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Journal of Physics A Mathematical and General

Quantum statistics of the stimulated Raman effect

H D Simaan

Published Oct 1, 1975• 15 citations
Publisher

Abstract

The nonlinear process of the stimulated Raman effect is treated theoretically. Simple expressions are derived for the initial rates of change and limiting steady state values of the first two moments, the degrees of second-order coherence and the correlation function of the pump and Stokes beams. An analytical solution for the time dependence of the joint photon probability distribution of the two light beams is obtained and then employed to calculate some numerical results for various special cases of interest, and the significance of these results is discussed in physical terms. Simpler approximate expressions are also derived for the case where the pump beam is much more intense than the Stokes beam.

DOI
10.1088/0305-4470/8/10/016

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The nonlinear process of the stimulated Raman effect is treated theoretically. Simple expressions are derived for the initial rates of change and limiting steady state values of the first two moments, the degrees of second-order coherence and the correlation function of the pump and Stokes beams. An analytical solution for the time dependence of the joint photon probability distribution of the two light beams is obtained and then employed to calculate some numerical results for various special cases of interest, and the significance of these results is discussed in physical terms. Simpler approximate expressions are also derived for the case where the pump beam is much more intense than the Stokes beam.
The light initially prepared in a coherent state runs the stimulated and spontaneous Raman processes in a second-order nonlinear medium. Using analytical expressions of field operators for the light modes, we determine the quantum statistical properties of the modes in the stimulated and spontaneous Raman processes. By a choice of phase, we obtain a boson-pair property correlating the pump and vibration modes and such a property correlating the pump and anti-Stokes modes. The Stokes and vibration modes exhibit the boson-pair property for all initial phase differences between the pump mode and the other ones. In the spontaneous Raman process only the Stokes and vibration modes show such a property.
We develop the quantum theory of stimulated hyper-Raman scattering (HRS) and discuss the quantum statistics of pump and Stokes fields. We show that the initially coherent pump field acquires a strong squeezing that exceeds the similar squeezing in other nonlinear processes also involving two-photon absorption. Stokes field statistics are analysed in detail as a function of the initial statistics of both modes. Bunching effects are shown to be amplified in the short-time region, while in asymptotics the antibunching of Stokes photons becomes dominant, which in many cases results in sub-Poissonian statistics of Stokes mode. We also find a number of correlation effects between the photons of the two modes.
The effects of two-photon absorption from a single beam of light on the statistical properties of the beam are considered. Simple expressions are obtained for the initial rates of change and limiting steady-state values of the mean photon number and degree of second-order coherence of the beam. The general time dependences of these properties of the light and of the complete photon probability distribution are evaluated for several initial types of beam. The physical significance of the results is described, and their relationship to calculations which use a classical representation of the light is discussed.
The process of two-photon absorption from two beams of light is treated theoretically. Expressions are derived for the time dependences of the joint photon probability distribution of the beams, their photon-number factorial moments and the photon-number correlation between the beams. These expressions are illustrated by numerical results for special cases and their significance is discussed in physical terms. Simpler approximate expressions are also derived for the case where one beam is much more intense than the other.
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.
Statistical properties of optical fields in nonlinear couplers composed of two waveguides in which Raman or Brillouin processes (with classical pumping) are in operation and which are mutually connected through the mutual Stokes and/or anti-Stokes linear interactions are investigated within the framework of a generalized superposition of coherent fields and quantum noise. Heisenberg equations describing the couplers are solved both analytically under special conditions and numerically in general cases. Regimes for nonclassical properties of optical fields, such as sub-Poissonian photon-number statistics, negative reduced moments of integrated intensity and squeezing of quadrature fluctuations are discussed for the cases of single and compound fields. General results are compared with those from the short-length approximation.