Influence of the diffraction size of the transmitting aperture and of the turbulence spectrum on the intensity fluctuations of laser radiation

The Huygens–Fresnel principle is used in an investigation of the influence of the diffraction size of the transmitting aperture and internal turbulence scale on the variance of the intensity fluctuations of laser radiation traveling in a turbulent atmosphere. The asymptotic formulas for the relative variance are derived for weak and strong fluctuations in a collimated beam whose transmitting aperture has the Fresnel number satisfying the condition Ω ≥ 1; corresponding formulas are obtained also for a focused beam and a spherical wave. An analysis is made allowing for the deviation of the turbulence spectrum from the power law in the dissipation range. In the case of strong fluctuations the asymptotic behavior of the variance of a spatially confined beam differs fundamentally from the behavior in the case of unbounded (plane and spherical) waves if the coherence radius of the field is much less than the internal turbulence scale. In this case the relative variance reaches saturation at unity for plane and spherical waves, whereas for a confined beam the saturation level is higher and it is governed by internal turbulence scale as well as by the Fresnel number of the transmitting aperture.