Based on the generalized Raleigh–Sommerfeld diffraction integrals, analytical nonparaxial propagation formulas for the elements of the cross-spectral density matrix of a vector partially coherent dark hollow beam (DHB) in free space are derived. The effect of spatial coherence and beam waist sizes on the statistical properties of a nonparaxial vector DHB is studied numerically. It is found that one can modulate the statistical properties of a nonparaxial vector DHB by varying its initial spatial coherence, which will be useful in some applications where nonparaxial beams are commonly encountered.
© 2013 Optical Society of America
Original Manuscript: January 31, 2013
Revised Manuscript: May 4, 2013
Manuscript Accepted: May 15, 2013
Published: June 17, 2013
Yangsheng Yuan, Shengcai Du, Yiming Dong, Fei Wang, Chengliang Zhao, and Yangjian Cai, "Nonparaxial propagation properties of a vector partially coherent dark hollow beam," J. Opt. Soc. Am. A 30, 1358-1372 (2013)