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Physical Review A

Experimental Investigation of Transient Stimulated Raman Scattering in a Linearly Dispersionless Medium

Robert L. Carman, M. Mack

Published Jan 1, 1972• 51 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.5.341

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Annual Meeting Optical Society of America•Jan 1, 1985•0 citations
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 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.
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.
A theory for selective-vibrational-dephasing experiments using transient stimulated Raman scattering in high laser depletion is presented. The transient stimulated Raman scattering equations are numerically solved including laser depletion for homogeneously and inhomogeneously broadened vibrational line shapes. A detailed account of the effects of low and high laser depletion on the vibrational amplitudes is given. An interpretation for excite-and-probe vibrational-dephasing experiments undertaken in the low- and high-laser-depletion regimes is developed. For a collinear laser probe pulse, high depletion of the excitation laser pulse leads to enhanced coherent Stokes probe scattering from one vibrational subgroup in the inhomogeneously broadened line shape. This selective scattering is greatly dependent upon the excitation laser pulse width and the off-resonance frequency of the vibrational subgroup. The enhanced selectivity in high laser depletion allows the homogeneous dephasing time T2{T}_{2}T2​ to be measured to a high level of accuracy.
We consider transient stimulated Raman amplification of trains of picosecond pulses. In this regime the gain of a single pulse is reduced from its steady-state value because of the inability of the nonlinear polarization to follow the time variations of the pump pulse. In addition oscillatory behavior of the pump and Stokes pulse amplitudes have been predicted in the transient regime in conditions of high pump depletion. When the pump radiation is in the form of a train of pulses whose separation is comparable to or shorter than the dephasing time of the nonlinear medium, increased gain can be experienced by later pulses in the train because they can grow from the material polarization created by earlier pulses. We have analyzed this type of amplification as a function of pulse spacing, pump energy, and pump intensity in the regime of high pump depletion. In addition we have considered the effects of Stark shifts of the two-photon resonant Raman level on the Stokes conversion efficiency. We find that at constant pulse intensity the conversion efficiency increases with time through the pulse train, gradually approaching steady state at low conversion efficiencies at times long compared to T2. The maximum conversion efficiency increases as the pulse spacing is decreased. If the pump depletion is too high the peak conversion of the Stokes oscillates through the train in a manner similar to the oscillations of the intensity of a single pulse. A Stark shift of the resonant level can cause reduced gain as well as introduce phase shifts on the Stokes and pump beams. The effects of these processes on the conversion efficiency are discussed.