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.
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