Caustics as Catastrophes

Kravtsov, Yu. A.; Orlov, Yu. I.

doi:10.1007/978-3-642-59887-6_3

Cited by 21 publications

(40 citation statements)

References 4 publications

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“…The use of classical ray theory to describe monochromatic, high-frequency solutions of the wave equation is described in various references [4,35,38]. The connection between rays and waves is standardly derived in the context of the Helmholtz equation…”

Section: Failure Of Eikonal Methods For Generic Dielectric Resonamentioning

confidence: 99%

“…Such an initial value solution can thus be extended until it encounters a point at which two or more distinct rays of the wavefront converge; at or nearby such a point will occur a focus or caustic at which the amplitude A will diverge and in the neighborhood of which the asymptotic representation becomes ill-defined. (A caustic is a curve to which all the rays of a wavefront are tangent; if the curve degenerates to a point it is a focus [38]). This causes only a local breakdown of the method and can be handled by a number of methods.…”

Section: Failure Of Eikonal Methods For Generic Dielectric Resonamentioning

confidence: 99%

“…The small parameter in the problem for attempting approximate solutions is the ratio of the wavelength to the perimeter λ/2πR = (kR) −1 . Eikonal methods [38] and Gaussian optical methods [62] both rely on the short wavelength limit to find approximate solutions. The Gaussian optical method can be used to find a subset of the solutions for generic ARCs, those associated with stable periodic ray orbits, as explained in detail in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Modes of wave-chaotic dielectric resonators

et al. 2005

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Dielectric optical micro-resonators and micro-lasers represent a realization of a wave-chaotic system, where the lack of symmetry in the resonator shape leads to non-integrable ray dynamics. Modes of such resonators display a rich spatial structure, and cannot be classified through mode indices which would require additional constants of motion in the ray dynamics. Understanding and controlling the emission properties of such resonators requires the investigation of the correspondence between classical phase space structures of the ray motion inside the resonator and resonant solutions of the wave equations. We first discuss the breakdown of the conventional eikonal approximation in the short wavelength limit, and motivate the use of phase-space ray tracing and phase space distributions. Next, we introduce an efficient numerical method to calculate the quasi-bound modes of dielectric resonators, which requires only two diagonalizations per N states, where N is approximately equal to the number of half-wavelengths along the perimeter. The relationship between classical phase space structures and modes is displayed via the Husimi projection technique. Observables related to the emission pattern of the resonator are calculated with high efficiency.

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Section: Failure Of Eikonal Methods For Generic Dielectric Resonamentioning

confidence: 99%

Section: Failure Of Eikonal Methods For Generic Dielectric Resonamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modes of wave-chaotic dielectric resonators

et al. 2005

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“…They are as familiar as rainbows, bright structure in a cup of coffee illuminated by slant sunlight, and many others [1][2][3]. Optical caustics can be tackled from two complementary aspects: geometric and ondulatory.…”

Section: Introductionmentioning

confidence: 99%

“…In the geometric approach, caustics are surfaces (in three-dimensional space) and curves (in two-dimensional space) where light rays are focused; i.e., they are concerned with envelopes of families of rays. In the ondulatory approach, caustics are regions where an electromagnetic field changes from an oscillatory behavior in the lit region, due to a strong interference effect, to an exponential decay in the shadow region, due to an evanescent field [1][2][3]. The stable caustics in physics present an isomorphic relationship to the elementary topological structures of catastrophe theory, being classified in the pioneering works of Whitney [4], Arnold [5], and Thom [6].…”

Section: Introductionmentioning

confidence: 99%

Caustics, catastrophes, and symmetries in curved beams

et al. 2015

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In this paper, a meaningful classification of optical caustic beams in two dimensions is presented. It is demonstrated that the phase symmetry of the beam's angular spectrum governs the optical catastrophe, which describes the wave properties of ray singularities, for cusp (symmetric phase) and fold (antisymmetric phase) caustics. In contrast to the established idea, the caustic classification arises from the phase symmetry rather than from the phase power, thus breaking the commonly accepted concept that fold and cusp caustics are related to the Airy and Pearcey functions, respectively. Nevertheless, the role played by the spectral phase power is to control the degree of caustic curvature. These findings provide straightforward engineering of caustic beams by addressing the spectral phase into a spatial light modulator or glass plate.

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Efficient Generation of Customized Caustics: Nondiffracting Deltoid and Pentagram Beams

Chen,

Gong,

Liu

et al. 2023

Annalen der Physik

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This study puts forward a powerful new strategy that allows highly efficient generation of the shaping transverse nondiffracting caustics that concentrate around the expected curve. First, under the condition of stationary phase approximation, as the typical example of caustic beams, the analytical formula of nondiffracting deltoid and pentagram caustics is theoretically derived. Based on the obtained analytical formula, the desired caustics of deltoid and pentagram are numerically simulated. Hence, their optical shape and the propagation characteristics of nondiffracting caustics can be investigated. Then, based on the given generating mechanism, the corresponding experimental system to experimentally explore the nondiffracting deltoid and pentagram caustics with good self-healing properties is constructed. Compared with the previous generating methods, the proposed method has a high light energy utilization.

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Caustics as Catastrophes

Cited by 21 publications

References 4 publications

Modes of wave-chaotic dielectric resonators

Modes of wave-chaotic dielectric resonators

Caustics, catastrophes, and symmetries in curved beams

Efficient Generation of Customized Caustics: Nondiffracting Deltoid and Pentagram Beams

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