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Optical and Quantum Electronics

Large signal analysis of phase variations and bistability in degenerate four-wave mixing

Kazuhito Tajima, Hsiung Hsu

Published Mar 1, 1985• 6 citations
Publisher
DOI
10.1007/bf00620785

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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.

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A large-signal theory of noncollinear degenerate four-wave mixing (DFWM) is presented, taking into account the pump depletion and the full nonlinear polarization density appropriate for the noncollinear geometry. Phases of all of the interacting fields, as well as the amplitudes, are obtained as functions of the spatial coordinate. Owing to the completeness of the set of analytic solutions, considerable physical insights into the physics of DFWM are obtained. The DFWM exhibits a variety of rich behaviors, including hysteresis and bistability, multistability, and multiple isolated branches. The authors show that all of these behaviors can be explained in a unified way, that is, in terms of mode hopping characteristics.>

IEEE Journal of Quantum Electronics•Sep 1, 1988•0 citations
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.
A large-signal theory of noncollinear degenerate four-wave mixing (DFWM) is presented, taking into account the pump depletion and the full nonlinear polarization density appropriate for the noncollinear geometry. Phases of all of the interacting fields, as well as the amplitudes, are obtained as functions of the spatial coordinate. Owing to the completeness of the set of analytic solutions, considerable physical insights into the physics of DFWM are obtained. The DFWM exhibits a variety of rich behaviors, including hysteresis and bistability, multistability, and multiple isolated branches. The authors show that all of these behaviors can be explained in a unified way, that is, in terms of mode hopping characteristics.>