Geometrical characterization of nondiffracting beams: geometric optical current and geometric vorticity for Bessel beams

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

doi:10.1088/2040-8986/ab0266

Cited by 3 publications

(3 citation statements)

References 37 publications

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“…First, integration along θ r is performed by recalling the properties of Dirac delta function given by Eqs. (7) and (8). Then, integration along φ r is done by utilizing the following integral formula 2π 0 cos ϕ sin ϕ e −ilϕ e iρ cos(ϕ−φ ) dφ…”

Section: Vector Wave Analysis Of the Bessel Beams Upon Reflectionmentioning

confidence: 99%

“…the so-called nondiffracting beams, has attracted much attention for its interesting properties and potential applications. [1][2][3][4][5][6][7][8][9] The best known example of such beams is the Bessel beams, which are the exact solutions of the Helmholtz wave equation in circular cylindrical coordinates and described by Bessel function of the first kind. [10][11][12][13][14][15][16][17] The intensity distributions of these beams exhibit circular symmetry and consist of a series of concentric rings.…”

Section: Introductionmentioning

confidence: 99%

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Local dynamical characteristics of Bessel beams upon reflection near the Brewster angle*

Cui¹,

Guo²,

Hui³

et al. 2021

Chinese Phys. B

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We analytically and numerically study the local dynamical characteristics of the Bessel beams reflected from an air—glass interface near the Brewster angle. A Taylor series expansion based on the angular spectrum component is applied to correct the reflection coefficients near the Brewster angle. Using a hybrid angular spectrum representation and vector potential method, the explicit expressions for the electric and magnetic field components of the reflected Bessel beams are derived analytically under paraxial approximation. The local energy, momentum, spin, and orbital angular momentum of the Bessel beams upon reflection near the Brewster angle are examined numerically by utilizing a canonical approach. Numerical simulation results show that the properties of these dynamical quantities for the Bessel beams near Brewster angle incidence change abruptly, and are significantly affected by their topological charge, half-cone angle, and polarization state. The present study has its importance in understanding the dynamical aspects of optical beams with vortex structure and diffraction-free nature during the reflection process.

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Section: Vector Wave Analysis Of the Bessel Beams Upon Reflectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Local dynamical characteristics of Bessel beams upon reflection near the Brewster angle*

Cui¹,

Guo²,

Hui³

et al. 2021

Chinese Phys. B

View full text Add to dashboard Cite

show abstract

“…In a series of papers [29,30,31,32,33], we describe the process to obtain the geometrical description of a wavefunction of the form…”

Section: The Geometrical Description Of a Wavefunctionmentioning

confidence: 99%

Classical Characterization of quantum waves: Comparison between the caustic and the zeros of the Madelung-Bohm potential

Espíndola-Ramos,

Silva-Ortigoza,

Sosa-Sánchez

et al. 2020

Preprint

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From a geometric perspective, the caustic is the most classical description of a wavefunction since its evolution is governed by the Hamilton-Jacobi equation. On the other hand, according to the Madelung-de Broglie-Bohm equations, the most classical description of a solution to the Schrödinger equation is given by the zeros of the Madelung-Bohm potential. In this work, we compare these descriptions and, by analyzing how the rays are organized over the caustic, we find that the wavefunctions with fold caustic are the most classical beams because the zeros of the Madelung-Bohm potential coincide with the caustic. For another type of beams, the Madelung-Bohm potential is in general distinct to zero over the caustic. We have verified these results for the one-dimensional Airy and Pearcey beams, which accordingly to the catastrophe theory, their caustics are stable. Finally, we remark that for certain cases, the zeros of the Madelung-Bohm potential are linked with the superoscillation phenomenon.

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Classical characterization of quantum waves: comparison between the caustic and the zeros of the Madelung–Bohm potential

et al. 2021

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From a geometric perspective, the caustic is the most classical description of a wave function since its evolution is governed by the Hamilton–Jacobi equation. On the other hand, according to the Madelung–de Broglie–Bohm equations, the most classical description of a solution to the Schrödinger equation is given by the zeros of the Madelung–Bohm potential. In this work, we compare these descriptions, and, by analyzing how the rays are organized over the caustic, we find that the wave functions with fold caustic are the most classical beams because the zeros of the Madelung–Bohm potential coincide with the caustic. For another type of beam, the Madelung–Bohm potential is in general distinct to zero over the caustic. We have verified these results for the one-dimensional Airy and Pearcey beams, which, according to the catastrophe theory, have stable caustics. Similarly, we introduce the optical Madelung–Bohm potential, and we show that if the optical beam has a caustic of the fold type, then its zeros coincide with the caustic. We have verified this fact for the Bessel beams of nonzero order. Finally, we remark that for certain cases, the zeros of the Madelung–Bohm potential are linked with the superoscillation phenomenon.

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Geometrical characterization of nondiffracting beams: geometric optical current and geometric vorticity for Bessel beams

Cited by 3 publications

References 37 publications

Local dynamical characteristics of Bessel beams upon reflection near the Brewster angle*

Local dynamical characteristics of Bessel beams upon reflection near the Brewster angle*

Classical Characterization of quantum waves: Comparison between the caustic and the zeros of the Madelung-Bohm potential

Classical characterization of quantum waves: comparison between the caustic and the zeros of the Madelung–Bohm potential

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