OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 10 — Apr. 1, 2012
  • pp: C231–C240

Rotational spin Hall effect in a uniaxial crystal

Tatyana A. Fadeyeva, Constantine N. Alexeyev, Alexander F. Rubass, Maksym O. Ivanov, Alexey O. Zinov’ev, Victor L. Konovalenko, and Alexander V. Volyar  »View Author Affiliations

Applied Optics, Vol. 51, Issue 10, pp. C231-C240 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1135 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We have considered the propagation process of the phase-matched array of singular beams through a uniaxial crystal. We have revealed that local beams in the array are rotated when propagating. However the right and left rotations are unequal. There are at least two processes responsible for the array rotation: the interference of local beams and the spatial depolarization. The interference takes place in the vortex birth and annihilation events forming the symmetrical part of the rotation. The depolarization process contributes to the asymmetry of the rotation that is called the rotational spin Hall effect. It can be brought to light due to the difference between the envelopes of the dependences of the angular displacement on the inclination angle of the local beams or the crystal length reaching the value of some angular degree. The direction of the additional array rotation is exclusively defined by the handedness of the circular polarization in the initial beam array.

© 2012 Optical Society of America

OCIS Codes
(260.0260) Physical optics : Physical optics
(260.1180) Physical optics : Crystal optics
(350.5030) Other areas of optics : Phase
(260.6042) Physical optics : Singular optics

Original Manuscript: November 28, 2011
Revised Manuscript: February 21, 2012
Manuscript Accepted: February 22, 2012
Published: April 2, 2012

Tatyana A. Fadeyeva, Constantine N. Alexeyev, Alexander F. Rubass, Maksym O. Ivanov, Alexey O. Zinov’ev, Victor L. Konovalenko, and Alexander V. Volyar, "Rotational spin Hall effect in a uniaxial crystal," Appl. Opt. 51, C231-C240 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. I. Fedorov, “On the theory of a total reflection,” Dokl. Akad. Nauk USSR 105, 465–468 (1955).
  2. C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circular polarized light beam,” Phys. Rev. D 5, 787–796 (1972). [CrossRef]
  3. A. Aiello and J. Woerdman, “Goos–Hänchen and Imbert–Fedorov shifts of a nondiffracting Bessel beam,” Opt. Lett. 36, 543–545 (2011). [CrossRef]
  4. A. Ya. Bekshaev, “Oblique section of a paraxial light beam: criteria for azimuthal energy flow and orbital angular momentum,” J. Opt. A 11, 094003 (2009). [CrossRef]
  5. A. Bekshaev, K. Bliokh, and M. Soskin, Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011). [CrossRef]
  6. V. Fedoseev, “The mechanisms of the specific effects accompanying the reflection and transmission of a light beam carrying the orbital angular momentum,” J. Opt. 13, 064025 (2011). [CrossRef]
  7. K. Yu. Bliokh and Yu. P. Bliokh, “Conservation of angular momentum, transverse shift and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96, 073903 (2006). [CrossRef]
  8. K. Yu. Bliokh and Yu. P. Bliokh, “Polarization, transverse shifts and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75, 066609 (2007). [CrossRef]
  9. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008). [CrossRef]
  10. K. Bliokh, I. Shadrivov, and Y. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34, 389–391 (2009). [CrossRef]
  11. M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004). [CrossRef]
  12. K. Bliokh, “Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index,” J. Opt. A 11, 094009 (2009). [CrossRef]
  13. V. Fedoseev, “Conservation laws and angular transverse shifts of the reflected and transmitted light beams,” Opt. Commun. 282, 1247 (2009). [CrossRef]
  14. M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, “Demonstration of a quasi-scalar angular Goos–Hänchen effect,” Opt. Lett. 35, 3562–3564 (2010). [CrossRef]
  15. A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45, 8204–8208 (1992). [CrossRef]
  16. A. Volyar, A. Gnatovskii, S. Lapayeva, and V. Myagkov, “Polarization splitting of the plane propagation of a local wave in a step-index multimode fiber,” Ukr. Phys. J. 37, 1468–1471 (1992).
  17. K. Bliokh, and M. Alonso, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” in Frontiers in Optics (FiO) (Optical Society of America, 2010), paper FWP4.
  18. A. Volyar and T. Fadeyeva, “Nonparaxial Gaussian beams: 2. Splitting of the singularity lines and the optical Magnus effect,” Tech. Phys. Lett. 26, 740–743 (2000). [CrossRef]
  19. T. Fadeyeva, A. Rubass, Yu. Egorov, A. Volyar, and G. Swartzlander, “Quadrefringence of optical vortices in a uniaxial crystal,” J. Opt. Soc. Am. A 25, 1634–1641 (2008). [CrossRef]
  20. T. Fadeyeva, A. Rubass, and A. Volyar, “Transverse shift of high-order paraxial vortex-beam induced by a homogeneous anisotropic medium,” Phys. Rev. A 79, 053815 (2009). [CrossRef]
  21. T. Fadeyeva, Yu. Egorov, A. Rubass, G. A. Swartzlander, and A. Volyar, “Indistinguishability limit for off-axis vortex beams in uniaxial crystals,” Opt. Lett. 32, 3116–3118 (2007). [CrossRef]
  22. Ya. Izdebskaya, T. Fadeyeva, V. Shvedov, and A. Volyar, “Vortex-bearing array of singular beams with very high orbital angular momentum,” Opt. Lett. 31, 2523–2525(2006). [CrossRef]
  23. Ya. Izdebskaya, V. Shvedov, and A. Volyar, “Symmetric array of off-axis singular beams: spiral beams and their critical points,” J. Opt. Soc. Am. A 25, 171–181 (2008). [CrossRef]
  24. E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. 174, 1273–1300 (2004). [CrossRef]
  25. F. Gori, G. Guattari, and C. Padovani, “Bessel-Gaussian beams,” Opt. Commun. 64, 491–495 (1987). [CrossRef]
  26. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005). [CrossRef]
  27. A. Volyar and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 450–457 (2006). [CrossRef]
  28. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, “Novel optical trap of atoms with a doughnut beam,” Phys. Rev. Lett. 78, 4713–4716 (1997). [CrossRef]
  29. T. Fadeyeva, V. Shvedov, N. Shostka, C. Alexeyev, and A. Volyar, “Natural shaping of the cylindrically polarized beams,” Opt. Lett. 35, 3787–3789 (2010). [CrossRef]
  30. O. V. Angelsky, Yu. Ya. Tomka, A. G. Ushenko, Ye. G. Ushenko, and Yu. A. Ushenko, “Investigation of 2D Mueller matrix structure of biological tissues for pre-clinical diagnostics of their pathological states,” J. Phys. D 38, 4227–4235 (2005). [CrossRef]
  31. O. V. Angelsky, A. G. Ushenko, and Ye. G. Ushenko, “Investigation of the correlation structure of biological tissue polarization images during the diagnostics of their oncological changes,” Phys. Med. Biol. 50, 4811 (2005). [CrossRef]
  32. L. Allen, S. Barnett, and M. Padgett, Optical Angular Momentum (IOP, 2003).
  33. A. Volyar, V. Shvedov, Ya. Izdebskaya, T. Fadeyeva, and A. Rubass, “Structure of orbital angular momentum of singular array of Gaussian beams,” Ukr. J. Phys. Opt. 7, 79–88 (2006). [CrossRef]
  34. Yu. Egorov, T. Fadeyeva, and A. Volyar, “The fine structure of singular beams in crystals: colours and polarization,” J. Opt. A 6, S217–S228 (2004). [CrossRef]
  35. T. Fadeyeva and A. Volyar, “Extreme spin-orbit coupling in crystal-traveling paraxial beams,” J. Opt. Soc. Am. A 27, 381–389 (2010). [CrossRef]
  36. A. V. Volyar, V. Z. Zhilaitis, and V. G. Shvedov, “Optical eddies in small-mode fibers: II. The spin-orbit interaction,” Opt. Spectrosc. 86, 593–598 (1999).
  37. A. Ciattoni, G. Cincotti, and C. Palma, “Angular momentum dynamics of a paraxial beam in a uniaxial crystal,” Phys. Rev. E 67, 036618 (2003). [CrossRef]
  38. H. Yan and B. Lü, “Dynamic evolution of an edge dislocation through alignedand misaligned paraxial optical ABCD systems,” J. Opt. Soc. Am. A 26, 985–992 (2009). [CrossRef]
  39. E. Cojocaru, V. Draganescu, and N. Herisanu, “Astigmatism together with longitudinal focal shift in off-axis optical systems,” Appl. Opt. 29, 4208–4211 (1990). [CrossRef]
  40. O. Angelsky, M. Gorsky, P. Maksimyak, A. Maksimyak, S. Hanson, and C. Zenkova, “Investigation of optical currents in coherent and partially coherent vector fields,” Opt. Express 19, 660–672 (2011). [CrossRef]
  41. O. Angelsky, A. Bekshaev, P. Maksimyak, A. Maksimyak, S. Hanson, and C. Zenkova, “Orbital rotation without orbital angular momentum: mechanical action of the spin part of the internal energy flow in light beams,” Opt. Express 20, 3563–3571 (2012) [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited