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Journal of Physics B Atomic and Molecular Physics

Transient stimulated Raman scattering in lossy media

D. Cotter, Richard R. Wyatt

Published Aug 14, 1980• 2 citations
Publisher

Abstract

The small-signal theory of transient stimulated Raman scattering is extended to include the effects of focusing, diffraction and absorption losses for both the pump and scattered Stokes light. There is good quantitative agreement between the predicted and experimentally observed threshold for stimulated electronic Raman scattering in caesium vapour with picosecond laser pulses.

DOI
10.1088/0022-3700/13/15/020

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International Conference on Ultrafast Phenomena•Jan 1, 1984•0 citations
The small-signal theory of transient stimulated Raman scattering is extended to include the effects of focusing, diffraction and absorption losses for both the pump and scattered Stokes light. There is good quantitative agreement between the predicted and experimentally observed threshold for stimulated electronic Raman scattering in caesium vapour with picosecond laser pulses.
The theory of transient stimulated Raman scattering has been extended to include an arbitrary shape of the laser pump pulse. It is shown that the maximum Stokes gain depends on the total energy content per unit area of the pump pulse, and not on the instanteous intensity for an exciting pulse of short duration. The Stokes pulse has a leading edge which rises sharply to a maximum, where the maximum occurs with some delay with respect to the maximum of the pump pulse. The trailing edge follows the decay of the pump. In a nondispersive medium, the gain is not reduced by frequency broadening of the laser output, while in a dispersive medium, considerable gain reduction is expected. Numerical results for various laser-pulse shapes and spectral distributions are presented.
Stimulated Raman scattering is considered in the transient limit where the pulse width is small compared with T2. In the case where diffraction, level saturation, anti-Stokes and higher-order Stokes radiation, and quantum noise can all be neglected, we show that there are three distinct evolution regimes: the I regime, where the Stokes pulse is small compared with the pump pulse; the transition regime, where the Stokes and pump pulses are comparable; and the J regime, where the pump pulse is small compared with the Stokes pulse. The characteristic behavior in each of these three regimes is explored by using a combination of analytical and numerical tools.
The results of numerical calculations of the transient stimulated Raman scattering reported previously have been verified experimentally under conditions where both linear dispersion and self-focusing effects were negligible. The existence of a delay between maxima of the laser and Stokes pulses is experimentally demonstrated for the first time, while the pulse shortening in time via Raman scattering is established more firmly than in previous work. The incident-laser-pulse duration, generated-Stokes-pulse duration, and delay between intensity maxima for the laser and Stokes pulses were measured with the two-photon absorption-fluorescence technique. The effective phonon-dephasing time is determined via spontaneous Raman scattering. By using these measured quantities, inferences are made as to the magnitude of the transient gain and the shape of the exciting picosecond laser pulse.
The authors have extended the theory of stimulated Raman scattering to include the effects of laser bandwidths, in both the transient and steady-state regimes. The case of two interacting laser beams, a pump laser and a probe (Stokes) laser, is treated. Using the phase-diffusion model for laser bandwidth, the authors demonstrate that in the absence of dispersion, the forward Raman gain is essentially independent of the laser bandwidths in the high-gain limit, while in the low-gain limit the gain coefficient is inversely proportional to the sum of the bandwidths. It is further shown that when the pump-laser bandwidth is much larger than the linewidth of the Raman medium, the stimulated Stokes output assumes the same spectrum as the pump laser in the high-gain limit. A possible interpretation of these results is discussed assuming a "phase-locking" of the Stokes phase to the fluctuations in the pump-laser phase, due to the nonlinear interaction of the two beams through the Raman medium.
From a classical point of view the generation of Stokes light by stimulated Raman scattering (SRS) is not possible unless a Stokes input signal is supplied. On the other hand, the gain in SRS can be so large that without input the spontaneous build-up of strong Stokes waves can be observed. A proper quantum theoretical description1 shows that this spontaneous initiation of Stokes generation is due to microscopic random fluctuations originating from quantum noise associated with the dynamical variable Q(t) which is active in the Raman process, e.g., a molecular normal mode coordinate. In highly transient SRS -when the duration of the excitation pulse is shorter than the dephasing time- the Stokes field is proportional to the initial Heisenberg operator Q(0) describing the state of the system just before the excitation pulse is turned on (t=0). In this case the statistics of the final Stokes pulse energy is determined by quantum mechanical uncertainties associated with the random Raman polarization of the initial state2. On the other hand, in a steady state situation the Stokes pulse fluctuations are substantially reduced and the Stokes pulse energy is stabilized as a result of damping processes.