Caustics, catastrophes, and symmetries in curved beams

Vaveliuk, Pablo; Lencina, Alberto; Rodrigo, José A.; Matos, Óscar Martínez

doi:10.1103/physreva.92.033850

Cited by 44 publications

(21 citation statements)

References 33 publications

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“…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. 38 The role played by the spectral phase power is to control the degree of caustic curvature. The even symmetry of the cubic phase is the generatrix of the cusp catastrophe structure.…”

Section: Resultsmentioning

confidence: 99%

Shaping symmetric Airy beam through binary amplitude modulation for ultralong needle focus

Fang

Ren

Gong

et al. 2015

Journal of Applied Physics

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Needle-like electromagnetic field has various advantages for the applications in high-resolution imaging, Raman spectroscopy, as well as long-distance optical transportation. The realization of such field often requires high numerical aperture (NA) objective lens and the transmission masks. We demonstrate an ultralong needle-like focus in the optical range produced with an ordinary lens. This is achieved by focusing a symmetric Airy beam (SAB) generated via binary spectral modulation with a digital micromirror device. Such amplitude modulation technique is able to shape traditional Airy beams, SABs, as well as the dynamic transition modes between the one-dimensional and two-dimensional (2D) symmetric Airy modes. The created 2D SAB was characterized through measurement of the propagating fields with one of the four main lobes blocked by an opaque mask. The 2D SAB was verified to exhibit self-healing property against propagation with the obstructed major lobe reconstructed after a certain distance. We further produced an elongated focal line by concentrating the SAB via lenses with different NAs and achieved an ultralong longitudinal needle focus. The produced long needle focus will be applied in optical, chemical, and biological sciences.

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Section: Resultsmentioning

confidence: 99%

Shaping symmetric Airy beam through binary amplitude modulation for ultralong needle focus

Fang

Ren

Gong

et al. 2015

Journal of Applied Physics

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“…Assume a two-dimensional (2D) curved beam propagating in free space in the z direction that is partially blocked by one obstacle placed along the transverse direction x. The starting point is the full phase of the beam angular spectrum of power n and symmetry q [14],…”

Section: A Geometric Approach From Catastrophe Theorymentioning

confidence: 99%

“…The more studied fold caustic beam is the * pablov@ciop.unlp.edu.ar AiB [1,2] while the Pearcey beam [3] and the symmetric Airy beam (SAB) [15][16][17] are examples of cusp-caustic beams. In fact, both caustic structures comprise an infinite number of beams with different curvatures depending on the value of the phase power that can be any real value [14]. Surely, the beams belonging to each caustic structure should behave in a different fashion facing identical setups of obstructions.…”

Section: Introductionmentioning

confidence: 99%

“…There is no explicit analysis of the beam behavior facing real obstacles in that work such that the predictions for this effect were indirectly induced from the analysis on the other properties of the Airy beam. There is, besides, another key matter related to the caustic structure of a curved beam that should affect its self-healing behavior: the symmetry of the spectral phase [14]. The odd symmetry gives rise to a fold-type caustic optical beam, while the even symmetry gives rise to a cusp-type one.…”

Section: Introductionmentioning

confidence: 99%

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Dual behavior of caustic optical beams facing obstacles

et al. 2017

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A full propagation analysis on both fold-type and cusp-type caustic optical beams under various setups of obstructions is theoretically and experimentally performed. It is demonstrated that the self-healing property of caustic optical beams that include the famous Airy beam is a quite relative property. In fact, fold-type and cusp-type beams cannot only behave as self-healing beams by blocking the main intensity peak, but also behave as self-breaking ones in a nonintuitive manner: by blocking a lateral side of the beam without touching the central intensity peak. The regeneration and rupture processes of caustic beams follow a nonlocal propagation dynamic unlike the other conventional beams. Moreover, deep differences between fold and cusp caustic beams are pointed out once facing certain obstructions. The cusp-caustic beam can be broken down by the obstacle placed in a dark zone outside the caustic region, while the fold-type one remains unaltered. This beam rupture confirms the key role of a hidden propagating field in the shadow region for cusp beams that coexist with the evanescent one. The obtained results cast down the established idea that the Airy beam is a robust self-healing beam since any caustic beam can behave in a dual manner depending on the obstruction location. These facts open up different perspectives for the applications in which the self-healing properties of the beam are relevant.

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“…Thus how to associate a desired propagating trajectory with an appropriate wave front remains a crucial problem. One strategy is to keep on finding other rare analytical solutions of the wave equation, while a more efficient way is based on the caustic method, which associates the desired trajectory with an optical caustic, the envelope of a family of light rays [24][25][26]. This method was first implemented in real space [27,28] and successfully realized arbitrary convex propagating trajectories for two-dimensional (2D) light fields, while the caustic method in Fourier space was also proposed subsequently [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Tailoring accelerating beams in phase space

et al. 2017

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This is the final published version of the article (version of record). It first appeared online via APS Physics at https://doi.org/10.1103/PhysRevA.95.023825 . Please refer to any applicable terms of use of the publisher. University of Bristol -Explore Bristol Research General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms PHYSICAL REVIEW A 95, 023825 (2017) Tailoring accelerating beams in phase space An appropriate wave-front design will enable light fields that propagate along arbitrary trajectories, thus forming accelerating beams in free space. Previous strategies for designing such accelerating beams rely mainly on caustic methods, which start from diffraction integrals and deal only with two-dimensional fields. Here we introduce an alternate perspective to construct accelerating beams in phase space by designing the corresponding Wigner distribution function (WDF). We find that such a WDF-based method is capable of providing both the initial field distribution and the angular spectrum in need by projecting the WDF into the real space and the Fourier space, respectively. Moreover, this approach applies to the construction of both two-and three-dimensional fields, greatly generalizing previous caustic methods. It may therefore open a new route for construction of highly tailored accelerating beams and facilitate applications ranging from particle manipulation and trapping to optical routing as well as material processing.

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Caustics, catastrophes, and symmetries in curved beams

Cited by 44 publications

References 33 publications

Shaping symmetric Airy beam through binary amplitude modulation for ultralong needle focus

Shaping symmetric Airy beam through binary amplitude modulation for ultralong needle focus

Dual behavior of caustic optical beams facing obstacles

Tailoring accelerating beams in phase space

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