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Annual Meeting Optical Society of America

Observation of temporal coherence modes in stimulated Raman scattering

Michael G. Raymer, zhenqian Li, Ian A. Walmsley

Published Jan 1, 1988• 0 citations
Publisher

Abstract

By use of a streak camera, the temporal variations of light pulses generated by stimulated Raman scattering have been observed when the pulse duration is of the order of the inverse Raman linewidth. In this regime, which is intermediate between transient and steady state, the pulse shapes undergo large shot-to-shot variations due to the effects of quantum moise. It is found that some of the pulses bear a strong resemblance to the temporal coherence modes, i.e., the eigenfunctions of the two-time field autocorrelation function.1 Probability distributions for the energy content of each of these modes are negative-exponential functions of energy. This explains why isolated modes are sometimes seen on a single shot.

DOI
10.1364/oam.1988.tux1

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By use of a streak camera, the temporal variations of light pulses generated by stimulated Raman scattering have been observed when the pulse duration is of the order of the inverse Raman linewidth. In this regime, which is intermediate between transient and steady state, the pulse shapes undergo large shot-to-shot variations due to the effects of quantum moise. It is found that some of the pulses bear a strong resemblance to the temporal coherence modes, i.e., the eigenfunctions of the two-time field autocorrelation function.1 Probability distributions for the energy content of each of these modes are negative-exponential functions of energy. This explains why isolated modes are sometimes seen on a single shot.
A quantum theory of stimulated Raman scattering is presented that takes into account three-dimensional propagation and collisional dephasing, allowing the study of the spatial and temporal coherence properties of the generated Stokes light. Maxwell-Bloch equations for the Stokes field operator and the collective atomic operators are solved analytically under low-signal-gain conditions, where the laser field and the atomic ground states remain undepleted. The intensity and the space-time autocorrelation function of the Stokes field are calculated. The Stokes field is expanded into a set of statistically independent ``coherence modes,'' which are determined explicitly for the case of a cylindrically shaped pumped volume. The Stokes pulse energy W is found to fluctuate from pulse to pulse. The probability distribution function for pulse energies P(W) is calculated for a range of Fresnel numbers of the excited volume and collisional dephasing rates. For small values of Fresnel number and dephasing rate, P(W) is a negative exponential distribution. For large values of either, P(W) narrows and approaches a Gaussian-shaped distribution. This occurs because many independent modes contribute to the Stokes emission, making it spatially and/or temporally incoherent.
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
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.
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.