Angular spread and directionality of the Hermite-Gaussian array beam propagating through atmospheric turbulence

Using the integral transform technique, the analytical expressions for the mean-squared beam width and the angular spread of the Hermite-Gaussian (H-G) array beam in turbulence are derived for the case of both coherent and incoherent combinations. It is shown that the angular spread of the H-G array beam for the coherent combination may be more or less affected by turbulence than that for the incoherent combination (or a single H-G beam) depending on the beam parameters. For the coherent combination, there exists the oscillatory behavior of the angular spread, and the influence of turbulence on the angular spread is not monotonic versus the beam parameters. In addition, for the coherent combination case, the angular spread of the H-G array beam is less affected by turbulence than that of the Gaussian array beam. On the other hand, it is found that under a certain condition, the H-G array beam may have the same directionality as a single Gaussian beam both in free space and in turbulence if the angular spread is chosen as the characteristic parameter of the beam directionality. The main results are explained physically.