Propagation and far-field beam quality of M × N Hermite–Gaussian beams propagating through atmospheric turbulence

Abstract

The analytical propagation equation of M×N Hermite–Gaussian (H–G) beams, which are combined incoherently and propagate through atmospheric turbulence, is derived, which enables us to study their propagation properties and far-field beam quality. The propagation of M×N Gaussian beams through atmospheric turbulence and M×N H–G beams in free space are treated as special cases of our general result. The power in the bucket (PIB), β-parameter and Strehl ratio are chosen as the parameters characterizing the beam quality in the far field. The dependence of PIB, β-parameter and Strehl ratio of M×N H–G beams through atmospheric turbulence on the refraction index structure constant C n ², beam numbers M, N, mode indices m, n and separate distances xd , yd is illustrated numerically and interpreted physically. It is found that M×N H–G beams are less sensitive to the effects of turbulence than M×N Gaussian beams.