线偏振拉盖尔·高斯光束的远场发散特性

Far-field divergent properties of linearly polarized Laguerre-Gauss beams

利用稳相法和矢量结构理论,导出了线偏振拉盖尔-高斯光束的矢量结构项TE项和TM项在远场的解析表达式.进而利用TE项和TM项的远场能流分布,给出了TE项和TM项的功率占总功率比例的度量式,同时还给出了线偏振拉盖尔-高斯光束、TE项和TM项三者远场发散角的解析式以及三者远场发散角间的关系式.所得到的公式不仅适用于傍轴情形,而且还适用于非傍轴情形.通过数值计算,分析了TE项和TM项在远场的功率占总功率的比例与参数.f和模数间的依赖关系;还分析了拉盖尔-高斯光束、TE项和TM项的远场发散角随参数f、模数和线偏振角的变化关系.这一研究从矢量结构本性揭示了线偏振拉盖尔-高斯光束的远场发散特性,丰富了对其传输特性的认识.

Based on the method of stationary phase and the theorem of the vectorial structure,the analytical expressions for the vectrorial terms,namely the TE and TM terms,of a linearly polarized Laguerre-Gauss beam are derived in the far-field.According to the far-field energy flux distributions of the TE and TM terms,the ratios of the powers of the TE and TM terms to the power of the Laguerre-Gauss beam are given.The analytical formulae of the far-field divergence angles of the Laguerre-Gauss beam and its TE and TM terms are presented,respectively.A relation among the far-field divergence angles of the TE term,the TM term,and the Laguerre-Gauss beam is also derived.The formulae obtained are applicable not only to the paraxial case,but also to the non-paraxial case.The dependences of the ratios of the powers of the TE and TM terms to the whole power on f-parameter and mode number are numerically examined.The effects of the f-parameter,the mode number,and the linearly polarized angle on the far-field divergence angle of the Laguerre-Gauss beam and its TE and TM terms are also analyzed.This research reveals the far-field divergent properties of the linearly polarized Laguerre-Gauss beam from the vectorial structure,and enriches the recognition of the propagation characteristics of the linearly polarized Laguerre-Gauss beam.