从瑞利-索末菲衍射积分出发,推导出任意阶非傍轴贝塞尔-高斯光束在自由空间传输的解析表达式.非傍轴贝塞尔光束和非傍轴高斯光束等的传输方程都可以作为本文一般结果的特例而得出.物理分析和数值计算表明,当高斯和贝塞尔部分的横向尺度与波长相比拟或小于波长时,应当用非傍轴方法处理.

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.