A comparative study of standard and elegant Hermite–Gaussian beams propagating through turbulent atmosphere

Abstract

Based on the extended Huygens–Fresnel principle and the definition of the second-order moments of the Wigner distribution function (WDF), the analytical expressions for the root-mean-square (rms) beam width and far-field divergence angle, curvature radius and M 2-factor of standard Hermite–Gaussian (SHG) and elegant Hermite–Gaussian (EHG) beams passing through turbulent atmosphere are derived and compared. It is shown that in turbulent atmosphere the far-field divergence angle of SHG and EHG beams is equal under the same conditions, but the rms beam width, curvature radius and the M 2-factor of SHG and EHG beams are different except for beam orders m = 0 and m = 1. The relative rms beam width, relative curvature radius and relative M 2-factor of SHG beams are less than those of EHG beams. Therefore, the conclusion that SHG beams are less influenced by turbulence than EHG beams can be drawn if we examine one of the above three relative beam parameters.