Far-field properties and beam quality of vectorial Hermite-Laguerre-Gaussian beams beyond the paraxial approximation

The far-field properties and beam quality of vectorial nonparaxial Hermite-Laguerre-Gaussian (HLG) beams are studied in detail, where, instead of the second-order-moments-based M-2 factor, the extended power in the bucket (PIB) and beta parameter are used to characterize the beam quality in the far field and the intensity in the formulae is replaced by the z component of the time-averaged Poynting vector (S-z). It is found that the (S-z) PIB and beta parameter of vectorial nonparaxial HLG beams depend on the mode indices n, m, alpha parameter and waist-width-to-wavelength ratio w(0)/lambda and the PIB and beta parameter are additionally dependent on the bucket's size taken. (c) 2006 Elsevier Ltd. All rights reserved.