Higher-order extrema with topological indices greater than unity are discussed. Explicit constructions are given for their wave functions, and simple geometric rules are presented for analysis of their topological indices. Experimental means for verifying the theory with use of Gaussian laser beams are considered, unusual properties of optical vortices contructed from this new type of critical point are described, and applications to topologically based optical arithmetic are suggested.
© 2000 Optical Society of America
Original Manuscript: June 1, 1999
Revised Manuscript: October 26, 1999
Manuscript Accepted: October 13, 1999
Published: March 1, 2000
Isaac Freund and Ari Belenkiy, "Higher-order extrema in two-dimensional wave fields," J. Opt. Soc. Am. A 17, 434-446 (2000)