Optical catastrophes of the swallowtail and butterfly beams

Zannotti, Alessandro; Diebel, Falko; Boguslawski, Martin; Denz, Cornélia

doi:10.1088/1367-2630/aa6ecd

Cited by 52 publications

(37 citation statements)

References 47 publications

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“…This similarity is additionally manifested in the distribution of Fourier components, since they are located on a parabola for both, the Pearcey and Sw (x, y, a 3 ) beam [13,18]:…”

Section: Dynamics Of a Swallowtail Beammentioning

confidence: 92%

“…Thus, for the optical swallowtail catastrophe three generic swallowtail beams arise as orthogonal cross-sections through the control parameter space, and correspondingly more for the butterfly beam Bu(a) = C 6 (a) that maps characteristics of the butterfly catastrophe. This approach is thoroughly presented in [18].…”

Section: The Propagation Of Optical Catastrophesmentioning

confidence: 99%

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Dynamics of the optical swallowtail catastrophe

Zannotti

Diebel

Denz

2017

Optica

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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.

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“…This similarity is additionally manifested in the distribution of Fourier components, since they are located on a parabola for both, the Pearcey and Sw (x, y, a 3 ) beam [13,18]:…”

Section: Dynamics Of a Swallowtail Beammentioning

confidence: 92%

Section: The Propagation Of Optical Catastrophesmentioning

confidence: 99%

Dynamics of the optical swallowtail catastrophe

Zannotti

Diebel

Denz

2017

Optica

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“…The implication was based on the analogy between the timedependent Schrödinger equation and the paraxial wave equation. A great variety of beams, nonparaxial as well as paraxial, nondiffracting and diffracting, and following a variety of trfajectories, have since been discovered theoretically and created in the laboratory [3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…Following the pioneering study [4] of the Pearcey beam, corresponding to the cusp catastrophe with codimension 2, a more general class of paraxial exact waves is presented; some are curved and some are not. For the codimension 3 swallowtail, whose different sections have been studied as the initial sections of optical beams [8], an exact paraxial propagating wave is presented; it is a distorted version of the canonical form.…”

Section: Introductionmentioning

confidence: 99%

Stable and unstable Airy-related caustics and beams

Berry

2017

J. Opt.

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Optical beams with an underlying caustic structure are stable under perturbation if the caustics belong to the catastrophe-theory classification; otherwise they are unstable. The original Airy beam in two spatial dimensions, with its curved caustic, is stable in this sense. But the separable Airy-product beam in three-dimensions is unstable: under separability-breaking perturbation, it unfolds into the hyperbolic umbilic diffraction catastrophe, which is stable. By including initial phase factors, a variety of new exact solutions of the paraxial wave equation can be generated, corresponding to Pearcey and higher-catastrophe beams with stable caustics, and with the associated diffraction catastrophes appearing in their canonical forms or as deformations of these.

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“…The case K = 5 corresponds to the so-called Wigwam diffraction catastrophe [24] and we obtain the following identities…”

Section: Introductionmentioning

confidence: 84%

Generation of Some Catastrophes in Optics by Binary Screens

Belafhal¹,

Hricha²,

Halba³

2019

OALib

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In this paper, the artificial generation of elementary catastrophe optics having odd codimensions K = 1, 3 and 5 such as the Fold, the Swallowtail and the Wigwam diffraction caustics is investigated theoretically. It is shown that the integral catastrophes with odd polynomials phase functions can be reduced to the well-known Airy-Hardy cosine integrals. In this connection, the caustic functions of the Fold, Swallowtail and Wigwam caustic beams are expressed in closed-form in terms of Airy-Hardy cosine functions. An optical method based on the Fourier transform similar to that described by Lohmann et al. [Optics Comm. 109 (1994) 361-367] is proposed for the generation of the Fold, Swallowtail and Wigwam caustic beams. The displaying of the catastrophe patterns with K = 1, 3 and 5 is optically implemented in the Fourier transform device by using simple binary screens with tailored polynomials transmission.

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Optical catastrophes of the swallowtail and butterfly beams

Cited by 52 publications

References 47 publications

Dynamics of the optical swallowtail catastrophe

Dynamics of the optical swallowtail catastrophe

Stable and unstable Airy-related caustics and beams

Generation of Some Catastrophes in Optics by Binary Screens

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