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Zbl 1137.58015
Nye, J.F.
Dislocation lines in the swallowtail diffraction catastrophe. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 463, No. 2078, 343-355 (2007). ISSN 1364-5021; ISSN 1471-2946/e

Summary: The three-dimensional distribution of amplitude and phase represented by the swallowtail catastrophe diffraction integral is based on a network of null lines for amplitude (wave dislocations or optical vortices), where the phase is singular. In the tail region there is four-wave interference, which results in an approximately repeating pattern of amplitude based on the monoclinic space group $C2/m$ and also an approximately repeating pattern of wave dislocations based on the black-white monoclinic space group $C2/m^{\prime}$. Helical dislocations spring from the plane of symmetry and gradually straighten out to be parallel to the two riblines of the caustic; eventually they become the straight dislocations of the Pearcey pattern for the cusp catastrophe. In the front region, where there are zero or two points of stationary phase, each dark Airy fringe surface associated with the fold surface condenses into a single dislocation in the plane of symmetry.

MSC 2000:: *58K35 Catastrophe theory
78A45 Diffraction, scattering (optics)

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

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