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Quantum mechanical pointing stability of stimulated Raman scattering

S. J. Kuo, D. T. Smithey, Michael G. Raymer, Ian A. Walmsley

Published May 21, 1990• 0 citations
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Abstract

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.

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AIP conference proceedings•Jan 1, 1989•0 citations
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.
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.
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.
An experimental study of stimulated Raman scattering (SRS) has been performed using a subnanosecond pulse to investigate the statistical properties of Stokes light generation.1 There are macroscopic fluctuations of Stokes pulse energy as well as random generation of spatial mode patterns. When the scattering volume has a low Fresnel number, the spatial patterns of the SRS resemble cavity modes. When the Fresnel number is large, there are irregular structures appearing across the Stokes profile in a random fashion. A theoretical study of the spatial and temporal coherence properties of Raman generation using a Gaussian-profile pump pulse has also been carried out. Using a Gaussian-Laguerre mode expansion technique,2 it is found that the higher-order spatial coherence modes1 experience different gain than the lower-order spatial coherence modes, and consequently the temporal coherence associated with each individual spatial coherence mode is different.
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.
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].