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Journal of the Optical Society of America A

Quantum theory of optical bistability with a spatially varying field mode in the good cavity limit (A)

M. Dagenais, Elisa Surkis, Wayne F. Sharfin, Herbert G. Winful

Published Jan 1, 1985• 0 citations
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Acta Physica Sinica•Jul 1, 1989•0 citations
A straightforward but general extension of the quantum theory of optical bistability is made to include spatial variations of the field mode in the good cavity limit. The analysis proceeds by dividing the field mode into small sections which are each microscopically large in terms of the atomic number to allow truncation of the generalized Fokker-Planck equation but which are macroscopically small to justify the assumption of constant field amplitude. In a linearized approximation, analytic expressions are obtained for the ratio of incoherent to coherent intensity and for the intensity correlation function of the transmitted field for the two particular examples of a Gaussian-mode field in a ring cavity and a plane-wave field in a standing-wave cavity. In the weak field limit the results of the plane-wave ring cavity are recovered independent of the form of the spatial dependence of the cavity mode. However, more generally a nonuniform distribution tends to suppress certain quantum features such as photon antibunching.
Squeezed state generation for a system of two-level atoms interacting with the field of a high-finesse cavity has been extensively discussed both experimentally and theoretically in recent years. Most theories describing these systems take the cavity field as a plane traveling wave for simplicity. With this assumption it is quite difficult to make quantitative comparisons between theory and recent experiments. However, by employing the formalism developed in Ref. 1, we are able to treat rather general spatial variations of the intracavity field subject to the constraint of the good-cavity limit of optical bistability. Squeezed state generation for the three particular examples of a plane-wave ring interferometer, a Gaussian-mode ring cavity, and a plane-wave field in a standing-wave interferometer are considered to illustrate the formalism. Somewhat surprisingly, in regimes for which the plane-wave theory predicts 50-70% squeezing (cooperatively C ~102–103), the standing-wave structure produces only modest reductions in the squeezing (a few percent), while the radial variations of the field reduce the squeezing by ~10%.
A single-mode dynamic equation is obtained from the Maxwell equation with the slowly-varying amplitude approximation, and the boundary conditions of the cavity. Here the mean-field limit and the good-quality cavity case have been used. This equation is useful in describing the dynamic behavior of intrinsic optical bistable systems and/or lasers with injected signals for any kinds of materials, including two-level atoms. Furthermore, according to the linear stability analysis, a generalized instability criterion is derived.