Concise and explicit expressions for typical spatial-structured light beams beyond the paraxial approximation.

Structured light beams with distinct spatial inhomogeneity of amplitude, phase, and polarization have garnered tremendous attention in recent years. A better understanding of the vectorial structure of such beams is helpful to reveal their important and interesting features for further applications. In this paper, explicit analytical expressions for the electric field components of typical spatial-structured light beams, including fundamental Gaussian beams, Hermite-Gaussian beams, Laguerre-Gaussian beams, Bessel/Bessel-Gaussian beams, and Airy beams, beyond the paraxial approximation are derived on the basis of the vectorial Rayleigh-Sommerfeld diffraction integrals. Compared with the existing expressions in the literature, the expressions given in this paper are very concise. Using the derived analytical expressions, distributions of the electric field components of these typical structured light beams are displayed and analyzed.