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Annual Meeting Optical Society of America

Macroscopic quantum fluctuations in stimulated Raman scattering

Michael Scalora, C. M. Bowden, Joseph W. Haus

Published Jan 1, 1992• 0 citations
Publisher

Abstract

We examine beam pointing fluctuations that arise when the Stokes field is initiated from vacuum fluctuations. Using a model that includes diffraction and pump depletion, we use stochastic boundary conditions to solve for the fields. We present results with one and two transverse coordinates and compare them with experimental observations. Using a Gaussian input pump beam, we find that δK, a measure of the transverse fluctuations, is essentially a linear function of Fresnel number, in both the linear and nonlinear regimes, with larger values in the latter case. For low Fresnel numbers, we find that our theory is in excellent agreement with experiment when one or two transverse coordinates are used. For larger Fresnel numbers, quantitative agreement with experiment is obtained only if both transverse coordinates are employed in the calculation.

DOI
10.1364/oam.1992.fgg6

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We examine beam pointing fluctuations that arise when the Stokes field is initiated from vacuum fluctuations. Using a model that includes diffraction and pump depletion, we use stochastic boundary conditions to solve for the fields. We present results with one and two transverse coordinates and compare them with experimental observations. Using a Gaussian input pump beam, we find that δK, a measure of the transverse fluctuations, is essentially a linear function of Fresnel number, in both the linear and nonlinear regimes, with larger values in the latter case. For low Fresnel numbers, we find that our theory is in excellent agreement with experiment when one or two transverse coordinates are used. For larger Fresnel numbers, quantitative agreement with experiment is obtained only if both transverse coordinates are employed in the calculation.
We use numerical methods to investigate stochastic and coherence properties of the fields transverse profiles in stimulated Raman scattering. In the linear regime with diffractive coupling, the amplified signal is characterized by fluctuations that are macroscopic. We find an interesting dependence of the beam-pointing fluctuations on photon conversion efficiency. Our results for the linear regime compare well with recent experiments, and we report an increase in beam-pointing fluctuations in the nonlinear regime. We discuss the results of modeling with one and two transverse dimensions.
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
We have studied the diffractive coupling of Stokes, anti-Stokes, and pump fields in stimulated Raman scattering. We find that, depending on the strength of the anti-Stokes field relative to that of the Stokes, both soliton dynamics and beam-pointing fluctuations are affected for finite Fresnel numbers. The generation of the anti-Stokes waves can inhibit a gain-focusing mechanism that we predicted for the Stokes field, when a soliton propagates in the medium. Although no qualitative differences arise in the beam-pointing fluctuations of the Stokes field, we predict that the anti-Stokes beam may be much more stable than the Stokes counterpart. Our analysis shows that for a Fresnel number of 5, the difference can be as large as 70%, while for Fresnel numbers of order unity, it is nearly 10%.
We present a measurement of the beam-pointing fluctuations of a transient Raman-amplifier output using an interferometric method and a theoretical treatment of the three-dimensional, spatial propagation of transient stimulated Raman scattering (SRS) including the fluctuations of the Stokes field giving rise to the beam-pointing fluctuations. The theory is based on an effective steady-state model for the transient SRS process. By using nonorthogonal transverse modes to expand the field, we incorporate the effects of excess spontaneous-emission noise associated with gain-guided amplifiers. The agreement of the measurements with the theoretical treatment demonstrates that the beam-pointing jitter is caused by quantum noise. The beam-pointing fluctuations increase as the Fresnel number of the interaction volume increases because more spatial modes are excited.
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].
The large-scale fluctuations of Stokes light generated by stimulated Raman scattering have been studied experimentally by measuring the probability density function of Stokes pulse energies. The size and shape of the scattering region and the rate of collisional dephasing of the scatterers determine the degree of coherence of the Stokes light, and this in turn determines the form of the probability distribution. The experiments were performed for several diameters of the scattering volume, and for various collisional dephasing rates. The results of the experiments are compared to a recently reported quantum theory, and qualitative agreement is found. The need for a more accurate theory is pointed out.