Coherent and incoherent combinations of radial array elliptical Gaussian beams beyond paraxial approximation

Starting from the Rayleigh-Sommerfeld diffraction integral, analytical expressions for the free-space propagation of radial array nonparaxial elliptical Gaussian beams in coherent and incoherent combinations are derived, and some special cases including the far-field distributions and paraxial expressions are given. It is shown that the intensity distribution of the resulting beam depends on the f-parameter, radial array radius, beam number, propagation distance and combination scheme. The far-field maximum intensity of the resulting beam with N beamlets in coherent and incoherent combinations is N2- and N-times of that of the single beamlet, respectively.