Scaled propagation invariant Bessel beams

Authors

  • F. Soto-Eguibar INAOE
  • I. Ramos-Prieto INAOE
  • D. Sánchez-de-la-Llave INAOE
  • U. Ruíz INAOE
  • J. A. Anaya-Contreras ESFM, IPN
  • A. Zúñiga-Segundo ESFM, IPN
  • H. M. Moya-Cessa INAOE

DOI:

https://doi.org/10.31349/RevMexFis.71.041301

Keywords:

Bessel; Gaussian

Abstract

We present a new family of Bessel solutions of the paraxial equation. Such solutions keep their form during propagation because of a quadratic phase factor that makes them scaled propagation invariant fields. When a Gaussian support is incorporated, the solution loses its invariant properties, although, over some volume, it closely resembles a scaled propagation invariant field. The Bessel beams we introduce have the particularity that they present a very strong focusing effect and do not necessarily require a Gaussian support.

References

J. Durnin, Exact solutions for nondiffracting beams. I. The scalar theory, J. Opt. Soc. Am. A 4 (1987) 651, https://doi.org/10.1364/JOSAA.4.000651

F. Gori, G. Guattari, C. Padovani, Bessel-Gauss beams, Optics Communications 64 (1987) 491, https://doi.org/https://doi.org/10.1016/0030-4018(87)90276-8

C. Caron, R. Potvliege, Bessel-modulated gaussian beams with quadratic radial dependence, Optics Communications 164 (1999) 83, https://doi.org/https://doi.org/10.1016/S0030-4018(99)00174-1

A. Belafhal, L. Dalil-Essakali, Collins formula and propagation of Bessel-modulated Gaussian light beams through an abcd optical system, Optics Communications 177 (2000) 181, https://doi.org/https://doi.org/10.1016/S0030-4018(00)00600-3

Y. Cai, X. Lu, Q. Lin, Hollow Gaussian beams and their propagation properties, Opt. Lett. 28 (2003) 1084, https://doi.org/10.1364/OL.28.001084

V. V. Kotlyar, R. V. Skidanov, S. N. Khonina, V. A. Soifer, Hypergeometric modes, Opt. Lett. 32 (2007) 742, https://doi.org/10.1364/OL.32.000742

E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, E. Santamato, Hypergeometric-Gaussian modes, Opt. Lett. 32 (2007) 3053, https://doi.org/10.1364/OL.32.003053

V. V. Kotlyar, A. A. Kovalev, Family of hypergeometric laser beams, J. Opt. Soc. Am. A 25 (2008) 262, https://doi.org/10.1364/JOSAA.25.000262

M. A. Bandres, J. C. Gutierrez-Vega, Circular beams, ´ Opt. Lett. 33 (2008) 177, https://doi.org/10.1364/OL.33.000177

D. Stoler, Operator methods in physical optics, J. Opt. Soc. Am. 71 (1981) 334, https://doi.org/10.1364/JOSA.71.000334

V. Arrizon, U. Ruiz, R. Carrada, L. A. González, Pixelated phase computer holograms for the accurate encoding of scalar complex fields, J. Opt. Soc. Am. A 24 (2007) 3500, https://doi.org/10.1364/JOSAA.24.003500

H. M. Moya-Cessa et al., Cauchy-Riemann beams, Phys. Rev. A 109 (2024) 043528, https://doi.org/10.1103/PhysRevA.109.043528

I. Ramos-Prieto, D. Sánchez-de-la-Llave, U. Ruíz, V. Arrizón, F. Soto-Eguibar, and H. M. Moya-Cessa, Cauchy-Riemann beams in GRIN media, Optik 309 (2024) 171864, https://doi.org/10.1016/j.ijleo.2024.171864

M. Abramowitz, I. A. Stegun, and R. H. Romer, Handbook of mathematical functions with formulas, graphs, and mathematical tables (American Association of Physics Teachers, 1988)

F. W. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Handbook of Mathematical Functions, (Cambridge University Press, 2010)

I. S. Gradshteyn, I. M. Ryzhik, Table of integrals, series, and products, (Academic press, 2014)

Downloads

Published

2025-07-01

How to Cite

[1]
F. Soto, “Scaled propagation invariant Bessel beams”, Rev. Mex. Fís., vol. 71, no. 4 Jul-Aug, pp. 041301 1–, Jul. 2025.