The theory of a parametric amplifier in a cavity is given for both the degenerate and the nondegenerate modes of operation. Previous work on the degenerate case is extended to include the effects of a coherent input and to derive the degrees of coherence and photodetection statistics of the output. Analogous calculations are performed for the nondegenerate parametric amplifier, and particular attention is given to the effects of correlations between the light beams formed from the two frequency components. These are contrasted with the analogous effects for the parametric media in free space often used in experimental studies.
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Collett et al. (1987) studied this question.
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