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Journal of the Optical Society of America B

Intensity cross-correlation functions in stimulated Raman scattering of colored chaotic light

Marek Trippenbach, Cao Long Van

Published Jun 1, 1986• 7 citations
Publisher

Abstract

The cross-correlation functions of a Stokes wave and the laser field of an arbitrary bandwidth in the process of stimulated Raman scattering were studied. The laser light was described as a stationary Gaussian stochastic process. A normalized second-order intensity cross-correlation function has been obtained both in transient and in steady-state limits. It exhibits an asymmetry with respect to zero, which is due to the buildup of Raman gain. We propose the functional method to be used in calculating the higher-order correlations.

DOI
10.1364/josab.3.000879

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The cross-correlation functions of a Stokes wave and the laser field of an arbitrary bandwidth in the process of stimulated Raman scattering were studied. The laser light was described as a stationary Gaussian stochastic process. A normalized second-order intensity cross-correlation function has been obtained both in transient and in steady-state limits. It exhibits an asymmetry with respect to zero, which is due to the buildup of Raman gain. We propose the functional method to be used in calculating the higher-order correlations.
The quantum theory of forward Stokes generation by means of stimulated Raman scattering is extended to the case of a colored (finite-bandwidth) chaotic pump, which has both amplitude and phase fluctuations. In both transient and steady-state limits the mean Stokes intensity is found to be enhanced over that resulting from a coherent pump. In the limit that the chaotic-pump bandwidth becomes large, the mean Stokes intensity becomes identical with that resulting from a coherent pump of the same total power.
A theory is presented for forward- and backward-stimulated Raman scattering of colored chaotic light in dispersive media. Both amplification of a coherent Stokes seed and spontaneous generation are treated. It is shown that group-velocity dispersion reduces the gain for the average Stokes intensity, while the intensity fluctuations in the pump enhance it. For a given bandwidth, chaotic light is scattered more efficiently than coherent light when its average intensity exceeds the critical intensity for overcoming the decorrelating effects of group-velocity dispersion on the pump and Stokes waves. The figures presented demonstrate the asymmetry in the intensity of forward and backward Raman scattering of nonmonochromatic light.
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
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
A three-dimensional quantum theory of stimulated Raman scattering is presented which takes into account a general transverse shape of the pump laser. The transverse spatial autocorrelation function and the intensity of the Stokes pulse are derived analytically, by use of the Maxwell-Bloch equations in low-signal-gain conditions and introduction of a many-spatial-modes approximation. We find that the spatial and temporal coherence are coupled. The transverse coherence depends on the pump-laser shape, and the coherence area increases with increasing gain. Time scales for the buildup of stimulated intensity and correlations for the various transverse parts of the Stokes pulse are obtained.