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AIP conference proceedings

Quantum and nonlinear theory of Stimulated Raman Scattering (SRS)

F. P. Mattar, Yves Claude, M. Burgess, Jiří Teichmann

Published Jan 1, 1989• 0 citations
Publisher

Abstract

Experimental studies of spatial and temporal coherence of SRS in hydrogen [1] have pointed out the need of a quantum theory in the nonlinear regime. Previous studies have dealt either with diffraction in a linearized regime [2] or with a nonlinear light‐matter description in the uniform‐plane‐wave regime [3]. Both diffraction and nonlinear effects are examined herein. The Stokes pulse builds up from quantum initiation as does the superfluorescence SF emission [4]. The interplay of diffraction coupling, transverse variations of the atomic density and quantum fluctuations on the Stokes buildup was simulated using a self‐consistant numerical algorithm [5] previously developed for finite beam effects in Self‐Induced‐Transparency [6,7].

DOI
10.1063/1.38705

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Experimental studies of spatial and temporal coherence of SRS in hydrogen [1] have pointed out the need of a quantum theory in the nonlinear regime. Previous studies have dealt either with diffraction in a linearized regime [2] or with a nonlinear light‐matter description in the uniform‐plane‐wave regime [3]. Both diffraction and nonlinear effects are examined herein. The Stokes pulse builds up from quantum initiation as does the superfluorescence SF emission [4]. The interplay of diffraction coupling, transverse variations of the atomic density and quantum fluctuations on the Stokes buildup was simulated using a self‐consistant numerical algorithm [5] previously developed for finite beam effects in Self‐Induced‐Transparency [6,7].
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.
The far field direction of propagation of light pulses generated by transient, single pass stimulated Raman scattering (SRS) is observed to fluctuate front pulse to pulse due to quantum mechanical uncertainties in the occupation numbers of different coherent spatial modes. When SRS is generated on the Q(l) vibrational transition in hydrogen with an interaction region Fresnel number near unity, the lowest-order coherent spatial mode dominates the generation process, leading to near-diffraction-limited Stokes light.
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.
Recent experiments1,2 have raised questions concerning the effects of transverse propagation (diffraction) and collisional dephasing on the quantum fluctuations of the energy of Stokes pulses generated by stimulated Raman scattering (SRS). It was originally believed that, if the Fresnel number of the laser-excited volume was close to unity, a theory based on one-dimensional spatial propagation should be adequate. This theory3 predicted that in the transient, unsaturated regime the pulse-energy probability distribution function P(W) should be essentially a negative exponential function of pulse energy W, with the maximum value of P(W) at W ≅ 0. Experiments2 showed, however, a maximum in P(W) at about one tenth of the mean pulse energy, in disagreement with the one-dimensional theory.
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.