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Optics Letters

Nonlinear Gaussian expansions of stochastic processes: super-Gaussian effects in coherent anti-Stokes Raman spectroscopy

Albert M. F. Lau, Roger L. Farrow

Published Apr 1, 1989• 7 citations
Publisher

Abstract

We propose a new approach to the analysis of stochastic processes (such as fluctuating laser fields) with super-Gaussian statistics: the expansion of stochastic processes in terms of first and higher powers of Gaussian components, which are used like a basis set. This approach is applied to treat the super-Gaussian correlation effects observed in coherent anti-Stokes Raman scattering experiments using frequency-doubled pump laser fields. Our results give much better agreement with experimental data than previous theories do.

DOI
10.1364/ol.14.000367

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We propose a new approach to the analysis of stochastic processes (such as fluctuating laser fields) with super-Gaussian statistics: the expansion of stochastic processes in terms of first and higher powers of Gaussian components, which are used like a basis set. This approach is applied to treat the super-Gaussian correlation effects observed in coherent anti-Stokes Raman scattering experiments using frequency-doubled pump laser fields. Our results give much better agreement with experimental data than previous theories do.
We propose a new approach to the analysis of stochastic processes (such as fluctuating laser fields) with non‐Gaussian statistics: the expansion of stochastic processes in terms of first and higher power of Gaussian components, which are used like a basis set. This approach is applied to treat the non‐Gaussian correlation effects observed in coherent anti‐Stokes Raman scattering experiments using frequency‐doubled pump‐laser fields. Our results give much better agreement with experimental data than previous theories.
The theory of coherent anti-Stokes Raman scattering (CARS) is extended to include the effect of pump fluctuations. The intensities and spectra of lines in resonant CARS are calculated to all orders in fields assuming a phase-diffusion model for waves at the two pump frequencies. The bandwidth of the two lasers enters in a much more complicated way than following a simple scaling of T1{T}_{1}T1​ or T2{T}_{2}T2​. Various resonances in CARS spectra due to dynamic splitting of the energy levels are discussed for a range of detunings, field intensities, and bandwidths. In contrast to the usual spectra in strong fields, the Rabi sidebands appear as dispersion-shaped structures. The laser linewidth is shown to change dramatically the CARS line shape. The case of no saturation is also treated, thus allowing for the inclusion of more general line shapes and fluctuations of the pump waves and the nonlinear susceptibility tensor ${\ensuremath{\chi}}^{(3)}$. Gaussian statistics of the pump field are shown to lead to enhancement factors in CARS intensity, similar to those appearing in the context of multiphoton absorption processes.
In the coherent anti-Stokes Raman scattering process, the spectrum of the generated optical phonon depends on the degree of temporal correlation between the pump laser field and the Stokes field. When the two fields are strongly correlated, such as when the Stokes field is generated with stimulated Raman scattering (SRS), the spectral shape of the optical phonon is found experimentally and theoretically to be the same as the gain-narrowed Raman line shape because the laser phase fluctuations cancel out totally, leaving only the collisional noise in the SRS process. When the two fields are uncorrelated, the shape of the optical-phonon spectrum is found to be the same as the Raman line shape without gain narrowing. When two fields are partially correlated, then the two spectral components appear together. We provide a method to measure the degree of correlation between two optical fields that have different central frequencies. The theory developed to interpret the experimental results is an extension of the quantum theory of SRS to include anti-Stokes scattering. We show that only in the high-gain limit can the quantum fluctuations be thought of as arising from a classical noise process.
The results of the investigation of Stokes energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump are presented. The pulse-energy distributions and their standard deviations were measured. The comparison of the experimental data with known ones for coherent pump shows the strong difference in the distribution shape and the standard deviation value. This difference is explained as a manifestation of the non-Gaussian (super-Gaussian) statistics in stimulated scattering with a broad-band pump. The results of numerical calculations for statistics of Stokes intensity are in a qualitative agreement with the experimental findings.
We investigate quantum phase properties of two-mode optical fields whose quasidistributions have Gaussian form. We show how to simplify the calculation of the joint phase distribution defined via radial integration of the quasidistribution related to s-ordering of the field operators. We find an analytical formula for the joint phase distribution when coherent components of both modes vanish. The general results are applied to analysis of quantum phase properties of the two-mode Stokes-anti-Stokes field generated by means of Raman scattering with a broad reservoir phonon system and strong coherent laser pumping.
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.