Effects of inner scale on beam wander of electromagnetic cosine-Gaussian Schell-model beams through atmospheric turbulence

Based on the extended Huygens-Fresnel principle and the Andrews beam wander theory, the beam wander properties of electromagnetic cosine-Gaussian Schell-model (ECGSM) beams propagating in atmospheric turbulence are investigated. Beam wander is considered as a large-scale turbulent eddy effect, which can theoretically be processed using a filtering function related to the beam width, but small-scale turbulent eddies play an important role in the beam spreading. To this end, the influence of inner scale on ECGSM beam wander is examined in detail both theoretically and numerically by using modified atmospheric spectrum. The simplified integral formulas of the root-mean-square (rms) beam wander and the relative beam wander for ECGSM beams in turbulence have been derived. Our results reveal that in a strong turbulence, the rms beam wander increases obviously with increasing inner scale and decreasing parameter n, and the relative beam wander can increase by 47 -104% as the inner scale increases from 1 to 20 mm. The relative beam wander is sensitive to the parameter n and has two evolution forms with propagation distance in turbulence. ECGSM beams with n not less than 5 have strong beam wander suppression ability and are significantly stronger than the corresponding electromagnetic Gaussian Schell-model (EGSM) beams. These findings may be used to effectively control the beam wander of ECGSM beams in lidar and free space optical communication.