Irradiance Fluctuations and the Assumption of Gaussian Statistics for a Beam Propagating in a Random Medium

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Abstract
In a previous paper [1] we obtained an asymptotic expression for the irradiance fluctuations of a finite beam propagating in a random medium in the strong-scattering case (i.e. the characteristic diffraction length is large compared to the characteristic scattering length). The solution was given as the product of a plane wave portion and a finite beam correction. We show here that if the statistics of the fluctuations of the infinite and finite beams are assumed to be gaussian (in which case the fourth-order coherence function may be expressed in terms of second-order coherence functions), then the finite beam result obtained is in disagreement with our previous result. Consequently, we conclude that the statistics of a finite beam cannot be gaussian. However, assuming that the statistics of the infinite beam are gaussian leads to no contradiction. This result is an indication of the importance of finite beam size effects in irradiance fluctuation studies.

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