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Classification of phase singularities for complex scalar waves

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83948

Title: Classification of phase singularities for complex scalar waves
Authors: ADACHI, Jiro Browse this author
ISHIKAWA, Go-o Browse this author
Keywords: wave dislocation
equi-phase portrait
optical vortex
Helmholtz equation
Issue Date: 2006
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 798
Start Page: 1
End Page: 17
Abstract: Motivated by the importance and universal character of phase singularities which are clarified recently, we study the local structure of equi-phase loci near the dislocation locus of complex valued planar and spatial waves, from the viewpoint of singularity theory of differentiable mappings, initiated by H. Whitney and R. Thom. The classification of phase-singularities are reduced to the classification of planar curves by radial transformations due to the theory of A. du Plessis, T. Gaffney and L. Wilson. Then fold singularities are classified into hyperbolic and elliptic singularities. We show that the elliptic singularities are never realized by any Helmholtz waves, while the hyperbolic singularities are realized in fact. Moreover, the classification and realizability of Whitney’s cusp, as well as its bifurcation problem are considered in order to explain the three points bifurcation of phase singularities. In this paper, we treat the dislocation of linear waves mainly, developing the basic and universal method, the method of jets and transversality, which is applicable also to non-linear waves.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69606
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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