Abstract

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

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  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]

2012

2011

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]

A. Aiello and J. Woerdman, “Goos–Hänchen and Imbert–Fedorov shifts of a nondiffracting Bessel beam,” Opt. Lett. 36, 543–545 (2011).
[CrossRef]

A. Bekshaev, K. Bliokh, and M. Soskin, Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

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]

2010

2009

K. Bliokh, I. Shadrivov, and Y. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34, 389–391 (2009).
[CrossRef]

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]

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]

K. Bliokh, “Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index,” J. Opt. A 11, 094009 (2009).
[CrossRef]

V. Fedoseev, “Conservation laws and angular transverse shifts of the reflected and transmitted light beams,” Opt. Commun. 282, 1247 (2009).
[CrossRef]

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]

2008

2007

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]

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]

2006

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]

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]

A. Volyar and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 450–457 (2006).
[CrossRef]

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]

2005

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]

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]

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

2004

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. 174, 1273–1300 (2004).
[CrossRef]

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

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]

2003

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]

2000

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]

1999

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).

1997

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]

1992

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]

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).

1990

1987

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gaussian beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

1972

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]

1955

F. I. Fedorov, “On the theory of a total reflection,” Dokl. Akad. Nauk USSR 105, 465–468 (1955).

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. 174, 1273–1300 (2004).
[CrossRef]

Aiello, A.

Alexeyev, C.

Allen, L.

L. Allen, S. Barnett, and M. Padgett, Optical Angular Momentum (IOP, 2003).

Alonso, M.

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.

Angelsky, O.

Angelsky, O. V.

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]

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]

Barnett, S.

L. Allen, S. Barnett, and M. Padgett, Optical Angular Momentum (IOP, 2003).

Bekshaev, A.

Bekshaev, A. Ya.

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]

Bliokh, K.

A. Bekshaev, K. Bliokh, and M. Soskin, Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

K. Bliokh, “Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index,” J. Opt. A 11, 094009 (2009).
[CrossRef]

K. Bliokh, I. Shadrivov, and Y. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34, 389–391 (2009).
[CrossRef]

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.

Bliokh, K. Yu.

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]

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]

Bliokh, Yu. P.

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]

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]

Ciattoni, A.

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]

Cincotti, G.

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]

Cojocaru, E.

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Dooghin, A. V.

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]

Draganescu, V.

Egorov, Yu.

Fadeyeva, T.

T. Fadeyeva and A. Volyar, “Extreme spin-orbit coupling in crystal-traveling paraxial beams,” J. Opt. Soc. Am. A 27, 381–389 (2010).
[CrossRef]

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]

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]

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]

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]

A. Volyar and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 450–457 (2006).
[CrossRef]

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]

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]

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]

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]

Fedorov, F. I.

F. I. Fedorov, “On the theory of a total reflection,” Dokl. Akad. Nauk USSR 105, 465–468 (1955).

Fedoseev, V.

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]

V. Fedoseev, “Conservation laws and angular transverse shifts of the reflected and transmitted light beams,” Opt. Commun. 282, 1247 (2009).
[CrossRef]

Gnatovskii, A.

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).

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gaussian beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Gorsky, M.

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gaussian beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Hanson, S.

Herisanu, N.

Hermosa, N.

Hirano, T.

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]

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[CrossRef]

Imbert, C.

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]

Izdebskaya, Ya.

Kivshar, Y.

Kuga, T.

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]

Kundikova, N. D.

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]

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[CrossRef]

Lapayeva, S.

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).

Liberman, V. S.

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]

Lü, B.

Maksimyak, A.

Maksimyak, P.

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Merano, M.

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Myagkov, V.

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).

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Padgett, M.

L. Allen, S. Barnett, and M. Padgett, Optical Angular Momentum (IOP, 2003).

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gaussian beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Palma, C.

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]

Rubass, A.

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]

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]

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]

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]

Sasada, H.

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]

Shadrivov, I.

Shimizu, Y.

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]

Shiokawa, N.

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]

Shostka, N.

Shvedov, V.

Shvedov, V. G.

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).

Soskin, M.

A. Bekshaev, K. Bliokh, and M. Soskin, Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

Swartzlander, G.

Swartzlander, G. A.

Tomka, Yu. Ya.

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]

Torii, Y.

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]

Ushenko, A. G.

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]

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]

Ushenko, Ye. G.

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]

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]

Ushenko, Yu. A.

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]

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. 174, 1273–1300 (2004).
[CrossRef]

Volyar, A.

T. Fadeyeva and A. Volyar, “Extreme spin-orbit coupling in crystal-traveling paraxial beams,” J. Opt. Soc. Am. A 27, 381–389 (2010).
[CrossRef]

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]

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]

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]

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]

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]

A. Volyar and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 450–457 (2006).
[CrossRef]

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]

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]

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]

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]

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).

Volyar, A. V.

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).

Woerdman, J.

Woerdman, J. P.

Yan, H.

Zel’dovich, B. Y.

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]

Zenkova, C.

Zhilaitis, V. Z.

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).

Appl. Opt.

Contemp. Phys.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Dokl. Akad. Nauk USSR

F. I. Fedorov, “On the theory of a total reflection,” Dokl. Akad. Nauk USSR 105, 465–468 (1955).

J. Opt.

A. Bekshaev, K. Bliokh, and M. Soskin, Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

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]

J. Opt. A

K. Bliokh, “Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index,” J. Opt. A 11, 094009 (2009).
[CrossRef]

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]

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]

J. Opt. Soc. Am. A

J. Phys. D

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]

Opt. Commun.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gaussian beams,” Opt. Commun. 64, 491–495 (1987).
[CrossRef]

V. Fedoseev, “Conservation laws and angular transverse shifts of the reflected and transmitted light beams,” Opt. Commun. 282, 1247 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectrosc.

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).

A. Volyar and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 450–457 (2006).
[CrossRef]

Phys. Med. Biol.

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]

Phys. Rev. A

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]

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]

Phys. Rev. D

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]

Phys. Rev. E

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]

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]

Phys. Rev. Lett.

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]

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]

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93, 083901 (2004).
[CrossRef]

Phys. Usp.

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Phys. Usp. 174, 1273–1300 (2004).
[CrossRef]

Science

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[CrossRef]

Tech. Phys. Lett.

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]

Ukr. J. Phys. Opt.

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]

Ukr. Phys. J.

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).

Other

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.

L. Allen, S. Barnett, and M. Padgett, Optical Angular Momentum (IOP, 2003).

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Figures (11)

Fig. 1.
Fig. 1.

(a) Positions of the axes of partial beams (solid lines) on the surface of the hyperboloid of revolution; (b) positions of the partial beams at the initial plane z=0; (c) inclination of the beam axis. C is a unit vector of the crystal optical axis.

Fig. 2.
Fig. 2.

Intensity distributions in RHP and LHP components of different types of the phase-matched beam arrays in the LiNbO3 crystal with no=2.2, ne=2.3, z=2cm: (a) and (b) {8, 1, 6}, r0=30μm, w0=30μm; (a) αo=1°; (b) αo=0.5°; (c) {8, 1, 6}, r0=w0=30μm, αo=0.57°; (d) {12, 1, 4}, w0=50μm, r0=50μm, αo=0.54°.

Fig. 3.
Fig. 3.

Propagation of the singular beam array along the uniaxial crystal with N=7, m=3, l=4, w0=50μm, no=2.2, ne=2.3: (a) r0=0, αo=1.2°; (b) spiral beam αo=0.244°, r0=50μm.

Fig. 4.
Fig. 4.

Deformation of the centered optical vortex in the LHP component E of the phase-matched beam array with different numbers N of partial beams: m=1, l=0, r0=0, αo=0.3°, z=1cm.

Fig. 5.
Fig. 5.

Energy efficiency η(z) and η(αo) for the beam array {8,1,1} and corresponding intensity distributions.

Fig. 6.
Fig. 6.

Rotation of the beam array.

Fig. 7.
Fig. 7.

Angular rotation Δϕ(z) of the array in the state {8,1,1} with (a) w0=100μm, r0=300μm and (b) w0=r0=30μm. The designations 1 and 2 correspond to the field components E+ and E, respectively, for the same values of the crystal length z.

Fig. 8.
Fig. 8.

Dependency of the angular displacement Δϕ on the number of local beams N in the array.

Fig. 9.
Fig. 9.

(a) Angular displacement Δϕ as a Δϕ as a function of the inclination angle αo. 1 and 2, the asymptotic curve [Eq. (23)]; the circlets are the difference between the upper and the lower envelopes of the curve 1 (in all 800 circlets); (b) evolution of the SAM Sz(αo).

Fig. 10.
Fig. 10.

Sketch of the experimental setup: P, polarizer; λ/4, quarter-wave retarder; M, spatial phase modulator; AX, axicon; D, diaphragm; L1,2,3, lenses; Cr, LiNbO3 crystal.

Fig. 11.
Fig. 11.

Theoretical (1) and experimental (2) curves Δϕ(αo) and corresponding intensity distributions in the LHP array component.

Equations (33)

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Ψo=[xniynw0σo]lexp(xn2+yn2w02σo)/σo,
(E+l)loc=[xni(ynαoz)w0σo]lΨ˜o+[xni(ynαez)w0σe]lΨ˜e,
(El)loc=p=0l(lp)(αozow0)lp×[(xni(yn+iαozo)w0σo)l2(l1σorn2w02σo2)Ψ˜o(xni(yn+iαozo)w0σe)l2(l1σern2w02σe2)Ψ˜e],
Ψ˜o,e=exp(x2+(y+iαozo)2w02σo,ekoαo2zo2)/σo,e.
(E+l)loc=[xn+i(ynαoz)w0σo]lΨ˜o+[xn+i(ynαez)w0σe]lΨ˜e,
(El)loc=p=0l(lp)(αozow0)lp(xn+i(yn+iαozo)w0)p+2×[j=0p+1(p+1)!j!(σo)j(rnw0)2(jp2)Ψ˜oj=0p+1(p+1)!j!(σe)j(rnw0)2(jp2)Ψ˜e],
xn=xcosφn+ysinφn+r0,yn=xsinφn+ycosφn,
eˆ±=(xˆn±iyˆn)exp(iφn),φn=2πNn,
E+l,m=Eol,m+Eel,m=n=1N{[xni(ynαoz)w0σo]lΨ˜o+[xni(ynαez)w0σe]lΨ˜e}eimφn,
El,m=n=1N{p=0l(lp)(αozow0)lp×[(xni(yn+iαozo)w0σo)l2(l1σorn2w02σo2)Ψ˜o(xni(yn+iαozo)w0σe)l2(l1σern2w02σe2)Ψ˜e]}ei(2+m)φn.
E+l,m=n=1N{p=0l(lp)(αozow0)lp×[(xn+i(yn+iαozo)w0σo)l2(l1σorn2w02σo2)Ψ˜o(xn+i(yn+iαozo)w0σe)l2(l1σern2w02σe2)Ψ˜e]}ei(2+m)φn,
El,m=n=1N{[xn+i(ynαoz)w0σo]lΨ˜o+[xn+i(ynαez)w0σe]lΨ˜e}eimφn.
E+l,m=n=1N{[xn+i(ynαoz)w0σo]lΨ˜o+[xn+i(ynαez)w0σe]lΨ˜e}eimφn,
El,m=n=1N{p=0l(lp)(αozow0)lp(xn+i(yn+iαozo)w0)p+2×[j=0p+1(p+1)!j!(σo)j(rnw0)2(jp2)Ψ˜oj=0p+1(p+1)!j!(σe)j(rnw0)2(jp2)Ψ˜e]}ei(2+m)φn.
E+l,m=n=1N{p=0l(lp)(αozow0)lp(xni(yn+iαozo)w0)p+2×[j=0p+1(p+1)!j!(σo)j(rnw0)2(jp2)Ψ˜oj=0p+1(p+1)!j!(σe)j(rnw0)2(jp2)Ψ˜e]}ei(2+m)φn,
El,m=n=1N{[xni(ynαoz)w0σo]lΨ˜o+[xni(ynαez)w0σe]lΨ˜e}eimφn.
rn2=r2+r02+2r0rcos(ϕϕn)2iαozorsin(ϕϕn)αo2zo2,
[xni(yn+iαozo)]2=rn4[xn+i(yn+iαozo)]2[xn+i(yn+iαozo)]2/(αozo)4.
exp[(t+1t)x2]=k=tkIk(x),
n=1Nexp{i(mp)2πNn}={N,ifmp=qN,q=0,±1,±2,0,otherwise.
Eq=(1)(qN+m)/2exp{i[2+qN+2m]φ}×[IqN+2m+2(ξo)ΨoIqN+2m+2(ξe)Ψe],
Q={m+2,N>2(m+2)m+2N,N<2(m+2)0,N=2(m+2),
Q+={m,N>2mmN,N<2m0,N=2m.
E+=Nq=(Rα¯R+α¯)qN+m2×ei(qN+m)φ[IqN+m(ξo)Ψo+IqN+m(ξe)Ψe].
E+[(R+α¯)/(Rα¯)]m/2×[Im(ξo)Ψo+Im(ξe)Ψe]exp(imφ).
E+[Ψoσom+Ψeσem]r|m|exp(imφ).
ηl,m={S|El,m|2dS}/(S|El,m|2dS+S|E+l,m|2dS),
Lz(z)+Sz(z)=Lz(z=0)+Sz(z=0),
Sz=(S|E+l,m|2dSS|El,m|2dS)/I,
Lz={E+(m)|iϕ|E+(m)+E(m)|iϕ|E(m)}/I,
Δx=2s/(koαo),
ΔϕΔx/r=2s/(koαoαmz),
tanφn(±)=φnφn+10|E±|2r2sinφdrdφ/φnφn+10|E±|2r2cosφdrdφ.

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