Abstract

Catastrophe science [1] is a branch of bifurcation theory in the study of dynamical systems; and it is also a special case of more general singularity physics. Bifurcation theory studies and classifies phenomena characterized by sudden shifts in dynamical behaviour arising from small changes in external control parameters, analysing how the qualitative nature of solutions depends on these control parameters. In singular optics, these dramatic changes manifest as geometrically stable caustics, which, as natural phenomena, are associated with the arcs close to rainbows, or may occur as high-intensity networks on the floor of shallow waters. Similar to their formation behind refractive index lenses with imperfections, the formation of corresponding structures has been observed for numerous kinds of designed lenses with significant importance in advanced optical instrumentation, astrophysics and surface analytics.

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