Axial intensity distribution of truncated Bessel–Gauss beams in a turbulent atmosphere

By means of the extended Huygens–Fresnel integral formula in the paraxial approximation and based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical expression for Bessel–Gauss beams propagating in a turbulent atmosphere truncated by an aperture has been derived. The result is more convenient for studying the axial intensity distribution properties of Bessel–Gauss beams with different topological charges in a turbulent atmosphere than the usual way by using diffraction integral directly. Utilizing the analytical expression, the axial intensity distribution of such kind of beam in a turbulent atmosphere is investigated numerically in detail. Results show that the intensity distribution on the axis changes with the variation of the beam topological charge m, the wavelength and beam waist width of the initial beam and the turbulent strength.