Abstract
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.
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