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

Abstract

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.

A Systematic Summary and Comparison of Scalar Diffraction Theories for Structured Light Beams

“…where a, b x , b y , and ρ are defined by Equation (25). 7) and utilizing the integral formulas [5] 2π…”

“…Substituting Equation (3) into Equation ( 17) and using the integral formulas given by Equations ( 31) and (32), we obtain the angular spectrum of the Laguerre-Gaussian beams as follows [5]:…”

“…Substituting Equation (4) into Equation ( 17), employing the integral formula given by Equation (31), and recalling the properties of the Dirac delta function [5]…”

“…Such light fields are usually called structured light beams, including the Hermite-Gaussian beams [1], the Laguerre-Gaussian beams [2], the Bessel beams [3], the Airy beams [4], and so on. Compared with conventional plane waves and fundamental Gaussian beams, structured light beams exhibit a variety of novel physical effects and phenomena, e.g., strong spatial inhomogeneity, phase singularity, diffraction-free propagation, transverse acceleration, and so on [5]. Owing to their fascinating properties and promising potential applications, structured light beams have become a research hotspot in optics and optoelectronics [6][7][8][9][10][11][12][13].…”