Unfolding of higher-order wave dislocations

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.