Explicit analytical expressions for the electromagnetic field components of typical structured light beams

Abstract

As typical structured light beams, Laguerre-Gaussian beams, Bessel beams, and Airy beams have attracted great attention for their fascinating features and wide potential applications. Explicit expressions for the electromagnetic field components of these beams obtained from a vector angular spectrum analysis are of particular importance to study a variety of problems involving the propagation, transmission, and reflection of laser beam, as well as light-matter interactions. In the present work, we first briefly recall the scalar expressions of typical structured light beams, including the Laguerre–Gaussian beams, Bessel beams, and Airy beams. Then we present the formulae of vector angular spectrum representation under different conditions. Finally, we derive in detail the analytical expressions for the electromagnetic field components of these structured light beams and provide some important integral formulae. Additionally, distributions of the electromagnetic fields, as well as the phase, Poynting vector and energy density are displayed and analyzed for these typical structured light beams.