Beam quality of radial Gaussian Schell-model array beams

Taking the Rayleigh range Z(R) and the M-2-factor as the characteristic parameters of beam quality, the beam quality of radial Gaussian Schell-model (GSM) array beams is studied. The analytical expressions for the Z(R) and the M-2-factor of radial GSM array beams are derived. It is shown that for the superposition of the cross-spectral density function Z(R) is longer and the M-2-factor is lower than that for the superposition of the intensity. For the two types of superposition, Z(R) increases and the M-2-factor decreases with increase in beam coherence parameter, and both Z(R) and the M-2-factor increase with increase in inverse radial fill-factor. For the superposition of the cross-spectral density function, Z(R) increases and the M-2-factor decreases with increase in beam number, while for the superposition of the intensity both the Z(R) and M-2-factor are independent of the beam number. (C) 2009 Elsevier Ltd. All rights reserved.