title: Analytical vectorial structure of controllable dark-hollow beams in the far field.
abstract: Based on the vector angular spectrum representation of electromagnetic beams and the method of stationary phase, the analytical vectorial structure of the controllable dark-hollow beam in the far field is derived. Analytical expressions of the energy flux for the TE term, the TM term, and the controllable dark-hollow beam in the far field are presented. The normalized energy flux distributions of the TE term, the TM term, and the controllable dark-hollow beam in the far field are illustrated and analyzed with numerical examples, and the effects of the different parameters on the normalized energy flux distributions are discussed in detail.
authors: School of Sciences, Zhejiang Forestry University, Lin'an, Zhejiang Province, China. zhouguoquan178@sohu.com
authors: Guoquan
authors: G
authors: Zhou