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

doi:10.1088/2040-8986/19/1/015603

Cited by 18 publications

(24 citation statements)

References 14 publications

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“…It is known that wavefronts of Durnin's photon beams have a shape of a generalized cone; see e.g. [50]. In our case, the tiling shifts in the z direction as we change the angle ϕ.…”

Section: Asymptotical Behavior For Large Values Of Rmentioning

confidence: 72%

Visualizing gravitational Bessel waves

et al. 2019

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We explicitly derive a vortex inspired solution for the metric perturbation within the linearized Einsteins general theory of relativity in arbitrary dimensions D ≥ 4. We focus on D = 4 where our solution is the gravitational analog of the well-known electromagnetic (or electron) Bessel vortex beams. Next we visualize the perturbed spacetime via tidal tendexes and frame-drag vortexes. We display and analyze mostly two-dimensional sections of the tendexes and the vortexes for different values of an angular momentum of the wave solution. Corresponding geodesic deviation equations are solved and the results are visualized. We show that the physically most important quadrupolelike case leads to a wave with rotating polarization. We discuss asymptotical features of the found solution. We provide also several 3D plots of tendex lines. One of them concerns a special cylindricallike case and we utilize the topological classification of singularities of the depicted line fields as an approach to characterize the radiation field.

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“…It is known that wavefronts of Durnin's photon beams have a shape of a generalized cone; see e.g. [50]. In our case, the tiling shifts in the z direction as we change the angle ϕ.…”

Section: Asymptotical Behavior For Large Values Of Rmentioning

confidence: 72%

Visualizing gravitational Bessel waves

et al. 2019

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“…In future work, we are going to study the image formation process by light rays and quantum particles in three dimensions such that their associated caustics be determined by the maxima of the intensity and the probability density respectively. In particular, it could be interesting to start with the Airy, non-diffracting and others general beams in three dimensions [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

Section: Discussionmentioning

confidence: 99%

Wavefronts, actions and caustics determined by the probability density of an Airy beam

Espíndola-Ramos

Silva-Ortigoza

Sosa-Sánchez

et al. 2018

J. Opt.

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The main contribution of the present work is to use the probability density of an Airy beam to identify its maxima with the family of caustics associated with the wavefronts determined by the level curves of a one-parameter family of solutions to the Hamilton–Jacobi equation with a given potential. To this end, we give a classical mechanics characterization of a solution of the one-dimensional Schrödinger equation in free space determined by a complete integral of the Hamilton–Jacobi and Laplace equations in free space. That is, with this type of solution, we associate a two-parameter family of wavefronts in the spacetime, which are the level curves of a one-parameter family of solutions to the Hamilton–Jacobi equation with a determined potential, and a one-parameter family of caustics. The general results are applied to an Airy beam to show that the maxima of its probability density provide a discrete set of: caustics, wavefronts and potentials. The results presented here are a natural generalization of those obtained by Berry and Balazs in 1979 for an Airy beam. Finally, we remark that, in a natural manner, each maxima of the probability density of an Airy beam determines a Hamiltonian system.

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“…Following [9], we consider an isotropic optical medium, which is characterized by a refraction index ( ) n r and raise the question: what are the conditions on the function, ( ) S r , so that…”

Section: Geometrical Analysismentioning

confidence: 99%

Parabolic non-diffracting beams: geometrical approach

Sosa-Sánchez

Silva-Ortigoza

Juárez-Reyes

et al. 2017

J. Opt.

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The aim of this work is to present a geometrical characterization of parabolic non-diffracting beams. To this end, we compute the corresponding angular spectrum of the separable non-diffracting parabolic beams in order to determine the one-parameter family of solutions of the eikonal equation associated with this type of beam. Using this information, we compute the corresponding wavefronts and caustic, and find that qualitatively the caustic corresponds to the maximum of the intensity pattern and the wavefronts are deformations of conical surfaces.

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Wavefronts and caustic associated with Durnin’s beams

Cited by 18 publications

References 14 publications

Visualizing gravitational Bessel waves

Visualizing gravitational Bessel waves

Wavefronts, actions and caustics determined by the probability density of an Airy beam

Parabolic non-diffracting beams: geometrical approach

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