Dependence of the probability density function of laser radiation power on the scintillation index and the size of a receiver aperture

Abstract

Power scintillations of a Gaussian laser beam propagated through a 7 km long horizontal atmospheric path for a wide range of turbulence strengths and different sizes of the receiver aperture were studied experimentally. The probability density function (PDF) and its properties were analyzed for a wide range of scintillation conditions. It was shown that the PDF can be described by the fractional exponential distribution in the strong scintillation regime (scintillation index of power measured on aperture σ PIB 2 > 1 ) for apertures with diameter d < a, where a is the size of the isoplanatic region, and by the gamma distribution in the weak scintillation regime ( σ PIB 2 < 1 ), as well as by the lognormal distribution for σ PIB 2 ≪ 1 . More than one distribution can be considered as a good approximation for experimental data for some ranges of d/a and σ PIB 2 , but the transition from one distribution to another as the best approximation occurs at certain characteristic values of these parameters. In the strong scintillation regime, the aperture averaging effect resulted in the transition from the fractional exponential distribution to the fractional gamma (FG) distribution when the aperture diameter is about the size of the isoplanatic region (d/a∼1). The FG distribution better approximates the experimental PDF because it accounts for the fact that the probability of zero power values becomes zero due to the averaging effect of the aperture. The fractional gamma distribution is the best approximation of the PDF for a finite aperture when σ PIB 2 > σ PIB,crit 2 = [ 0.7 − 0.8 ] , while the gamma distribution is the best approximation for σ PIB 2 < σ PIB,crit 2 .