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17th Congress of the International Commission for Optics: Optics for Science and New Technology

Stimulated Raman scattering spectra: quantum fluctuations and time evolution of linewidth

Владимир Григорьевич Беспалов

Published Sep 1, 1996• 0 citations

Abstract

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.

DOI: 10.1117/12.2316125

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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.

Stimulated Raman scattering is a quantum macroscopic process starting from unstable state. Any fluctuations, initial or boundary, classical or quantum in nature, lead to the macroscopic output fluctuations of the Stokes amplitude. Manifestation of these fluctuations in the statistics of the Stokes pulse energy and its spectrum have been studied extensively for the linear stage of the SRS [1]. Another fluctuation phenomena arises in nonlinear stage of the SRS - the random spikes, usually called soliton-like, are observed in the depleted pump [2]. Here we shown that the reason for these soliton-like spikes is the conservation of the relative phase Δϕ=ϕL−ϕS+ϕQ of the laser, Stokes and the polarization wanes [3].

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.

Stimulated Raman scattering (SRS) produces Stokes light pulses that originate from quantum noise and exhibit macroscopic amplitude and phase fluctuations from one shot to another.1 By using transient stimulated Raman scattering, we generated light pulses with macroscopic energy and temporal coherence times that were long compared to their duration. Stokes pulses were generated independently in each arm of an interferometer and were interfered together at the output. The position, modulation depth, and brightness of the interference fringes fluctuated randomly from one shot to the next. We obtained both the ensemble-averaged intensity and the fourth-order intensity correlation function of the interfered Stokes light. The average has a smooth envelope and shows no modulation, whereas the intensity correlation function has a depth of modulation of 0.35 for Stokes generation in the unsaturated (thermal-like) regime and 0.46 in the saturated (laser-like) regime. This is in agreement with predicted values of 0.33 and 0.5.2

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.

We have observed fluctuations in the direction of propagation of light pulses generated by stimulated Raman scattering (SRS). This fluctuation is analogous to the pointing fluctuation of laser beams,1 and is due to quantum mechanical uncertainties in the occupation numbers of different spatial modes. When SRS is generated in an interaction region with Fresnel number less than unity, the lowest order spatial mode dominates the generation process, but higher order spatial modes are also weakly and randomly excited. This results in small fluctuations in the wavefront of the light field. The direction of propagation is characterized by the transverse component of an average wave-vector determined by the gradient of the wave-front. We report experimental results by measuring the "center of mass" of the far-field intensity pattern of a single Stokes beam, and the fringe separation of an interference pattern formed by superposing two independently generated Stokes pulses. The experimental results are compared to theory.2