Propagation of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams through paraxial optical systems in turbulent atmosphere

Based on the extended Huygens-Fresnel diffraction integral, the expressions for the average intensity and the effective size of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams propagating through a paraxial ABCD optical system are obtained in the turbulent atmosphere. The influences of the source coherence and atmospheric turbulence on the propagation of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams in the turbulent atmosphere are investigated in detail. It is found that the beam profile will eventually evolve into a Gaussian-like distribution through turbulence in contrast to ring-shaped far-field pattern in free space. The effective size of Laguerre-Gaussian and Bessel-Gaussian Schell-model beams with lower source coherence is less affected by turbulence. The parameter β and index n of the sources have some effects on intensity distribution and beam spreading through atmospheric turbulence.