Propagation properties of nonparaxial radial array Gaussian laser beams

Analytical expressions for the propagation of nonparaxial radial array Gaussian laser beams in coherent and incoherent combinations are derived and used to study their propagation properties in free space, where the effect of array beam parameters on the intensity distribution of the resulting beam is stressed. It is shown that the ratio of array radius to waist width is a key parameter. The intensity distribution of the resulting beam in both coherent and incoherent combinations remain unchanged under the condition that the ratio of array radius to waist width is kept fixed, while the intensity distribution and the axial intensity maximum in the far field of the resulting beam depend on the combination scheme.