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Journal of Physics B Atomic and Molecular Physics

Theory of near-resonant spontaneous Raman scattering spectra

P. L. Knight

Published Dec 14, 1980• 7 citations
Publisher

Abstract

A theoretical analysis of the time development of spontaneous Raman scattering lineshapes is presented. Particular attention is paid to transients caused by the sharp turn-on of the laser fields. The author examines the breakdown of lowest order perturbative ideas, the role of induced widths and shifts and of Rabi oscillations in final-state spectra for large pump intensities.

DOI
10.1088/0022-3700/13/23/013

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Physical Review A•Oct 1, 1981•358 citations
A theoretical analysis of the time development of spontaneous Raman scattering lineshapes is presented. Particular attention is paid to transients caused by the sharp turn-on of the laser fields. The author examines the breakdown of lowest order perturbative ideas, the role of induced widths and shifts and of Rabi oscillations in final-state spectra for large pump intensities.
The resonant Raman scattering in a three level system produces an optical pumping of molecules from the initial to the final states which are radiatively coupled to the intermediate resonant state. We consider the pumping that is produced by an intense, pulsed, monochromatic radiation field that is near-resonant with the initial resonance frequency. The Heitler–Ma damping theory is solved exactly for the case when the resonance fluorescence is weak compared to the Raman scattering, or any other processes which might cause irreversible decay of the resonant state. In particular, we examine the usefulness of dressed states to describe the intense field limit. The spectral line shape for the Raman scattering is obtained. The transient behavior following the onset of the laser pulse is examined and a careful analysis of the pumping rate and its relationship to both weak and strong field theories is presented.
We demonstrate explicitly that the quantum theories that predict that stimulated Raman scattering is initiated from zero-point fluctuations of either the material oscillators or the electromagnetic field are equivalent and that the process can be viewed as arising from both types of fluctuation. We further demonstrate experimentally that in the transient regime the spontaneous Stokes intensity reproduces the pump in amplitude and phase, as predicted by quantum theory, without any of the integrating effects normally associated with transient processes.
The theory of coherent anti-Stokes Raman scattering (CARS) is extended to include the effect of pump fluctuations. The intensities and spectra of lines in resonant CARS are calculated to all orders in fields assuming a phase-diffusion model for waves at the two pump frequencies. The bandwidth of the two lasers enters in a much more complicated way than following a simple scaling of T1{T}_{1}T1​ or T2{T}_{2}T2​. Various resonances in CARS spectra due to dynamic splitting of the energy levels are discussed for a range of detunings, field intensities, and bandwidths. In contrast to the usual spectra in strong fields, the Rabi sidebands appear as dispersion-shaped structures. The laser linewidth is shown to change dramatically the CARS line shape. The case of no saturation is also treated, thus allowing for the inclusion of more general line shapes and fluctuations of the pump waves and the nonlinear susceptibility tensor ${\ensuremath{\chi}}^{(3)}$. Gaussian statistics of the pump field are shown to lead to enhancement factors in CARS intensity, similar to those appearing in the context of multiphoton absorption processes.
The theory of resonance Raman effect, resonantly enhanced two-photon absorption, and resonance fluorescence---valid also for strong fields---is treated in a unified and simplified way. Dressed states, Bloch equations, and perturbation theory are used to calculate line positions, and integrated intensities both for steady state and transient excitation. The case of adiabatic following is solved explicitly; it occurs when an off-resonance incident pulse is turned on and off slowly. It leads to the identification of Raman scattering, two-photon absorption, and Rayleigh scattering with an adiabatic process while fluorescence and consecutive two-photon absorption with nonadiabaticity. Time-dependent spectra are defined in a rigorous way. Our formulas agree in the various limits with those that appear in the literature.
A theory of stimulated Raman scattering (SRS) is presented which treats in a unified manner the buildup of SRS from spontaneous Raman scattering and the spatial propagation which leads to gain. Maxwell-Bloch equations describe the coupling between the Stokes field operator and the collective atomic operators, which are driven by a classical laser field under low-signal-gain conditions, where the atomic ground states and laser field remain undepleted. An analytic expression is derived for the forward-propagating Stokes field operator in a one-dimensional spatial approximation when the Fresnel number of the excited medium is unity. Steady-state and transient Stokes intensities are evaluated under low-gain (spontaneous) and high-gain (stimulated) conditions. The Stokes intensity is found to be exactly independent of a laser bandwidth arising solely from phase fluctuations. The power spectrum of steady-state SRS is evaluated, giving a gain-narrowed spectral profile when the laser is narrow band, and a spectrum identical to the laser spectrum when the laser is broad band. A strong analogy between SRS and two-level superfluorescence is found; in both cases the macroscopic, collective dipole moment is initiated by quantum fluctuations.