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

Abstract

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 onf-parameter and mode number are numerically examined. The effects of thef-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.