Wavefronts and caustic associated with Durnin's beams

Omar De Jesús Cabrera-Rosas, Ernesto Espíndola-Ramos, Salvador Alejandro Juárez-Reyes, Israel Julián-Macías, Paula Ortega-Vidals, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, Citlalli Teresa Sosa-Sánchez

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

© 2016 IOP Publishing Ltd. The aim of the present work is to give a geometrical characterization of Durnins beams. That is, we compute the wavefronts and caustic associated with the nondiffracting solutions to the scalar wave equation introduced by Durnin. To this end, first we show that in an isotropic optical medium ψ(r, t) = ei[k0S(r)-wt] is an exact solution of the wave equation, if and only if, S is a solution of both the eikonal and Laplace equations, then from one and two-parameter families of this type of solution and the superposition principle we define new solutions of the wave equation, in particular we show that the ideal nondiffracting beams are one example of this type of construction in free space. Using this fact, the wavefronts and caustic associated with those beams are computed. We find that their caustic has only one branch, which is invariant under translations along the direction of evolution of the beam. Finally, the Bessel beam of order m is worked out explicitly and we find that it is characterized by wavefronts that are deformations of conical ones and the caustic is an infinite cylinder of radius proportional to m. In the case m = 0, the wavefronts are cones and the caustic degenerates into an infinite line.
Original languageAmerican English
JournalJournal of Optics (United Kingdom)
DOIs
StatePublished - 1 Jan 2017

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Caustics
Wavefronts
alkalies
Wave equations
wave equations
Laplace equation
eikonal equation
Cones
cones
scalars
radii

Cite this

Cabrera-Rosas, O. D. J., Espíndola-Ramos, E., Juárez-Reyes, S. A., Julián-Macías, I., Ortega-Vidals, P., Silva-Ortigoza, G., ... Sosa-Sánchez, C. T. (2017). Wavefronts and caustic associated with Durnin's beams. Journal of Optics (United Kingdom). https://doi.org/10.1088/2040-8986/19/1/015603
Cabrera-Rosas, Omar De Jesús ; Espíndola-Ramos, Ernesto ; Juárez-Reyes, Salvador Alejandro ; Julián-Macías, Israel ; Ortega-Vidals, Paula ; Silva-Ortigoza, Gilberto ; Silva-Ortigoza, Ramón ; Sosa-Sánchez, Citlalli Teresa. / Wavefronts and caustic associated with Durnin's beams. In: Journal of Optics (United Kingdom). 2017.
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Cabrera-Rosas, ODJ, Espíndola-Ramos, E, Juárez-Reyes, SA, Julián-Macías, I, Ortega-Vidals, P, Silva-Ortigoza, G, Silva-Ortigoza, R & Sosa-Sánchez, CT 2017, 'Wavefronts and caustic associated with Durnin's beams', Journal of Optics (United Kingdom). https://doi.org/10.1088/2040-8986/19/1/015603

Wavefronts and caustic associated with Durnin's beams. / Cabrera-Rosas, Omar De Jesús; Espíndola-Ramos, Ernesto; Juárez-Reyes, Salvador Alejandro; Julián-Macías, Israel; Ortega-Vidals, Paula; Silva-Ortigoza, Gilberto; Silva-Ortigoza, Ramón; Sosa-Sánchez, Citlalli Teresa.

In: Journal of Optics (United Kingdom), 01.01.2017.

Research output: Contribution to journalArticle

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T1 - Wavefronts and caustic associated with Durnin's beams

AU - Cabrera-Rosas, Omar De Jesús

AU - Espíndola-Ramos, Ernesto

AU - Juárez-Reyes, Salvador Alejandro

AU - Julián-Macías, Israel

AU - Ortega-Vidals, Paula

AU - Silva-Ortigoza, Gilberto

AU - Silva-Ortigoza, Ramón

AU - Sosa-Sánchez, Citlalli Teresa

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N2 - © 2016 IOP Publishing Ltd. The aim of the present work is to give a geometrical characterization of Durnins beams. That is, we compute the wavefronts and caustic associated with the nondiffracting solutions to the scalar wave equation introduced by Durnin. To this end, first we show that in an isotropic optical medium ψ(r, t) = ei[k0S(r)-wt] is an exact solution of the wave equation, if and only if, S is a solution of both the eikonal and Laplace equations, then from one and two-parameter families of this type of solution and the superposition principle we define new solutions of the wave equation, in particular we show that the ideal nondiffracting beams are one example of this type of construction in free space. Using this fact, the wavefronts and caustic associated with those beams are computed. We find that their caustic has only one branch, which is invariant under translations along the direction of evolution of the beam. Finally, the Bessel beam of order m is worked out explicitly and we find that it is characterized by wavefronts that are deformations of conical ones and the caustic is an infinite cylinder of radius proportional to m. In the case m = 0, the wavefronts are cones and the caustic degenerates into an infinite line.

AB - © 2016 IOP Publishing Ltd. The aim of the present work is to give a geometrical characterization of Durnins beams. That is, we compute the wavefronts and caustic associated with the nondiffracting solutions to the scalar wave equation introduced by Durnin. To this end, first we show that in an isotropic optical medium ψ(r, t) = ei[k0S(r)-wt] is an exact solution of the wave equation, if and only if, S is a solution of both the eikonal and Laplace equations, then from one and two-parameter families of this type of solution and the superposition principle we define new solutions of the wave equation, in particular we show that the ideal nondiffracting beams are one example of this type of construction in free space. Using this fact, the wavefronts and caustic associated with those beams are computed. We find that their caustic has only one branch, which is invariant under translations along the direction of evolution of the beam. Finally, the Bessel beam of order m is worked out explicitly and we find that it is characterized by wavefronts that are deformations of conical ones and the caustic is an infinite cylinder of radius proportional to m. In the case m = 0, the wavefronts are cones and the caustic degenerates into an infinite line.

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Cabrera-Rosas ODJ, Espíndola-Ramos E, Juárez-Reyes SA, Julián-Macías I, Ortega-Vidals P, Silva-Ortigoza G et al. Wavefronts and caustic associated with Durnin's beams. Journal of Optics (United Kingdom). 2017 Jan 1. https://doi.org/10.1088/2040-8986/19/1/015603