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.
© 2009 Optical Society of America
Lasers and Laser Optics
Original Manuscript: March 11, 2009
Revised Manuscript: May 15, 2009
Manuscript Accepted: May 29, 2009
Published: June 22, 2009
Guoquan Zhou, "Analytical vectorial structure of controllable dark-hollow beams in the far field," J. Opt. Soc. Am. A 26, 1654-1660 (2009)