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Journal of the Optical Society of America B

Optical phase conjugation with smooth pump profiles

Joseph W. Haus, C. M. Bowden, Chi C. Sung

Published Feb 1, 1987• 0 citations
OpenAlex

Abstract

Degenerate four-wave mixing (DFWM) is a common method used to generate a phase conjugate signal. Analytic results have been available for pumps that have a square profile, and their predictions have been in good agreement with experiments.1 Nevertheless, it is important to determine what effect inhomogeneities in the pump profile will have on the phase conjugate signal.

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Degenerate four-wave mixing (DFWM) is a common method used to generate a phase conjugate signal. Analytic results have been available for pumps that have a square profile, and their predictions have been in good agreement with experiments.1 Nevertheless, it is important to determine what effect inhomogeneities in the pump profile will have on the phase conjugate signal.
One more promising application of the four-wave mixing process is the correction of arbitrary phase aberrations in an optical beam. In such applications, the fidelity as well as the efficiency of the phase-conjugation process needs to be considered in practice. The process which has received the most extensive attention to date is degenerate four-wave mixing (DFWM). The nonlinear interaction in this case is known to result in a perfect phase-conjugate provided high-quality pump beams are available and competing effects such as local self-focusing (or defocusing) can be neglected.
Large signal analyses for degenerate four-wave mixing (DFWM) have been reported for sometime(1-3). It was nevertheless not obvious why, in specific examples(1,2). DFWM exhibits hysteresis and bistability characteristics, whereas in the case of ideal phase conjugation(3), there is no such instability. The objective of this paper is to show that hysteresis and bistability are caused by phase variations in the interaction. These phase variations are detrimental to phase conjugation and may Indeed up-set the basic characteristies of phase conjugation.
The nonlinear response of resonant saturable materials giving rise to degenerate four-wave mixing (DFWM) has been shown both experimentally and theoretically to provide the potential for very large efficiencies for phase conjugation and Doppler-free spectra for high resolution spectroscopy. The geometry for this interaction consists of two counter- propagating pumps (Ef and Ep) and a probe (Ep) intersecting the pumps at some angle θfp. The simultaneous action of one pump and the probe produces spatial hole burning resulting in a spatial modulation of the saturating absorption and dispersion which scatters the remaining pump to produce the signal.
Degenerate four-wave mixing (DFWM) spectroscopy is a potentially powerful technique for quantitative measurement of minor species in gas-phase media [1-3]. In this paper we compare the DFWM signal levels and lineshapes obtained using two different phase-matching geometries: the phase-conjugate geometry and the forward phase-matched geometry. DFWM signal levels are calculated by solving the time-dependent density matrix equations using direct numerical integration (DNI) [4, 5] for a two-level system interacting with three laser beams. This numerical analysis includes the effects of molecular motion, intermolecular collisions, and high laser intensities, all of which have been shown to affect the DFWM signal level.