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Optics and Spectroscopy

Raman echo induced by ultimately short pulses under conditions of strong nonresonant pumping

С. В. Сазонов

Published Mar 1, 2003• 10 citations
Publisher

Abstract

On the basis of quantum-mechanical approach, a theoretical study of the primary Raman photon echo was carried out under conditions of excitation of a medium by pulses with a duration on the order of one period of electromagnetic oscillations (ultimately short pulses) and by strong quasi-monochromatic nonresonant pumping. It is shown that the intensities of the pumps determine to a considerable extent the time of formation of the echo signal, its duration, the direction of emission, and the power and that the use of ultimately short pulses promotes the substantial simplification of the schemes of prospective experiments. The possibilities of echo generation at the Stokes and anti-Stokes frequencies in the regimes of two-, one-, and zero-pulse excitations are revealed. In the last case, the Raman-active transitions are excited by two pumps with different intensities.

DOI
10.1134/1.1563686

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On the basis of quantum-mechanical approach, a theoretical study of the primary Raman photon echo was carried out under conditions of excitation of a medium by pulses with a duration on the order of one period of electromagnetic oscillations (ultimately short pulses) and by strong quasi-monochromatic nonresonant pumping. It is shown that the intensities of the pumps determine to a considerable extent the time of formation of the echo signal, its duration, the direction of emission, and the power and that the use of ultimately short pulses promotes the substantial simplification of the schemes of prospective experiments. The possibilities of echo generation at the Stokes and anti-Stokes frequencies in the regimes of two-, one-, and zero-pulse excitations are revealed. In the last case, the Raman-active transitions are excited by two pumps with different intensities.
A generalization of the Bloembergen-Shen model was supposed on cases those Raman active molecules with an arbitrary number of normal modes. On the basic of this model were investigated Raman echo signal characteristics when medium was excited by pulses of widths up to one period of optical oscillations. It was shown that a large number of echo responses on Stokes and anti-Stokes components could arise even under a two-pulse action in a continuous monochromatic pumping field. The number of echo responses depended on the number of molecular normal modes and the geometry of experiments. At small exciting pulse “areas,” the echo responses whose Stokes and anti-Stokes components corresponded to normal vibrational modes of a molecule.
A generalization of the Bloembergen-Shen model to Raman active molecules with an arbitrary number of normal modes was suggested. The generalized model was used to study Raman echo signal characteristics when a system of molecules was excited by pulses of widths up to one period of optical oscillations. It was shown that a large number of echo responses on Stokes and anti-Stokes components could arise even under a two-pulse action in a continuous monochromatic pumping field. The number of echo responses depended on the number of molecular normal modes and the geometry of measurements. At small exciting pulse “areas,” the echo responses whose Stokes and anti-Stokes components corresponded to normal vibrational modes of a molecule had the highest intensity, whereas the components formed by normal mode combinations were strongly suppressed.
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.
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.
An analysis is made of parametric excitation of anti-Stokes components of stimulated Raman scattering in an optical resonator filled with a medium whose refractive index is dispersion-free. The case of steady generation of the first Stokes component is considered. Expressions are obtained for the amplitudes of steady-state fluctuations of the anti-Stokes components in the case of a weak reaction of these components on the pump radiation and on the first Stokes component. Various cases of frequency dependences of the intrinsic resonator losses are considered. Conditions are found under which a large number of anti-Stokes components with similar intensities is excited so that the anti-Stokes radiation leaving the resonator is a periodic sequence of ultrashort (femtosecond) pulses with one pulse per period.