Quantum Statistics of Multiple-Mode, Superposed Coherent and Chaotic Radiation

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Abstract
This paper is concerned with the determination of the quantum statistics of the photoelectric detection, and the E‐field detection of multiple‐mode superposed chaotic and coherent radiation. The Glauber P‐representation is utilized extensively, and results are obtained by a fully quantum‐mechanical treatment. The generating function, the mean, and the variance of the photocount statistics are derived for illumination times of arbitrary duration and for modes of arbitrary statistical interdependence. For short illumination times, the complete photocount distribution is obtained. The distribution has the same form as that for a single mode of superposed chaotic and coherent radiation. The multiple‐mode distribution, however, is nonstationary. The difference between experimental determinations of the mean and variance which utilize periodic sampling and those which utilize random sampling is derived. A method for determining the P‐representation for modulated fields is described, and the detection statistics are derived. The statistics of the E field are found to be Gaussian, and it is found that for multiple‐mode classical statistics and quantum statistics differ.