Structurally stable three-dimensional and two-dimensional laser half pearcey beams
A.A. Kovalev
, V.V. Kotlyar, S.G. Zaskanov

Full text of article: Russian language.

Abstract:
We obtain a new solution of the paraxial Helmholtz equation that describes a family of three-dimensional and two-dimensional structurally stable half-Pearcey beams (HP-beams). HP-beams generalize Pearcey beams obtained in Opt. Express, 20, 18955 (2012), since these Pearcey beams can be considered as the sum of two first-order HP-beams. Three-dimensional HP-beams have angular spectrum of plane waves, which is non-zero at a half of parabola. For functions of HP-beams complex amplitudes, the orthogonality properties have been revealed. For two-dimensional HP-beam acceleration and deceleration of trajectory has been shown for areas before and beyond the focal plane respectively.

Key words:
paraxial laser beam, structurally stable laser beam, Pearcey beam, accelerating beam.

References:

  1. Durnin, J. Exact solutions for nondiffracting beams. I. The scalar theory // Journal of the Optical Society of America A. – 1987. – V. 4(4). – P. 651-654.
  2. Kotlyar, V.V. Diffraction-free asymmetric elegant Bessel beams with fractional orbital angular momentum / V.V. Kotlyar, A.A. Kovalev, V.A. Soifer // Computer Optics. – 2014. – V. 38(1). – P. 4-10.
  3. Kotlyar, V.V. Asymmetric Bessel modes / V.V. Kotlyar, A.A. Kovalev, V.A. Soifer // Optics Letters. – 2014. – V. 39(8). – P. 2395-2398.
  4. Gutierrez-Vega, J.C. Experimental demonstration of optical Mathieu beams / J.C. Gutiérrez-Vega, MD Iturbe-Cas­tillo, G.A. Ram?rez, E. Tepich?n, R.M. Rodr?guez-Dagnino, S. Chávez-Cerda, G.H.C. New // Optics Communications. – 2001. – V. 195(1). – P. 35-40.
  5. Berry, M.V. Nonspreading wave packets / M.V. Berry, N.L. Balazs // American Journal of Physics. – 1979. – V. 47(3). – P. 264-267.
  6. Siegman, A.E. Lasers / A.E. Siegman. – University Science, 1986.
  7. Kotlyar, V.V. Hypergeometric modes / V.V. Kotlyar, R.V. Skidanov, S.N. Khonina, V.A. Soifer // Optics Letters. – 2007. – V. 32. – P. 742-744.
  8. Ring, J. Auto-focusing and self-healing of Pearcey beams / J. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia and M. Dennis // Optics Express. – 2012. – V. 20. – P. 18955-18966.
  9. Pearcey, T. The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic / T. Pearcey // Philosophical Magasine. – 1946. – V. 7(37). – P. 311-317.
  10. Berry, M.V. Integrals with coalescing saddles [Electronical Resource] / M.V. Berry and C.J. Howls. – http://dlmf.nist.gov/36.2. – Digital Library of Mathematical Functions, National Institute of Standards and Technology, 2012.
  11. Deng, D. Virtual Source of a Pearcey beam / D. Deng, C. Chen, X. Zhao, B. Chen, X. Peng, Y. Zheng // Optics Letters. – 2014. – V. 39(9). – P. 2703-2706.

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; e-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20