Two types of definitions for Rayleigh range

A comparison of the Rayleigh range between the two types of definitions (defined by the mean-squared beam width and the effective radius of curvature) is studied analytically and numerically, where the propagation of partially coherent beams both in free space and in atmospheric turbulence are considered. It is shown that the two types of the Rayleigh range definitions are consistent in free space. However, in turbulence the Rayleigh range defined by the mean-squared beam width is smaller than that defined by the effective radius of curvature. The main results obtained in this paper are illustrated by numerical calculation examples, where partially coherent Hermite–Gaussian (PCH–G) beams are considered.

► Two types of the Rayleigh range definitions (i.e., the Rayleigh range defined by the mean-squared beam width and by the effective radius of curvature) are consistent in free space.
► In turbulence the Rayleigh range defined by the mean-squared beam width is smaller than that defined by the effective radius of curvature.
► The analytical expression for the Rayleigh range defined by the mean-squared beam width of general partially coherent beams in turbulence is derived.