Self-focusing of hypergeometric laser beams
V.V. Kotlyar, A.A. Kovalev

Image Processing Systems Institute of the RAS,
Samara State Aerospace University

Full text of article: Russian language.

Abstract:
We have obtained explicit nonparaxial expressions for three components of the electric vector of the hypergeometric laser beam (HyG-beam). For HyG-beams with topological charge n = 0, 1 explicit expressions for on-axis intensity have been derived and it follows that position of the beam waist depends on HyG-beam parameters (g, m) and is displaced from the input plane z = 0. Such displacement of maximal on-axis intensity has been called self-focusing of the HyG-beam and formulae for this displacement (focusing distance) have been obtained. Numerical simulation of HyG-beam propagation with n = 0 has been done by the FDTD-method and it is shown that displacement of beam waist and on-axis intensity are in good accordance with values predicted by approximate formulae.

Key words:
vortex laser beam, hypergeometric laser beam, nonparaxial diffraction, on-axis intensity, displacement of laser beam waist, self-focusing.

References:

  1. Kuga, T. Novel Optical Trap of Atoms with a Doughnut Beam / T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, H. Sasada // Phys. Rev. Lett. – 1997. – Vol. 78. – P. 4713–4716.
  2. Soskin, M.S., Singular optics / M.S. Soskin, M.V. Vasnetsov // Progress in Optics. – 2001. – Vol. 41.
  3. Bandres, M. Circular beams / M. Bandres, J. Gutierrez-Vega // Opt. Lett. – 2008. – Vol. 33. – P. 177-179.
  4. Kotlyar, V.V. Family of hypergeometric laser beams / V. Kotlyar, A. Kovalev // J. Opt. Soc. Am. A. – 2008. – Vol. 25. – P. 262-270.
  5. Cai, Y. Hollow Gaussian beams and their propagation properties / Y. Cai, X. Lu, Q. Lin // Opt. Lett. – 2003. – Vol. 28. – P. 1084-1086.
  6. Zeng-Hui, G. Nonparaxial Dark-Hollow Gaussian Beams / Gao Zeng-Hui, Lü Bai-Da // Chinese Phys. Lett. – 2006. – Vol. 23(1). – P. 106-109.
  7. Kotlyar, V.V. Nonparaxial propagation of a Gaussian optical vortex with initial radial polarization / V. Kotlyar, A. Kovalev // J. Opt. Soc. Am. A. – 2010. – Vol. 27. – P. 372-380.
  8. Shin, Y. Diffraction-limited dark laser spot produced by a hollow optical fiber / Y. Shin, K. Kim, J. Kim, H. Noh, W. Jhe, K. Oh, U. Paek // Opt. Lett. -2001. – Vol. 26. – P. 119-121.
  9. Lopez-Mago, D. Propagation of Whittaker-Gaussian beams / D. Lopez-Mago, M.A. Bandres, J.C. Gutierrez-Vega // Proc. SPIE – 2009. – Vol. 7430. – P. 743013-8.
  10. Bandres, M.A. Higher-order moments and overlaps of rotationally symmetric beams / M.A. Bandres, D. Lopez-Mago, J.C Gutierrez-Vega // J. Opt. – 2010. – Vol. 12(1). – P. 015706 (10pp).
  11. Gradshteyn, I.S. Table of Integrals, Series, and Products / I.S. Gradshteyn, I.M. Ryzhik – Elsevier, 2007.
  12. Handbook of Mathematical Functions / edited by M. Abramowitz, I.A. Stegun – National Bureau of Standards, Washington, DC, 1964. – 1044 p.
  13. Lit, J.W.Y. Focal depth of a transmitting axicon / J.W.Y. Lit, R. Tremblay // J. Opt. Soc. Am. – 1973. – Vol. 63(4). – P. 445-449.

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