and space. The otherQ echo signals of all the allowed frequencies all arise at the time 2τ 21 (τ 21 is the time interval between application of the first and second pulses to the medium) and are collinear with one another.
The effect of two-pulse photon echoes at the complicated action on a two-level medium with large inhomogeneous broadening of supremely short and quasiresonant pulses is investigated. Two versions of the action sequence of both pulses are considered. It is shown that the temporal properties of the echo signal are depended largely on the action order of indicated pulses. The effect of suppression of the optical echoes in the both cases at the action on a medium of the supremely short zeroth 'area' pulse is predicted. The qualitative procedure of definition of the complicated echoes spatial properties has been proposed and applied. It is shown that in indicated cases the diagrams of the echo signal intensity direction are not so peaked as in the case of common light echo.