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Propagation Properties of Hermite-Gaussian Beams Through the Turbulent Atmosphere

Based on the general Huygens-Fresnel principle,the propagation equation of three-dimensional intensity of HermiteGaussian(H-G) beams through the turbulent atmosphere is derived.The propagation properties of H-G beams through the turbulent atmosphere are studied.It is shown that a H-G beam retains its beam characters when it propagates in free space;but a H-G beam in turbulence undergoes three stages of evolution,and at last it turns into Gaussian-like profile in the far field.Furthermore,the process of the three stages of H-G beams propagating in turbulence can be accelerated with the increase of turbulence.The turbulence results in a beam spreading and decrease of the maximum intensity.However,H-G beams with higher order numbers m and n are less affected by the turbulence than those with lower m and n.