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Asymptotic theory of irradiance fluctuations in a beam propagating in a random medium

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Abstract

We consider the irradiance fluctuations in a finite gaussian beam propagating in a random medium. We obtain a solution for the strong-scattering case (i.e., the characteristic diffraction length is large compared to the characteristic scattering length) as the product of plane-wave portion and a finite-beam correction. We obtain an analytic expression for the finite-beam segment, and make explicit calculations for a modified Kolmogorov spectrum. The plane-wave part is shown to depend on a single parameter. If the plane-wave solution for the variance of the irradiance fluctuations approaches a constant value, the normalized variance for the beam diverges at a rate proportional to z3, where z is the propagation distance. The unnormalized variance approaches zero at a rate proportional to 1/z3. We conjecture that the solution obtained is valid for all ratios of characteristic diffraction length to characteristic scattering length, in the limit z → ∞.

© 1975 Optical Society of America

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