Semiclassical derivations of the fluctuations of light beams have relied on limiting procedures in which the average number, 〈N〉, of scattering elements, photons, or superposed wave packets approaches infinity. We show that the fluctuations of thermal light having a Bose–Einstein photon distribution and of light with an amplitude distribution based on the modified Bessel functions, Kα−1, which has been found useful in describing light scattered from or through turbulent media, may be derived with a quantum-mechanical analysis as the superposition of a random number, N, of single-photon eigenstates with finite 〈N〉. The analysis also provides the P representation for K-distributed noise. Generalizations of K noise are proposed. The factor-of-2 increase in the photon-number second factorial moment related to photon clumping in the Hanbury Brown–Twiss effect for thermal (Gaussian) fields is shown to arise generally in these random superposition models, even for non-Gaussian fields.
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