A comparative study on the vector description of typical structured light beams

Abstract Recent years have witnessed a surge of interest in studying structured light beams, which exhibit a series of interesting properties and have potential applications in many fields, especially in the field of optical trapping and manipulation. An accurate description of the structured light beams is the theoretical basis for such an application. As a special type of electromagnetic waves, the structured light beams need to be described using full vector methods. In this paper, we report a comparative study of the vector potential method and the vector angular spectrum representation for describing the structured light beams. The basic principles and formulas of these two full vector methods are presented. Explicit expressions for the electric and magnetic field components of the typical structured light beams, including the fundamental Gaussian beams, Hermite-Gaussian beams, Laguerre-Gaussian beams, Bessel beams, and Airy beams, are systematically derived. The results obtained from the two methods are compared and analyzed. Our results are very useful to the implementation of the structured light beams in various theoretical and numerical methods for scattering by particles.