Analytical paraxial and nonparaxial propagation expressions for vectorial elegant Laguerre-Gaussian (eLG) beam together with its even and odd modes are introduced by use of the vectorial Rayleigh-Sommerfeld formulas and the relations between eLG and elegant Hermite-Gaussian (eHG) modes. The propagation features of vectorial eLG beams are studied and analyzed comparatively in the paraxial and nonparaxial regimes with vivid illustration. It is shown that the propagation behavior of nonparaxial vectorial eLG beams is notably different from that of paraxial cases.
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