2017/05/01 by Alessandro Zannotti, Falko Diebel, Cornelia Denz
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Catastrophe theory #Caustic (mathematics) #Classical mechanics #Cusp (singularity) #Engineering #Geometry #Laser-Matter Interactions and Applications #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Orbital Angular Momentum in Optics #Parameter space #Physics #Quantum mechanics #State (computer science) #Statistical physics #physics.optics
paper · pdf · doi:10.1364/optica.4.001157
published as Optica 4, 1157-1162 (2017)
arxiv created 2017/05/01 · openalex publication_date 2017/09/21 · arxiv updated 2017/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Perturbing the external control parameters of nonlinear systems leads to dramatic changes of its bifurcations. A branch of singular theory, the catastrophe theory, analyses the generating function that depends on state and control parameters. It predicts the formation of bifurcations as geometrically stable structures and categorizes them hierarchically. We evaluate the catastrophe diffraction integral with respect to two-dimensional cross-sections through the control parameter space and thus transfer these bifurcations to optics, where they manifest as caustics in transverse light fields. For all optical catastrophes that depend on a single state parameter, we analytically derive a universal expression for the propagation of all corresponding caustic beams. We reveal that the dynamics of the resulting caustics can be expressed by higher-order optical catastrophes. We show analytically and experimentally that particular swallowtail beams dynamically transform to higher-order butterfly caustics, whereas other swallowtail beams decay to lower-order cusp catastrophes.