Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence

The closed-form expression for the mean-squared beam width of partially coherent Hermite-Gaussian (H-G) beams propagating through atmospheric turbulence is derived. The influence of turbulence on the spreading of partially coherent H-G beams is studied quantitatively by examining the mean-squared beam width. It is found that the smaller the coherence length σ0 of the source is, and the larger the beam order m and the wavelength λ are, the less partially coherent H-G beams are affected by the turbulence, although the beams with smaller σ0, larger m, and larger λ have greater spreading in free space. In addition, it is shown that two partially coherent H-G beams may generate the same angular spread and that there exist equivalent partially coherent H-G beams that may have the same directionality as a fully coherent Gaussian beam in free space and also in turbulence. The results are illustrated by examples, and a comparison with previous work is also made.