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Physical Review A

Theory of transient stimulated Raman scattering in H2

Burke Ritchie

Published Jun 1, 1987• 10 citations
Publisher

Abstract

Calculations are performed for stimulated Raman scattering in ${\mathrm{H}}_{2}$ in the transient regime. The production of anti-Stokes radiation depends strongly on phase matching in the dispersive medium, and a predictive theory requires at least two spatial dimensions to describe the process.

DOI
10.1103/physreva.35.5108

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Calculations are performed for stimulated Raman scattering in H2{\mathrm{H}}_{2}H2​ in the transient regime. The production of anti-Stokes radiation depends strongly on phase matching in the dispersive medium, and a predictive theory requires at least two spatial dimensions to describe the process.
It is shown that transient anti-Stokes stimulated Raman scattering (SRS) acts as a vacuum field fluctuations amplifier at Stokes frequency, the fluctuations being amplified up to macroscopic values. This makes their investigation possible by studying macroscopic energy fluctuations of transient SRS anti-Stokes pulses. The proposed theory also gives a quantitative description of angular distribution of self-generated anti-Stokes emission around the exact phase-matching angle recently observed by Duncan et al. ( Opt. Lett. , 11 (1986) 803) in the transient regime.
A calculation is made of the intensity of the Stokes radiation in the stimulated Raman scattering of ultrashort light pulses in a dispersive medium employing the asymptotic approximation for arbitrary modulation of the amplitude and phase of the pump pulse. Particular attention was paid to the effect of phase modulation on the stimulated Raman scattering. Calculations were also made of the intensity of the anti-Stokes component in the scattering of an ultrashort pulse in a dispersive medium and of the optimal angle for the observation of the anti-Stokes rings.
A general theory of transient stimulated Raman scattering and the phase-matching diagrams are developed based on an interaction Hamiltonian which includes all the possible competing interaction channels. In a Raman system pumped by multiple crossing beams with multiple Stokes and anti-Stokes components, these channels are defined by the interactions among fields at different frequencies and/or k vectors of the pump pairs and Stokes and anti-Stokes fields. An ensemble-averaged equation of motion for the active phonon mode is derived within the Markovian approximation in which the phonon-phonon coupling (pressure effect) is reduced to an energy relaxation and a phase fluctuation. A complete set of transient coupled equations including phase modulation, Stark shift, medium (anharmonic) saturation, and all the possible four-wave-mixing channels is presented. In the transient regime, it is found that the effects of the Stark shift on the Raman efficiency are mainly governed by the input pump energy in contrast to the steady-state theory where the pump intensity plays the main role. Both analytic and numerical methods are developed in describing the nonlinear effects due to the energy feedback mechanism in the strong pump-depletion regime. Twelve possible four-wave-mixing channels are analyzed for nonlinear phase diagrams characterized by the angles among pump pairs, and Stokes and anti-Stokes fields. Finally, numerical examples are shown for the effects of the coherence lengths of high-order Stokes fields and pump pairs on the generation of low-order Stokes fields.
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.