%0 Journal Article
%A Nye, J.F
%T Dislocation lines in the hyperbolic umbilic diffraction catastrophe
%D 2006
%R 10.1098/rspa.2006.1683
%J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
%P 2299-2313
%V 462
%N 2072
%X The three-dimensional pattern of the hyperbolic umbilic diffraction catastrophe is computed from an integral representation. A detailed description is given of the geometrical arrangement of the wave dislocation lines (optical vortices) on which the diffraction pattern is based. From a crossed grid of nodal lines in the focal plane, two bundles of dislocation lines spring out symmetrically into the regions of 4-wave interference. Each dislocation line then follows a chain of curved segments which approximate successive steps along lattice vectors in the space group Fmmm. The result is a bundle of helices of non-circular cross-section that gradually straighten out until, far from the focal plane, they become the dislocations of the Pearcey diffraction pattern for the cusp catastrophe. A new phenomenon is the multiple puncturing of the caustic surface by a series of helical dislocations.
%U http://rspa.royalsocietypublishing.org/content/royprsa/462/2072/2299.full.pdf