线偏振拉盖尔-高斯光束的远场发散特性

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.

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

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.