Nonparaxial Hankel vortex beams of the first and second types
V.V. Kotlyar, A.A. Kovalev, V.A. Soifer

 

Image Processing Systems Institute, Russian Academy of Sciences,

Samara State Aerospace University

Full text of article: Russian language.

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Abstract:
We consider new solutions of the nonparaxial Helmholtz equation in the cylindrical coordinates, which are treated as nonparaxial scalar vortex Hankel beams of the 1st, 2nd and 3rd types. The beams can be obtained from each other by differentiation. Higher-order types of Hankel beams show lower divergence than the lower-order types. The lowest- (zero-) order Hankel beam of the first type represents a spherical wave.

Keywords:
nonparaxial propagation, Hankel beam, optical vortex, spherical wave, beam divergence.

Citation:
Kotlyar VV, Kovalev AA, Soifer VA. Nonparaxial Hankel vortex beams of the first and second types. Computer Optics 2015; 39(3): 299-304. DOI: 10.18287/0134-2452-2015-39-3-299-304.

References:

  1. Born M, Wolf E. Principles of Optics 6 ed. New York: Pergamon; 1986.
  2. Durnin J, Miceli JJ, Eberly JH. Difraction-free beams. Physical Review Letters 1987; 58: 1499-501.
  3. Gutierrez-Vega JC, Iturbe-Castillo MD, Chavez-Cerda S. Alternative formulation for invariant optical fields: Mathieu beams. Optics Letters 2000; 25(20): 1493-5.
  4. Bandres MA, Gutierrez-Vega JC, Chavez-Cedra S. Parabolic nondiffracting optical wave fields. Optics Letters 2004; 29(1): 44-6.
  5. Kotlyar VV, Kovalev AA, Soifer VA. Hankel-Bessel laser beams. Journal of the Optical Society of America A 2012; 29(5): 741-7.
  6. Kotlyar VV, Kovalev AA, Soifer VA. Asymmetric Bessel modes. Optics Letters 2014; 39(8): 2395-8.
  7. Cerjan A, Cerjan C. Orbital angular momentum of Laguerre-Gaussian beams beyond the paraxial approximation. Journal of the Optical Society of America A 2011; 28(11): 2253-60.
  8. Allen L, Beijersergen MW, Spreeuw RJC, Woerdman JP. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Physical Review A 1992; 45: 8185-9.
  9. Volke-Sepulveda K, Garces-Chavez V, Chavez-Cedra S, Arlt J, Dholakia K. Orbital angular momentum of a high-order Bessel light beam. Journal of Optics B: Quantum and Semiclassical Optics 2002; 4: S82-9.
  10. Prudnikov AP, Brychkov YuA, Marichev OI. Integrals and Series, Vol. 2, Special Functions. New York: Gordon & Breach Sci. Publ.; 1990.
  11. Guo CS, Liu X, He JL, Wang HT. Optimal annulus structures of optical vortices. Optics Express 2004; 12: 4625-34.
  12. Kotlyar VV, Kovalev AA, Soifer VA, Tuvey CS, Davis JA. Sidelobe contrast reduction for optical vortex beams using a helical axicon. Optics Letters 2007; 32: 921-3.
  13. Guo J, Wei Z, Liu Y, Huang A. Analysis of optical vortices with suppressed sidelobes using modified Bessel-like function and traepzoid annulus modulation structures. Journal of the Optical Society of America A 2015; 32(2): 195-203.
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