Diffraction-free asymmetric elegant bessel beams with fractional orbital angular momentum
V.V. Kotlyar, A.A. Kovalev, V.A. Soifer

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Full text of article: Russian language.

DOI: 10.18287/0134-2452-2014-38-1-4-10

Pages: 4-10.

Abstract:
This paper introduces a new family of diffraction-free asymmetric elegant Bessel beams (EB-beams) with fractional orbital angular momentum (OAM). EB-beams are modes of free space and described by the n-th order Bessel function of the first kind with a complex argument. Functions of complex amplitudes of EB-beams are orthogonal by continuous scaling parameter and not orthogonal on a discrete parameter (topological charge). The intensity distribution of EB-beams has a countable number of isolated zeros of intensity, located on the horizontal axis. These zeros are centers of optical vortices with unit topological charge and opposite signs on different sides of the origin. Isolated intensity zero on the optical axis generates an optical vortex with topological charge of n. OAM of the EB-beams is (n + 0,69777)h per photon, where h is the Planck's constant.

Key words:
diffraction-free laser beam, Bessel beam, orbital angular momentum, complex argument.

References:

  1. Miller Jr., W. Symetry and separation of variables / W. Miller Jr. – Addison-Wesley Pub. Comp., 1977.
  2. Durnin, J. Exact solutions for nondiffracting beams. I. The scalar theory / J. Durnin // J. Opt. Soc. Am. A. – 1987. – V. 4(4). – P. 651-654.
  3. Kotlyar, V.V. Algorithm for the generation of non-diffrac­ting Bessel beams / V.V. Kotlyar, S.N. Khonina, V.A. Soifer // J. Mod. Opt. – 1992. – V. 42(6). – P. 1231-1239.
  4. Gutierrez-Vega, J.C. Alternative formulation for invariant optical fields: Mathieu beams / J.C. Gutierrez-Vega, M.D. Iturbe-Castillo, S. Chavez-Cedra // Opt. Lett. – 2000. – V. 25(20). – P. 1493-1495.
  5. Chavez-Cedra, S. Elliptic vortices of electromagnetic wave fields / S. Chavez-Cedra, J.C. Gutierrez-Vega, G.H.C. New // Opt. Lett. – 2001. – V. 26(22). – P. 1803-1805.
  6. Kotlyar, V.V. Hermite-Gaussian modal laser beams with orbital angular momentum / V.V. Kotlyar, A.A. Kovalev // J. Opt. Soc. Am. A. – 2014. – V. 31(2). – P. 274-282.
  7. Dennis, M.R. Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams / M.R. Dennis, J.D. Ring // Opt. Lett. – 2013. – V. 38(17). – P. 3325-3328.
  8. Prudnikov, A.P. Integrals and series. Special functions / A.P. Prudnikov, J.A. Brychkov, O.I. Marichev. – Moscow: “Science” Publisher, 1983. – (In Russian).
  9. Gradshteyn, I.S. Table of Integrals, Series, and Products / I.S. Gradshteyn, I.M. Ryzhik. – New York: Academic, 1965.
  10. Abramovitz, M. Handbook of mathematical functions / M. Abramovitz, I.A. Stegun. – Dover Publications, 1965.
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