Wave dislocation reactions, for example, one dislocation splitting into three, are organized by dislocations of higher order. A reaction can be regarded as an unfolding of a higher-order dislocation, rather as singularities in catastrophe theory unfold into clusters of lower-order ones. The paper lists the forms of the first few higher-order wave dislocations. It shows how the reaction reported by Karman [Opt. Lett. 22, 1503 (1997)], in which an Airy dark ring surrounding a focus splits into three, followed by the annihilation of an inner fourth ring by the central ring, is part of the unfolding of a fourth-order dislocation.
© 1998 Optical Society of America
Original Manuscript: September 3, 1997
Revised Manuscript: December 15, 1997
Manuscript Accepted: December 23, 1997
Published: May 1, 1998
J. F. Nye, "Unfolding of higher-order wave dislocations," J. Opt. Soc. Am. A 15, 1132-1138 (1998)