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Journal of the Optical Society of America B

Analysis of Raman-enhanced nondegenerate four-wave mixing with factorized time correlator diagrams

Eric C. Booth, Britt G. Berger, Zachary C. Johnson, Thao M. Ta, Lindsay R. Weisel, Darin J. Ulness

Published Apr 27, 2006• 3 citations
Publisher

Abstract

The work of Fu et al. regarding temporal signal behavior in noisy light-induced, Raman-enhanced, nondegenerate four-wave mixing (I(2)RENFWM) is reassessed using factorized time correlation (FTC) analysis. Close correspondence is observed between the FTC predictions and the prior analysis. Strikingly, the observed experimental and theoretical behavior of the I(2)RENFWM signal is largely captured by a single FTC diagram, from which physical insight can be obtained.

DOI
10.1364/josab.23.000885

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The work of Fu et al. regarding temporal signal behavior in noisy light-induced, Raman-enhanced, nondegenerate four-wave mixing (I(2)RENFWM) is reassessed using factorized time correlation (FTC) analysis. Close correspondence is observed between the FTC predictions and the prior analysis. Strikingly, the observed experimental and theoretical behavior of the I(2)RENFWM signal is largely captured by a single FTC diagram, from which physical insight can be obtained.
The effects of field correlation on Raman-enhanced nondegenerate four-wave mixing (RENFWM) have been investigated by examining the RENFWM spectra as a function of time delay between two beams. We present a theory in which the underlying physics is emphasized. The field correlation has little influence on the RENFWM spectra when the laser has narrow bandwidth. In contrast, the ratio between the resonant and nonresonant RENFWM signal intensities increases as time delay is increased when the laser has broadband linewidth. Experiments with CS2{\mathrm{CS}}_{2}CS2​ as sample have been performed to demonstrate the field-correlation effects on the RENFWM spectra.
A nearly degenerate, four-wave mixing (ND4WM) setup with noisy light called I^(2)ND4WM(-) is investigated both experimentally and theoretically through factorized-time-correlation (FTC) diagram analysis. This third order nonlinear signal is of interest because the phenomenon of color-locking appears very directly in the measured signal. Color locking is a fundamental aspect of noisy-light spectroscopies that often plays a critical but subtle role in production of the signal. For I^(2)ND4WM(-), color-locking results in complete cancellation of the spectrally broad noise carried by the noisy light used to create it. When combined with FTC diagram analysis the qualitative features of the I^(2)ND4WM(-) can be understood. In addition to the striking noise cancellation, the qualitative features addressed in this work include the time profile, dynamic range, and polarization dependence of the signal. For comparison the spectrally broad I^(2)ND4WM(+) signal is presented.
We have employed phase-diffusion model to study the effects of laser field correlation on the Raman-enhanced nondegenerate four-wave mixing (RENFWM). The different roles of the field fluctuations have been pointed out. A time-delayed method has been proposed to suppress the thermal background. An enhancement of the ratio between the resonant and nonresonant RENFWM signal intensities was found as the time delay is increased when the laser has broadband linewidth. When the lasers have Gaussian line shape, we also present a second-order coherence function theory to elucidate the temporal asymmetry behavior of the RENFWM.
Coherent Raman scattering using broadband, incoherent (noisy) light (termed I(2)CRS{\mathrm{I}}^{(2)}\mathrm{CRS}I(2)CRS---the I for interferometric and the superscript 2 for twice acting noisy fields) is treated for a multiply resonant, multicomponent mixture of molecules. Both the resonant-resonant and resonant-nonresonant hyperpolarizability contributions to the signal intensity are included in this formalism. The emphasis is on the physical understanding of this spectroscopy. To this end, factorized time correlator (FTC) diagram analysis is used to characterize the I(2)CRS{\mathrm{I}}^{(2)}\mathrm{CRS}I(2)CRS signal. The FTC diagram technique also serves to organize the terms that arise through the stochastic averaging of the noise at the intensity level. In addition to the FTC diagram analysis, a spectral filter analogy is employed to provide further insight into the physics behind I(2)CRS.{\mathrm{I}}^{(2)}\mathrm{CRS}.I(2)CRS.