Optical Bistability, Chaos in the Coherent Two-Photon Processes
In this paper recent work1–4 on intracavity coherent two-photon processes is reviewed and some new results are presented. Various instabilities due to the cooperative interaction between the atoms as reflected in the outp field are described. This study is moti-vated by the recent work 5–7 on the instabilities in single-photon processes. We solve the coupled Maxwell-Bloch equations for coherent two-photon processes8 with boundary conditions appropriate to a ring cavity using Ikeda5 et al.’s method and obtain a two-dimensional map characterizing the output field. The mean field behavior and the resulting critical exponents are discussed. Several different routes to chaos are shown to be possible. We also comment on the oscillator models of two-photon instabilities.
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