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Annual Meeting Optical Society of America

Fourth-order interference between two independent sources of stimulated Raman scattering

D. T. Smithey, S. J. Kuo, Michael G. Raymer

Published Jan 1, 1990• 0 citations
Publisher

Abstract

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

DOI
10.1364/oam.1990.mr6

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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
We observed single-shot spatial interference from two independent pulsed-light sources using stimulated Raman scattering (SRS) in the transient, macroscopic-field regime. By measuring the phase distribution of the Stokes field and the fourth-order spatial correlation function, we verified that the Stokes field obeys thermallike statistics in the unsaturated SRS gain regime. This reflects the properties of the underlying quantum noise in the vacuum field and scattering medium. A transition from thermallike to laserlike statistics occurs when the gain becomes saturated.
A pencil shaped region of a Raman-active medium forms a source for Stokes-shifted light via stimulated Raman Scattering (SRS) when driven by an intense laser pulse. Stokes photons are scattered spontaneously at first, and then amplified during propagation through the medium. Since the scattering is initiated by quantum noise, the actual number of photons produced in any given pulse will be highly uncertain, even if the pulse energy of the driving laser is constant1. As the Stokes light propagates through such an extended region, it's coherence properties will be changed. The spatial coherence is determined by the size and shape of the region, which may be characterized by its Fresnel number F, defined as F= A/λSL, where A is the cross-sectional area of the interaction region, which has length L, and λS is the Stokes wavelength. The rate at which the microscopic scatterers (atoms or molecules) are dephased by collisions affects the temporal coherence of the Stokes light, characterised by the temporal coherence parameter Γτ /gL, where Γ is the collisional dephasing rate, τ is the laser pulse duration and g is the steady-state Raman gain coefficient.
We have carried out an experiment to study the spatial correlation of the Stokes pulses in transient stimulated Raman scattering. The spatial pattern of Stokes pulses is known to fluctuate from shot to shot due to the buildup of the pulses from quantum noise. We have measured a series of spatial profiles of the Stokes intensity for different Fresnel numbers and Raman gains. A correlation area of the Stokes pulses is obtained by calculating the autocorrelation function of an ensemble of the intensity profiles for each set of parameters. The measured results are compared to existing theories.1
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
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.
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.