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Journal of Modern Optics

Time-dependent Spectrum in Quantum Theory of Stimulated Raman Scattering from a Two-level System

K. Grygiel, S. Kielich

Published Jan 1, 1987• 2 citations
Publisher

Abstract

The time-dependent (physical) spectrum of stimulated Raman scattering (SRS) from a two-level system is calculated, proving the influence of the spectral width Γ of the detector on the obtained spectral line shape. In addition, the time evolution of the process leading to the Raman line is investigated. For a partially excited system, the scattered field intensity exhibits oscillations in time, and Γ is found to affect the amplitude of the oscillations in the Raman line intensity. A numerical analysis of the result is performed for the case of monochromatic external fields.

DOI
10.1080/09500348714550141

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Journal of Physics B Atomic and Molecular Physics•Oct 14, 1985•0 citations
The time-dependent (physical) spectrum of stimulated Raman scattering (SRS) from a two-level system is calculated, proving the influence of the spectral width Γ of the detector on the obtained spectral line shape. In addition, the time evolution of the process leading to the Raman line is investigated. For a partially excited system, the scattered field intensity exhibits oscillations in time, and Γ is found to affect the amplitude of the oscillations in the Raman line intensity. A numerical analysis of the result is performed for the case of monochromatic external fields.
Manifestations of quantum fluctuations in stimulated Raman scattering ( SRS ) have been intensively studied lately1. Quantum noise present in spontaneous scattering stimulates fluctuations both in phase and in amplitude characteristics of output Stokes emission. At present statistical properties of amplitude fluctuations are studied in detail and it is shown that in linear transient regime of SRS without pump depletion statistical scatter of Stokes energy Es has negative exponential distribution2. In saturation regime of SRS the amplitude fluctuations are almost suppressed simultaneously with pump depletion. The phase fluctuations manifest both in linear and in nonlinear SRS and produce beam pointing fluctuations3, a change in Stokes emission spectra from pulse to pulse4 and cause soliton appearance in Rayleigh component of SRS5. Phase noise is observed in saturation regime due to relation between phases of Stokes and phonon waves which is preserved in processes of stationary and quasistationary SRS amplification. Spectrum phase fluctuations manifest as fine structure of SRS spectrum4, fluctuations of average Stokes frequency and Stokes linewidth fluctuations. The evolution of phase fluctuations in time is determined by the nature of spontaneous scattering and polarization of Raman media and is of great interest as one can follow its development from vacuum modes level to saturation regime. However up to now this problem has not been studied yet.
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.
Abstract The theory of multifrequency stimulated Raman scattering (SRS) of light on rotational transitions of molecules, which are simulated by a three-level quantum system, is developed. It is shown that the application of bichromatic pumping increases the scattered radiation spectrum width. The exact algebraic solution for the wave amplitudes is obtained in the simplest version of synchronous SRS on transitions with a negligibly low eigenfrequency. It is found that an increase in the ratio of the Raman transition frequency to the pump radiation frequency leads to predominance of the anti-Stokes scattering branch. The effect of wave asynchronism emerging due to linear and nonlinear dispersion of the medium as well as the phase difference of the pump waves on SRS is considered. All types of asynchronism narrow generated frequency spectrum and suppress the anti-Stokes scattering branch. Nonlinear dispersion ensures positive values of wave amplitudes due to phase jumps by π during the propagation of waves in a medium.
An investigation was made of the influence of the geometric excitation conditions on the energy dependences of the stimulated scattering of focused laser pulses of ~ 10 −8 sec duration when the sharpness and depth of focusing were varied. The experimental results obtained in this study were interpreted theoretically on the basis of a quantum analysis of stimulated Raman scattering in a two-level system. The experimental relationships could be explained only if an allowance was made for the changes in the populations of the levels participating in the Raman transition. It was possible to select the experimental conditions so that reconstruction of the wavefront of the pump radiation was observed under stimulated scattering conditions in a wide energy range.
Abstract Presupposing exponentially decaying states (with phenomenological lifetimes) of the particle system interacting with the radiation field, the shape and width of Raman lines is discussed on a quantum‐mechanical basis for the most important types of excitation: non‐resonance, pre‐resonance, rigorous resonance with a continuum level and with a discrete, non‐degenerate, and isolated level; monochromatic and non‐monochromatic irradiation. Attention is called to peculiar intensity distributions of the secondary radiation obtainable by sufficiently monochromatic excitation in near resonance to an isolated state (resonance fluorescence case) which deviate characteristically from those customary in traditional fluorescence and scattering spectra.
The passage of strong monochromatic laser radiation through a resonance medium consisting of three-level atoms is investigated. It is shown that if collisions are taken into account in the scattered waves the resonances at combination frequencies occur to first order in the laser field intensity. A numerical analysis of the dependence of the stimulated electronic Raman scattering (SERS) components' gain factors on the pump frequency is carried out. The dispersion curves of the SERS components' gain (absorption) factors for fixed values of pump frequency and intensity are plotted.