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Annual Meeting Optical Society of America

Cross-correlation measurements between the pump and Stokes intensities in stimulated Raman scattering

Lynn A. Westling, M. G. Raymer

Published Jan 1, 1985• 0 citations
Publisher

Abstract

The cross-correlation function between the pump and Stokes intensities in stimulated Raman scattering has been measured. It has previously been conjectured 1 and theoretically shown2 that the Stokes light generated in the presence of a multimode or broadband pump is generated with mode amplitudes and phases in perfect correlation with those of the pump. We present here experimental evidence of such cross correlations for scattering in hydrogen gas. The measurement technique used is the same as that previously used for measuring the intensity autocorrelation function of a multimode dye laser.3 This technique is based on detecting the frequency doubled light from a nonlinear crystal as a function of time delay between the pump and Stokes beams. We have performed cross-correlation measurements using as a pump the light from a multimode dye laser which is operated in two different cavity configurations: one in which the mode spacing Δυ is large compared with the spontaneous linewidth of the Raman transition Γ, Δυ > Γ; and one in which the mode spacing is small, Δυ < Γ.

DOI
10.1364/oam.1985.tuq1

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Annual Meeting Optical Society of America•Jan 1, 1987•1 citation
The cross-correlation function between the pump and Stokes intensities in stimulated Raman scattering has been measured. It has previously been conjectured 1 and theoretically shown2 that the Stokes light generated in the presence of a multimode or broadband pump is generated with mode amplitudes and phases in perfect correlation with those of the pump. We present here experimental evidence of such cross correlations for scattering in hydrogen gas. The measurement technique used is the same as that previously used for measuring the intensity autocorrelation function of a multimode dye laser.3 This technique is based on detecting the frequency doubled light from a nonlinear crystal as a function of time delay between the pump and Stokes beams. We have performed cross-correlation measurements using as a pump the light from a multimode dye laser which is operated in two different cavity configurations: one in which the mode spacing Δυ is large compared with the spontaneous linewidth of the Raman transition Γ, Δυ > Γ; and one in which the mode spacing is small, Δυ < Γ.
An experimental and theoretical study of the temporal correlations between the intensities of a broadband pump laser and Stokes light in stimulated Raman generation has been carried out. Direct measurements have been made of the pump laser and Stokes light intensity autocorrelation functions and of the intensity cross-correlation function between the two. Strong cross correlations are found. Nevertheless, the correlations are not perfect; that is, the Stokes intensity does not follow exactly the intensity variations of the laser. Transient effects and quantum fluctuations are shown, by theoretical modeling, to be responsible for the absence of perfect correlations.
The degree of phase cross correlation between a fluctuating pump wave and the Stokes wave, which is generated by stimulated Raman scattering, can be determined by observing the spectrum of anti-Stokes light generated by coherent anti-Stokes Raman scattering (CARS). The spectrum of the anti-Stokes light has two distinct features: one that arises from scattering through an off-resonant virtual level and one that arises from resonant scattering through the real level. This provides a method to measure the phase cross correlation between two optical fields of different color. The intensity of the anti-Stokes signal strongly depends on the degree of cross correlation. Depending on the detuning from Raman resonance in the CARS process, the anti-Stokes intensity can be either enhanced or suppressed with respect to the case of uncorrelated fields.1
The quantum theory-of Stokes generation by stimulated Raman scattering of a multimode laser is developed and analyzed. For large laser-mode spacing, the generated Stokes intensity is found to be independent of the number of laser modes for both high and low gains. The result applies to both free-running and mode-locked lasers and is in contrast to that in the Raman amplifier, in which gain is found to depend on the number of modes. The Stokes light is generated with mode amplitudes and phases in perfect correlation with those of the laser. Also, in steady state the instantaneous Stokes intensity is found to follow exactly the rapid fluctuations of the laser intensity.
A theoretical and experimental investigation was made of the amplification of a Stokes signal in a multimode pump field when the ratio of the spectral widths of the interacting fields was varied. In the pump intensity range I p < I cr ( I cr was a critical intensity) the gain increment was considerably less than the static value and it was governed entirely by the spectral distributions of the pump and Stokes signal. In the range I p > I cr the gain increment tended to the static value. An anomalous scatter of the Raman amplifier gain was observed experimentally for Δ ν s ≈Δ ν p ≫Δ ν l (Δ ν s ,Δ ν p , and Δ ν l were the line widths of the Stokes signal, pump, and spontaneous stimulated Raman scattering). A theory developed for the purpose indicated that the scatter was observed because the phase relationships between the interacting waves at the input into the medium varied from one measurement to another.
We address the problem of pumping Stokes radiation by broadband incoherent laser beams in contrast to aberrated beams. While for aberrated beams the transversal phase variations in any given plane of reference are constant in time, they will fluctuate in time for incoherent beams. As is well known for Raman scattering by broadband lasers, the frequency mode structure of the amplified Stokes beam will be modified by the pump laser, leading to an increase in temporal correlation between pump and Stokes. For collinear pumping by an incoherent pump this implies that the amplified Stokes beam will also be incoherent, even if seeded initially with a coherent beam. For transversal pumping geometries Stokes beam coherence will be affected by the reduced temporal correlation between the pump fields at different transversal locations. In the case of resonant scattering (linewidth much smaller than mode spacing), we show that the transversal Stokes coherence length is limited by the longitudinal coherence length of the pump. In addition, a reduction in gain occurs. We present analytical and numerical results which indicate corresponding limitations for intermediate scattering (linewidth comparable to mode spacing), which is the case of practical interest in gases.
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.