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Soviet Journal of Quantum Electronics

Doppler-free resonances of the second-order Raman scattering

V. A. Ulybin

Published Dec 31, 1989• 0 citations
Publisher

Abstract

An analysis is made of the possibility of observation of Raman scattering resonances free of the influence of the Doppler effect. Such Doppler-free resonances result from the excitation of a standing wave of Raman vibrations in a gas by two standing optical waves differing in frequency by half the Raman frequency. Complete compensation of the Doppler shifts occurs as a result of simultaneous interaction of atomic particles with two pairs of counterpropagating waves. Scattering of traveling pump waves by a standing wave of Raman vibrations in the fifth order with respect to the field gives rise to resonances in the radiation at the Stokes and anti-Stokes frequencies. Coherent scattering is observed in the presence of dispersion. A resonance in the number of particles excited to the upper level of a Raman transition appears in the eighth order in the field. The expressions obtained are applied to the specific example of neon.

DOI
10.1070/qe1989v019n12abeh010177

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An analysis is made of the possibility of observation of Raman scattering resonances free of the influence of the Doppler effect. Such Doppler-free resonances result from the excitation of a standing wave of Raman vibrations in a gas by two standing optical waves differing in frequency by half the Raman frequency. Complete compensation of the Doppler shifts occurs as a result of simultaneous interaction of atomic particles with two pairs of counterpropagating waves. Scattering of traveling pump waves by a standing wave of Raman vibrations in the fifth order with respect to the field gives rise to resonances in the radiation at the Stokes and anti-Stokes frequencies. Coherent scattering is observed in the presence of dispersion. A resonance in the number of particles excited to the upper level of a Raman transition appears in the eighth order in the field. The expressions obtained are applied to the specific example of neon.
The influence of a strong field resonant to the Raman transition on the behavior of the Stokes harmonic in saturated two-wave stimulated Raman scattering is theoretically considered based on the description of a gas of three-level atoms by medium density matrix equations. The vibrational mode of energy redistribution between laser and scattered radiation, threshold with respect to the resonant field intensity, is predicted. The action of optical fields on the absorption and amplification of the resonant field in a Raman medium is described.
The influence of phase memory effects on the spectrum of resonance Raman scattering by three-level atoms with the Λ configuration of levels experiencing collisions with buffer gas atoms in a strong monochromatic radiation field is studied theoretically. Systems with a small Doppler broadening compared to the collision frequency (large buffer gas pressures) are analysed in the general case of an arbitrary change (from complete change to complete preservation) in the phase memory at any of three transitions in the Λ system. It is shown that in the absence of the collision relaxation of the low-frequency coherence at the transitions between two lower levels of the Λ system, the radiation scattering spectrum has a spectrally narrow component at the Raman frequency, which, despite the homogeneous broadening of the absorption line, exhibits a strongly pronounced anisotropy. In the direction, close to the propagation direction of exciting radiation, this line maximally narrows down. It is significant that upon optical pumping to the level unaffected by a strong field the resonance Raman spectrum noticeably differs from the spectrum in the case of the probe field. A simple expression is proposed for calculating the degree of the phase memory preservation in collisions from the relative amplitude of the Raman resonance.
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.
The temperature effect on the resonance Raman scattering from molecules is investigated. Considering a total system consisting of a molecular system, a heat bath, and the weak radiation field, a general expression for the relaxation processes is derived utilizing the Liouville operator technique for the time evolution of the density matrix of the total system. By using the perturbation method with respect to the radiation and matter up to second order, rate constants for zero photon (radiationless processes), one-photon and two-photon processes are derived after taking the long time limit in the Markoff approximation. Assuming a weak interaction between the molecular system and heat bath, a temperature-dependent resonance Raman scattering cross section is formulated in the adiabatic basis set for the molecular systems. In the displaced harmonic oscillator model, we obtain an analytical expression for the temperature-dependent Raman scattering cross section for the multimode case, which is suitable for both weak coupling and strong coupling cases. Analytical expressions for the Stokes and anti-Stokes bands of the jth order vibrational transition in the one oscillator model can easily be obtained from the general expression for the resonance Raman scattering cross section derived. An approximate Stokes to anti-Stokes ratio is given up to the second order of the dimensionless displacement Δ. The resonance Raman scattering cross section and the excitation energy profiles are numerically calculated as a function of physical constant such as temperature, molecular vibrational frequency and Δ. It is shown that the excitation profiles of the anti-Stokes band of the jth order vibrational transition have the similar envelope of the corresponding Stokes band shifted by jh/ω. The inverse Raman effect which is closely related to the ordinary Raman effect is also discussed.
A new variant of active Raman spectroscopy is proposed. Instead of two-frequency pumping, radiation in resonance with the scattering transition is used and a static electric field is applied simultaneously. This variant may have an advantage over the conventional method in the case of a large Stokes shift which is found, for example, in the Raman scattering due to electronic transitions. An analysis is made of the dynamics of the interacting waves and the optimal length of nonlinear medium to which a static electric field should be applied is determined.
An analysis is made of the propagation of a short coherent optical pulse in a three-level resonant medium with an essentially nonequidistant spectrum as a function of the degree of preexcitation of the medium. It is found that in addition to self-induced transparency and resonance scattering, stimulated Raman scattering (Stokes or anti-Stokes) should be observed under certain spatial phase-matching conditions. The area theorem is formulated for all radiation components. An analysis is made of the case of propagation of a resonant electromagnetic pulse of frequency ω in a system of three-level atoms having an equidistant spectrum. Under conditions of preexcitation of the medium at the frequency 2ω by longitudinal acoustic pulses, a scattered transverse acoustic wave at the frequency ω may be observed.