Semiclassical derivations of the fluctuations of light beams have relied on limiting procedures in which the average number, 〈<i>N</i>〉, 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, <i>K</i><sub>α-1</sub> , 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, <i>N</i>, of single-photon eigenstates with finite 〈<i>N</i>〉. The analysis also provides the <i>P</i> representation for <i>K</i>-distributed noise. Generalizations of <i>K</i> 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.
© 1988 Optical Society of America
Edward B. Rockower, "Quantum derivation of K-distributed noise for finite 〈N〉," J. Opt. Soc. Am. A 5, 730-734 (1988)