Theoretical investigation of vortex Gaussian beams focusing along the axis of the crystal

Abstract

In this paper we investigate analytically and numerically sharp focusing of uniformly polarized laser Gaussian beams with a vortex phase along the axis of an anisotropic crystal. Two models are used for the analysis: geometrical optics, implemented in the software product ZEMAX, and wave optics based on the expansion in plane waves. An analytical expression is obtained in the frame of nonparaxial wave optics for a complex amplitude in focusing a vortex Gaussian beam in an anisotropic medium. It is shown that when focusing is weak ordinary and extraordinary beams are mixed and the beam formed has a mixed "spiral" type of polarization. In case of sharp focusing two focuses corresponding to the ordinary and extraordinary beams are formed along the crystal axis. If a first-order vortex phase is present in an incident beam with circular polarization cylindrical vector distributions with azimuthal polarization for the ordinary beam and those with radial polarization for the extraordinary beam occur in these focuses. Analytical calculations are illustrated by the results of numerical simulation. Both the intensity distribution for components of the generated laser fields and their polarization states are shown in detail. The studies completed are useful for the development of devices that perform polarization conversion.

About the authors

S. N. Khonina

Image Processing Systems Institute of the Russian Academy of Sciences, Samara

Author for correspondence.
Email: khonina@smr.ru

Doctor of Physics and Mathematics; Professor

Leading Researcher

Russian Federation

S. G. Volotovsky

Image Processing Systems Institute of the Russian Academy of Sciences, Samara

Email: sv@smr.ru

Principal Software Engineer

Russian Federation

A.V. Ustinov

Samara State Aerospace University

Email: andr@smr.ru

Postgraduate Student of the Department of Technical Cybernetics

Russian Federation

A. P. Krasnov

Samara State Aerospace University

Email: kraan2009@yandex.ru

Undergraduate student

Russian Federation

References

  1. Stamnes J.J., Jiang D. Focusing of electromagnetic waves into a uniaxial crystal. Optics Communications. 1998. V. 150, Iss. 1-6. P. 251-262.
  2. Jiang D., Stamnes J.J. Numerical and asymptotic results for focusing of two-dimensional waves in uniaxial crystals. Optics Communications. 1999. V. 163, Iss. 1. P. 55-71.
  3. Jiang D., Stamnes J.J. Numerical and experimental results for focusing of two-dimensional electromagnetic waves into uni-axial crystals. Optics Communications. 2000. V. 174, Iss. 5-6. P. 321-334.
  4. Stallinga S. Axial birefringence in high-numerical-aperture optical systems and the light distribution close to focus. Journal of the Optical Society of America A: Optics and Image Science, and Vision. 2001. V. 18, no. 11. P. 2846-2859.
  5. Stallinga S. Light distribution close to focus in biaxially birefringent media. Journal of the Optical Society of America A: Optics and Image Science, and Vision. 2004. V. 21, no. 9. P. 1785-1798.
  6. Li J., Jiang H., Xiao J., Gong Q. The mechanism of multi-focusing of lasers into uniaxial crystals. Journal of Optics A: Pure and Applied Optics. 2007. V. 9, no. 7. P. 664-672.
  7. Yonezawa K., Kozawa Y., Sato S. Focusing of radially and azimuthally polarized beams through a uniaxial crystal. Journal of the Optical Society of America A: Optics and Image Science, and Vision. 2008. V. 25, no. 2. P. 469-472.
  8. Zhang Z., Pu J., Wang X. Tight focusing of radially and azimuthally polarized vortex beams through a uniaxial birefringent crystal. Applied Optics. 2008. V. 47, no. 12. P. 1963-1967.
  9. Khonina S.N., Golub I. Optimization of focusing of linearly polarized light. Optics Letters. 2011. V. 36, no. 3. P. 352-354.
  10. Khilo N.A., Ryzhevich A.A., Petrova E.S. Transformation of the order of Bessel beams in uniaxial crystals. Quantum Electronics. 2001. V. 31, no. 1. P. 85-89.
  11. Ciattoni A., Cincotti G., Palma C. Circularly polarized beams and vortex generation in uniaxial media. Journal of the Optical Society of America A: Optics and Image Science, and Vision. 2003. V. 20, no. 1. P. 163-171.
  12. Marrucci L., Manzo C., Paparo D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Physical Review Letters. 2006. V. 96, no. 16. Article number 163905.
  13. Fadeyeva T.A., Shvedov V.G., Izdebskaya Y.V., Volyar A.V., Brasselet E., Neshev D.N., Desyatnikov A.S., Krolikowski W., Kivshar Y.S. Spatially engineered polarization states and optical vortices in uniaxial crystals. Optics Express. 2010. V. 18, no. 10. P. 10848-10863.
  14. Loussert C., Brasselet E. Efficient scalar and vectorial singular beam shaping using homogeneous anisotropic media. Optics Letters.2010. V. 35, no. 1. P. 7-8.
  15. Picon A., Benseny A., Mompart J., Calvo G.F. Spin and orbital angular momentum propagation in anisotropic media: theory. Journal of Optics. 2011. V. 13, no. 6. Article number 064019.
  16. Khilo N.A. Diffraction and order conversion of Bessel beams in uniaxial crystals. Optics Communications. 2012. V. 285, no. 5. P. 503-509.
  17. Khonina S.N., Volotovsky S.G., Kharitonov S.I. Periodic intensity change for laser mode beams propagating in anisotropic uniaxial crystals. Izvestiya Samarskogo nauchnogo tsentra RAN. [News of Samara Science Center of the Russian Academy of Science]. 2012. V. 14, no. 4. P. 18-27. (In Russ.)
  18. Khonina S.N., Morozov A.A., Karpeev S.V. Effective transformation of a zero-order Bessel beam into a second-order vortex beam using a uniaxial crystal. Laser Physics. 2014. V. 24, no. 5. Article number 056101.
  19. ZEMAX. Optical Design Program. User’s Guide. ZEMAX Development Corporation, June 9, 2009. 766 p.
  20. Khonina S.N., Kharitonov S.I. Analog of the Rayleigh-Sommerfeld integral for anisotropic and gyrotropic media. Journal of Modern Optics. 2013. V. 60, no. 10. P. 814-822.
  21. Krasnov A.P., Khonina S.N. Comparative modelling of laser beam propagation in a uniaxial crystal based on integral operators. Vestnik of Samara State Aerospace University. 2014. No. 1(43). P. 238-252. (In Russ.)
  22. Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integraly I ryady. Т. 2. Spetsial'nye funktsii [Integrals and Series. V. 2. Special functions]. Moscow: Nauka Publ., 1983. 750 p.

Statistics

Views

Abstract: 3466

PDF (Russian): 1780

Dimensions

PlumX

Refbacks

  • There are currently no refbacks.

Copyright (c) 2015 VESTNIK of the Samara State Aerospace University

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies