Beam spreading of truncated Gaussian beams in Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle and the hard-edge aperture function expanded as the sum of finite-term complex Gaussian function, analytical expression for average intensity of truncated Gaussian beam in Kolmogorov turbulence is derived, and some limiting cases are discussed. The influences of many factors, such as Fresnel number, wavelength, truncation parameter and structure constant on beam spreading are studied with the help of the average intensity formula. We found that the peak value of average intensity decreases and the beam spot spreads with the decrease of Fresnel number. The change of peak intensity against Fresnel number is slower with large aperture than that with small aperture. When Fresnel number is not small enough the influence of turbulence on intensity profiles is so small that can be neglected if structure constant is small.