Far-field divergent properties of linearly polarized Laguerre-Gauss beams
线偏振拉盖尔-高斯光束的远场发散特性

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.