Stokes surfaces of diffraction catastrophes with codimension three
Stokes surfaces of diffraction catastrophes with codimension three
The Stokes set, where exponentially small complex (i.e. evanescent) rays appear and disappear, is the locus of wavefield positions where stationary points of a diffraction integral have equal phase. In three dimensions, it is a surface. Stokes surfaces are calculated and displayed for the diffraction patterns decorating the swallowtail, elliptic and hyperbolic umbilic singularities. The surfaces are smooth apart from cusped edges where they meet the cusp lines of the real bifurcations set (caustic), and finite-angled creases at the complex whiskers of the singularity.
Stokes phenomenon, Stokes Surface, Diffraction Catastrophe, Catastrophe theory, complex rays, Bifurcation Sets, Stokes Set
Berry, M.V.
ec39b1ad-7f54-4abf-9fcf-e5a3d1c2ab84
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
1990
Berry, M.V.
ec39b1ad-7f54-4abf-9fcf-e5a3d1c2ab84
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Berry, M.V. and Howls, C.J.
(1990)
Stokes surfaces of diffraction catastrophes with codimension three.
Nonlinearity, 3 (2), [281].
(doi:10.1088/0951-7715/3/2/003).
Abstract
The Stokes set, where exponentially small complex (i.e. evanescent) rays appear and disappear, is the locus of wavefield positions where stationary points of a diffraction integral have equal phase. In three dimensions, it is a surface. Stokes surfaces are calculated and displayed for the diffraction patterns decorating the swallowtail, elliptic and hyperbolic umbilic singularities. The surfaces are smooth apart from cusped edges where they meet the cusp lines of the real bifurcations set (caustic), and finite-angled creases at the complex whiskers of the singularity.
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Published date: 1990
Keywords:
Stokes phenomenon, Stokes Surface, Diffraction Catastrophe, Catastrophe theory, complex rays, Bifurcation Sets, Stokes Set
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Local EPrints ID: 496794
URI: http://eprints.soton.ac.uk/id/eprint/496794
ISSN: 0951-7715
PURE UUID: a6e50cd4-645f-4ea3-915f-cec06758b7bd
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Date deposited: 08 Jan 2025 07:07
Last modified: 10 Jan 2025 02:39
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Author:
M.V. Berry
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