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Physical Review A

Generation of four-wave mixing and stimulated Raman signals in focused Gaussian beams

Hans Moosmüller, S. B. Anderson, C. Y. She

Published Dec 1, 1989• 6 citations
Publisher

Abstract

The signal generation in four-wave-mixing Raman spectroscopy and stimulated Raman spectroscopy is theoretically investigated for focused Gaussian beams. Signal strength as a function of interaction length and total signal generation are calculated for both types of coherent Raman spectroscopies. We further discuss the application of our theory to spatially inhomogeneous broadening, especially optical Stark broadening, induced by one of the laser beams. Intensity and phase contours of a Gaussian beam are also presented to enhance the understanding of intensity-dependent interactions.

DOI
10.1103/physreva.40.6977

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Kei Hagiwara, Atsushi Okamoto, Hiroyuki Kaneko +2 more

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Electronics and Communications in Japan (Part II Electronics)•Apr 1, 1997•0 citations
The signal generation in four-wave-mixing Raman spectroscopy and stimulated Raman spectroscopy is theoretically investigated for focused Gaussian beams. Signal strength as a function of interaction length and total signal generation are calculated for both types of coherent Raman spectroscopies. We further discuss the application of our theory to spatially inhomogeneous broadening, especially optical Stark broadening, induced by one of the laser beams. Intensity and phase contours of a Gaussian beam are also presented to enhance the understanding of intensity-dependent interactions.
We present a theoretical analysis of the spatial shape of two symmetric signals of degenerate four-wave mixing induced by Gaussian beams in a thin sample of two-level atoms. Our calculations take into account the full spatial and spectral dependences of the relevant nonlinear susceptibilities that govern the two processes. This reveals two interesting effects. The first one is that the total power of incident beams affects the transverse profile of the four-wave-mixing signals at the medium exit and their free propagation. The second one is the influence of the spectral characteristics of the medium on the longitudinal profile of both generated signals upon free propagation. We argue that the first effect can be seen as the saturation of the medium in regions of higher intensity, while the second can be understood as the result of a nonlinear contribution to the refractive index inside the atomic medium. These effects can be symmetric between the two signals, with asymmetries induced by different detunings from the resonance of the incident fields.
Four-wave mixing processes with double and triple resonances are discussed in detail. Explicit expressions for the resonant nonlinear susceptibilities of various cases are derived. It is shown that in some cases, four-wave mixing can yield a spectrum with reduced inhomogeneous broadening. Possible applications of multiresonant four-wave mixing as a spectroscopic technique are considered. They include high-resolution spectroscopy, deduction of transition matrix elements, study of transitions between excited states, measurement of longitudinal relaxation times, distinction between resonant Raman scattering and resonant fluorescence, etc. Selective polarization arrangement allows us to suppress the nonresonant background, separately measure the real and imaginary parts of the resonant nonlinear susceptibility, minimize the effects of absorption and laser intensity fluctuations, and greatly enhance the signal-to-noise ratio.
The effects of inhomogeneous broadening, spatial hole burning, and Gaussian beams are calculated for the four coefficients derived in previous papers in this series [Phys. Rev. A 31, 3112 (1985); 31, 3124 (1985)] on the quantum theory of multiwave mixing. These coefficients uniformly describe how one or two strong classical-field modes and one or two weak quantum-field modes interact in a two-level medium. The phenomena for which this theory is applicable includes resonance fluorescence, Rayleigh scattering, laser and/or optical bistability instabilities, and phase conjugation. The averaged formulas are illustrated by resonance-fluorescence spectra. We find the sidepeaks can be ``washed out'' and that asymmetries can occur.
The delayed or time-domain four-wave-mixing experiment is treated in the regime of intense near-resonant pulses. The interaction with the radiation during both pump and probe pulses is considered to all powers of the electric field amplitude. Analytical results are obtained for an effective four-level system. These include the dependence of the coherence amplitudes on the ratio of the pump-field intensities when there is a large vibrational discrepancy between ground and excited electronic states and a general solution for the unitary time development during the probe pulse. For the first time, delayed coherent anti-Stokes Raman scattering is detected from highly dilute (10-ppm) guest molecules. Illustrative examples are presented for the system of pentacene in benzoic acid at low temperature. Vibronic-free induction decay and the effect of field inhomogeneity across the beam profile are found to be essential for understanding the observed intensity and spectral distribution of the signal beam in the region of optimum pulse intensity.
With progress in phase conjugate optics, studies on forward four-wave mixing have been actively carried out. From the practical optical system design point of view, it is important to understand the angular dependence of phase conjugate intensity when pumping beams with limited spot size are used, especially with beam separation taken into consideration. In this paper, the angular dependence of phase conjugate intensity distribution is theoretically analyzed for the first time, in forward four-wave mixing when an optical Kerr medium is used. First, the phase conjugate intensity is calculated for a nonlinear medium thinner than the overlapping region of two pumping beams, where the intensity is relatively low. The results are used to calculate the output angle of the phase conjugate beam against the z-axis and the azimuth angle in the x-y plane. Then, a similar analysis is conducted for a medium sufficiently thick to cover the interaction region of two pumping beams. The differences between the above two cases are described and comparison with plane-wave pumping is made. Finally, the effects of spot size and curvature variation with Gaussian beam pumping on conjugate beam intensity are discussed for the case of a thick medium. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 2, 80(4): 67–75, 1997