Propagation of nonparaxial Bessel-Gaussian beams in free space
非傍轴贝塞尔-高斯光束在自由空间的传输

Stating from the Rayleigh-Sommerfeld diffraction integral, the closed-form propagation expression for nonparaxial Bessel-Gaussian beams of any order in free space was derived. The propagation equations of nonparaxial Bessel and Gaussian beams were deduced as special case of our general result. Physical analysis and numerical calculations show that,if the transversal scale of Gaussian and Bessel parts are comparable with or less than the wavelength,the nonparaxial approach should be used.