The angular spread and directionality of general partially coherent beams in atmospheric turbulence

Abstract

Based on the extended Huygens–Fresnel principle and Rytov's approximation of the phase structure function, the analytical expressions for the beam width and angular spread of general partially coherent beams with Schell-model correlator in atmospheric turbulence are derived, and used to study the angular spread and directionality of general partially coherent beams. The relative angular spread, i.e., the ratio of the angular spread of a general partially coherent beam in turbulence to the angular spread of the same general partially coherent beam in free space, is introduced to study the sensitivity of general partially coherent beams to the effect of turbulence. It is shown that the angular spread of general partially coherent beams, including partially coherent Hermite–sin-Gaussian (H-SiG), Hermite–cos-Gaussian (H-CoG), Hermite–sinh-Gaussian (H-ShG), and Hermite–cosh-Gaussian (H-ChG) beams, with smaller spatial correlation length σ0, smaller waist width w0, and larger beam orders m, n, is less affected by turbulence than that of general partially coherent beams with larger σ0, w0, and smaller m, n. The larger the parameter Ω0 is, the less the angular spread of partially coherent H-SiG and H-CoG beams is affected by turbulence, whereas the angular spread of partially coherent H-ShG and H-ChG beams with smaller Ω0 is less affected by turbulence. There exist equivalent partially coherent and fully coherent H-SiG, H-CoG, H-ShG, and H-ChG beams, which have the same directionality as a fully coherent Gaussian laser beam. The results are illustrated by numerical examples and their validity is interpreted physically.