Beam quality of truncated laser beams with amplitude modulations and phase fluctuations in turbulence

The closed-form expressions for the Rayleigh range zR and the M2-factor of truncated laser beams with amplitude modulations (AMs) and phase fluctuations (PFs) in turbulence are derived, and the beam quality is studied by taking the zR and the M2-factor as the characteristic parameters of beam quality. The M2-factor of truncated laser beams with AMs and PFs is always larger than that of truncated Gaussian beams both in free space and in turbulence. However, in turbulence the beam quality of truncated laser beams with AMs and PFs may be better than that of truncated Gaussian beams if the zR is taken as the characteristic parameter of beam quality. For laser beams with AMs and PFs in turbulence, the beam quality expressed in terms of zR is consistent with that in terms of the M2-factor versus the phase fluctuation parameter α, but not versus the intensity modulation parameter σA. The beam quality of truncated laser beams with AMs and PFs is less sensitive to turbulence than that of truncated Gaussian beams. The beam quality of laser beams with smaller α and larger σA is less affected by turbulence than those with larger α and smaller σA.