一般光束等效曲率半径的传输方程

Propagation Equation of the Effective Radius of Curvature of General Beams

给出了一般光束等效曲率半径在湍流大气和自由空间中的传输方程,推导出等效曲率半径达到最小值时光束的传输距离公式,解析地讨论了等效曲率半径的特性,并用数值计算例加以说明。研究表明,在自由空间中,一般光束等效曲率半径的传输方程与理想高斯光束的相同,当传输距离足够远时一般光束的等效等相面可以看成球面。但是,在湍流大气中,当传输距离足够远时一般光束的等效曲率半径仍然与光束参数有关,等效曲率半径随湍流的增强而减小。

The propagation equation of the effective radius of curvature of general beams in atmospheric turbulence and free space is given,and the formula of the position where the effective radius of curvature reaches its minimum is also derived.The properties of the effective radius of curvature are studied analytically,and illustrated by numerical calculation examples.It is shown that the effective radius of curvature of general beams obeys the same free-space propagation equation as the wavefront curvature of an ideal Gaussian beam.In free space the wavefront of general beams can be regarded as a spherical surface when the propagation distance is long enough.However,in turbulence the effective radius of curvature of general beams depends on the beam parameters when the propagation distance is long enough,and the effective radius of curvature decreases when the strength of turbulence-increases.