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Zbl 1149.35389
Nye, J.F.
Dislocation lines in the hyperbolic umbilic diffraction catastrophe. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 462, No. 2072, 2299-2313 (2006). ISSN 1364-5021; ISSN 1471-2946/e

Summary: 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.

MSC 2000:: *35L67 Shocks, etc.

Keywords: diffraction; diffraction catastrophes; wave dislocations; singularity optics; optical vortices

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