Nonparaxial propagation of gaussian beams on the angle to the axis of the anisotropic crystal
S.N. Khonina, O.V. Zoteeva, S.I. Kharitonov

Full text of article: Russian language.

Abstract:
In this article propagation of laser beams in anisotropic crystals at an angle to a crystal axis also is analytically and numerically investigated. For an uniaxial crystal with use of a method of a stationary phase the analytical expressions showing dependence of astigmatic distortion from polarisation of the falling bunch are received. Also it is shown that a laser beam propagating at an angle to a crystal axis undergoes the birefringence effect which can disappear in accordance with of a plane of an inclination of a beam and a plane of linear polarisation. For Gaussian beams the expression connecting parametres of a beam and a crystal at which there is visual division of ordinary and extraordinary beams is received.

Key words:
anisotropic media, Gaussian beam, birefringence effect.

References:

  1. Zhan, Q. Cylindrical vector beams: from mathematical concepts to applications // Advances in Optics and Photonics. - 2009. - Vol. 1. - P. 1-57.
  2. Niziev, V.G. Influence of Beam Polarization on Laser Cutting Efficiency / V.G. Niziev, A.V. Nesterov // Journal of Physics D. - 1999. - V. 32. - P. 1455-1461.
  3. Khonina, S.N. Minimization of light or dark focal spot size with controllable growth of side lobes in focusing systems with the high numerical aperture / S.N. Khonina, S.G. Volotovsky, // Computer Optics - 2011. - Vol. 35, N 4. - P. 438-451. - (In Russian).
  4. Tidwell, S.C. Generating radially polarized beams interferometrically / S.C. Tidwell, D.H. Ford, W.D. Kimura // Applied Optics. - 1990. - V. 29. - P. 2234-2239.  
  5. Khonina, S.N. Polarization converter for higher-order laser beams using a single binary diffractive optical element as beam splitter / S.N. Khonina, S.V. Karpeev, S.V. Alferov // Opt. Lett. - 2012. - Vol. 37, N 12. - P. 2385-2387.  
  6. Yonezawa, K. Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal / K. Yonezawa, Y. Kozawa and S. Sato // Opt. Lett. - 2006. - V. 31(14). - P. 2151-2153.
  7. Kawauchi, H. Simultaneous generation of helical beams with linear and radial polarization by use of a segmented half-wave plate / H. Kawauchi, Y. Kozawa, S. Sato, T. Sato and S. Kawakami // Opt. Lett. - 2008. - V. 33(4). - P. 399-401.
  8. Ciattoni, A. Circularly polarized beams and vortex generation in uniaxial media / A. Ciattoni, G. Cincotti, C. Palma // J. Opt. Soc. Am. A. - 2003. - Vol. 20(1). - P. 163-171.
  9. Marrucci, L. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media / L. Mar­rucci, C. Manzo and D. Paparo // Phys. Rev. Lett. - 2006. - Vol. 96. - P. 163905-163909.
  10. Fadeyeva, T.A. Spatially engineered polarization states and optical vortices in uniaxial crystals / T.A. Fadeyeva, V.G. Shve­dov, Y.V. Izdebskaya, A.V. Volyar, E. Bras­se­let, D.N. Ne­shev, A.S. Desyatnikov, W. Krolikowski and Y.S. Kiv­shar // Opt. Expr. - 2010. - Vol. 18(10). - P. 10848-10863.
  11. Picon, A. Spin and orbital angular momentum propagation in anisotropic media: theory / A. Picon, A. Benseny, J. Mompart and G.F Calvo // J. Opt. - 2011. - Vol. 13. - P. 064019-064026.
  12. Fleck, J.A. Jr. Beam propagation in uniaxial anisotropic media / J.A. Fleck, Jr. and M.D. Feit // J. Opt. Soc. Am. - 1983. - Vol. 73(7). - P. 920-926.
  13. Ciattoni, A. Vectorial theory of propagation in uniaxially anisotropic media / A. Ciattoni, B. Crosignani and P.Di Porto // J. Opt. Soc. Am. A. - 2001. - Vol. 18(7). - P. 1656-1661.
  14. Zhao, Y. Spin-to-orbital angular momentum conversion in a strongly focused optical beam Phys / Y. Zhao, J.S. Edgar, G.D.M. Jeffries, D. McGloin and D.T. Chiu // Rev. Lett. - 2007. - Vol. 99. - P. 073901.
  15. Chen, L. Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam / L. Chen and W. She // Opt. Lett. - 2008. - Vol. 33. - P. 696-698.
  16. Khonina, S.N. Controlling the contribution of the electric ?eld components to the focus of a high-aperture lens using binary phase structures, / S.N. Khonina, S.G. Volotovsky // J. Opt. Soc. Am. A. - 2010. - Vol. 27, N 10. - P. 2188-2197.
  17. Stallinga, S. Axial birefringence in high-numerical-aper­ture optical systems and the light distribution close to focus / S. Stallinga // J. Opt. Soc. Am. A. - 2001. - Vol. 18(11). - P. 2846-2859.
  18. Seshadri, S.R. Beam dynamics of two modes propagating along the optic axis in a uniaxial crystal / S.R. Seshadri // J. Opt. Soc. Am. A. - 2005. - Vol. 22(2). - P. 361-369.
  19. Liu, D. Various dark hollow beams propagating in uniaxial crystals orthogonal to the optical axis / D. Liu and Z. Zhou // J. Opt. A: Pure Appl. Opt. - 2008. - Vol. 10. - P. 095005-095014.
  20. Zusin, D.H. Bessel beam transformation by anisotropic crystals / D.H. Zusin, R. Maksimenka, V.V. Filippov, R.V. Chulkov, M. Perdrix, O. Gobert and A.S. Grabtchi­kov // J. Opt. Soc. Am. A. - 2010. - Vol. 27(8). - P. 1828-1833. 
  21. Doskolovich, L.L. Integral representations for solutions of Maxwell’s equations for anisotropic media / L.L. Do-skolovich, N.L. Kazanskiy, S.I. Kharitonov // Computer Optics. - 2010. - Vol. 34, N 1. - P. 52-57. - (In Russian).
  22. Khonina, S.N. Analogue of Rayleigh - Sommerfeld integral for anisotropic and gyrotropic media / S.N. Khonina, S.I. Kharitonov // Computer Optics. - 2012. - Vol. 36, N 2. - P. 172-182. - (In Russian).
  23. Luneburg, R.K. Mathematical Theory of Optics / R.K. Luneburg. - University of California Press, Berkeley, California, 1966.
  24. Seshadri, S.R. Basic elliptical Gaussian wave and beam in a uniaxial crystal / S.R. Seshadri // J. Opt. Soc. Am. A. - 2003. - Vol. 20, N 9. - P. 1818-1826.
  25. Khonina, S.N. Periodic intensity change for laser mode beams propagating in anisotropic uniaxial crystals / S.N. Khonina, S.G. Volotovsky, S.I. Kharitonov // Izv. SNC RAS - 2012. - Vol. 14, N 4 (accepted for publication). - (In Russian).
    © 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