Abstract

We describe how the propagation of light through uniaxial crystals can be used as a versatile tool towards the spatial engineering of polarization and phase, thereby providing an all-optical technique for vectorial and scalar singular beam shaping in optics. Besides the prominent role played by the linear birefringence, the influence of circular birefringence (the optical activity) is discussed as well and both the monochromatic and polychromatic singular beam shaping strategies are addressed. Under cylindrically symmetric light-matter interaction, the radially, azimuthally, and spirally polarized eigen-modes for the light field are revealed to be of a fundamental interest to describe the physical mechanisms at work when dealing with scalar and vectorial optical singularities. In addition, we also report on nontrivial effects arising from cylindrical symmetry breaking, e.g. tilting the incident beam with respect to the crystal optical axis.

© 2010 Optical Society of America

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2010 (3)

2009 (10)

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103, 103903 (2009).
[CrossRef] [PubMed]

Y. Luo and B. Lü, “Phase singularities of high numerical aperture radially and azimuthally polarized beams in the focal region,” J. Opt. A 11, 015707 (2009).

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[CrossRef]

I. Buinyi, V. Denisenko, and M. Soskin, “Topological structure in polarization resolved conoscopic patterns for nematic liquid crystal cells,” Opt. Commun. 282, 143–155 (2009).
[CrossRef]

V. Denisenko, V. Shvedov, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, A. Volyar, M. Soskin, and Yu. S. Kivshar, “Determination of topological charges of polychromatic optical vortices,” Opt. Express 17, 23374–23379 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23374.
[CrossRef]

T. A. Fadeyeva, A. F. Rubass, B. V. Sokolenko, and A. V. Volyar, “The vortex-beam ’precession’ in a rotating uniaxial crystal,” J. Opt. A 11, 094008 (2009).

E. Brasselet, Ya. Izdebskaya, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of optical spin-orbit coupling in uniaxial crystals,” Opt. Lett. 34, 1021–1023 (2009).
[CrossRef] [PubMed]

Ya. Izdebskaya, E. Brasselet, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of linear polarization conversion in uniaxial crystals,” Opt. Express 20, 18196–18208 (2009), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-18196.
[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 (5)

2006 (6)

2005 (5)

2004 (5)

R. Borghi and M. Santarsiero, “Nonparaxial propagation of spirally polarized optical beams,” J. Opt. Soc. Am. A 21, 2029–2037 (2004).
[CrossRef]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt. Lett. 29, 238–240 (2004).
[CrossRef] [PubMed]

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).

A. Volyar, Yu. Egorov, A. Rybas, and T. Fadeyeva, “The fine structure of “white” optical vortices in crystals,” Tech. Phys. Lett. 30, 82–89 (2004).
[CrossRef]

A. Ciattoni and C. Palma, “Anisotropic beam spreading in uniaxial crystals,” Opt. Commun. 231, 79–92 (2004).
[CrossRef]

2003 (5)

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]

A. Ciattoni, G. Cincotti, and C. Palma, “Circular polarized beams and vortex generation in uniaxial media,” J. Opt. Soc Am. A 20, 163–171 (2003).
[CrossRef]

A. Volyar and T. Fadeyeva, “Generation of singular beams in uniaxial crystals,” Opt. Spectrosc. 94, 264–274 (2003).
[CrossRef]

A. Volyar and T. Fadeyeva, “Decay and fusion of polarization umbilics of singular beam in crystal,” Opt. Spectrosc. 95, 285-29 (2003).
[CrossRef]

D. J. Armstrong, M. C. Philips, and A. V. Smith, “Generation of radially polarized beams with an imagerotating resonator,” Appl. Opt. 42, 3550–3554 (2003).
[CrossRef] [PubMed]

2002 (4)

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002).
[CrossRef]

Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10, 324–331 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-7-324.
[PubMed]

F. Treussart, R. Alleaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, and J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

C. Varin and M. Piche, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
[CrossRef]

2001 (4)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B. 72, 109–113 (2001).

F. Gori, “Polarization basis for vortex beams,” J. Opt. Soc. Am. A 18, 1612–1617 (2001).
[CrossRef]

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using spacevariant subwavelength metal strip grating,” Appl. Phys. Lett. 79, 1587–1589 (2001).
[CrossRef]

M. Soskin and M. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219 (2001).
[CrossRef]

2000 (2)

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express 7, 77–87 (2000), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-2-77.
[CrossRef] [PubMed]

1997 (1)

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]

1996 (1)

1991 (1)

1974 (1)

J. Nye and M. Berry, “Dislocations in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[CrossRef]

1936 (1)

R. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Ait-Ameur, K.

Alexeyev, C.

C. Alexeyev, A. Volyar, and M. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research Trends, ed. L. I. Chen(Nova Science Pub., 2007) pp. 131–223.

Alleaume, R.

F. Treussart, R. Alleaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, and J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Allen, L.

L. Allen, S. M. Barnet, and M. J. Padgett, “Optical Angular Momentum” (IOP Publishing, Bristol, 2003).

Alonso, M. A.

R. Borghi, M. Santarsiero, and M. A. Alonso, “Highly focused spirally polarized beams,” J. Opt. Soc Am. A 22, 1420–1431 (2005).
[CrossRef]

Armstrong, D. J.

Barnet, S. M.

L. Allen, S. M. Barnet, and M. J. Padgett, “Optical Angular Momentum” (IOP Publishing, Bristol, 2003).

Berry, M.

J. Nye and M. Berry, “Dislocations in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[CrossRef]

Beth, R.

R. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Biener, G.

Blit, S.

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Bomzon, Z.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002).
[CrossRef]

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using spacevariant subwavelength metal strip grating,” Appl. Phys. Lett. 79, 1587–1589 (2001).
[CrossRef]

Borghi, R.

R. Borghi, M. Santarsiero, and M. A. Alonso, “Highly focused spirally polarized beams,” J. Opt. Soc Am. A 22, 1420–1431 (2005).
[CrossRef]

R. Borghi and M. Santarsiero, “Nonparaxial propagation of spirally polarized optical beams,” J. Opt. Soc. Am. A 21, 2029–2037 (2004).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergaman, Oxfod, 1975).

Brasselet, E.

C. Loussert and E. Brasselet, “Efficient scalar and vectorial singular beam shaping using homogeneous anisotropic media,” Opt. Lett. 35, 7–9 (2010).
[CrossRef] [PubMed]

E. Brasselet, Ya. Izdebskaya, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of optical spin-orbit coupling in uniaxial crystals,” Opt. Lett. 34, 1021–1023 (2009).
[CrossRef] [PubMed]

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103, 103903 (2009).
[CrossRef] [PubMed]

Ya. Izdebskaya, E. Brasselet, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of linear polarization conversion in uniaxial crystals,” Opt. Express 20, 18196–18208 (2009), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-18196.
[CrossRef]

Brown, T. G.

Buinyi, I.

I. Buinyi, V. Denisenko, and M. Soskin, “Topological structure in polarization resolved conoscopic patterns for nematic liquid crystal cells,” Opt. Commun. 282, 143–155 (2009).
[CrossRef]

Ciattoni, A.

A. Ciattoni and C. Palma, “Anisotropic beam spreading in uniaxial crystals,” Opt. Commun. 231, 79–92 (2004).
[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]

A. Ciattoni, G. Cincotti, and C. Palma, “Circular polarized beams and vortex generation in uniaxial media,” J. Opt. Soc Am. A 20, 163–171 (2003).
[CrossRef]

Cincotti, G.

A. Ciattoni, G. Cincotti, and C. Palma, “Circular polarized beams and vortex generation in uniaxial media,” J. Opt. Soc Am. A 20, 163–171 (2003).
[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]

Courty, J. M.

F. Treussart, R. Alleaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, and J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Davidson, N.

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[CrossRef]

Denis, R. de Saint

Denisenko, V.

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

F. Flossman, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901 (2005).
[CrossRef]

Desyatnikov, A. S.

Ya. Izdebskaya, E. Brasselet, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of linear polarization conversion in uniaxial crystals,” Opt. Express 20, 18196–18208 (2009), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-18196.
[CrossRef]

E. Brasselet, Ya. Izdebskaya, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of optical spin-orbit coupling in uniaxial crystals,” Opt. Lett. 34, 1021–1023 (2009).
[CrossRef] [PubMed]

V. Denisenko, V. Shvedov, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, A. Volyar, M. Soskin, and Yu. S. Kivshar, “Determination of topological charges of polychromatic optical vortices,” Opt. Express 17, 23374–23379 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23374.
[CrossRef]

V. Shvedov, Ya. Izdebskaya, A. Rode, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Generation of optical bottle beams by incoherent white-light vortices,” Opt. Express 16, 20902–20907 (2008), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20902.
[CrossRef] [PubMed]

D. Neshev, A. Dreischuh, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Observation of polychromatic vortex solitons,” Opt. Lett. 33, 1851–1853 (2008).
[CrossRef] [PubMed]

A. Volyar, V. Shvedov, T. Fadeyeva, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Generation of single-charge optical vortices with an uniaxial crystal,” Opt. Express 14, 3724–3729 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3724.
[CrossRef]

A. Rubass, T. Fadeyeva, Yu. Egorov, V. Shvedov, A. Volyar, A. S. Desyatnikov, and Yu. S. Kivshar, “Spiral-like singular beams in gyrotropic crystals,” Proc. SPIE 624, 62540H-1–8 (2006).

V. Shvedov, W. Krolikowski, A. Volyar, D. N. Neshev, A. S. Desyatnikov, and Yu. S. Kivshar, “Focusing and correlation properties of white-light optical vortices,” Opt. Express 13, 7393–7398 (2005), http: //www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-19-7393.
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S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B. 72, 109–113 (2001).

Dreischuh, A.

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B. 72, 109–113 (2001).

Egorov, Yu.

T. Fadeyeva, A. Rubass, Yu. Egorov, A. Volyar, and G. Shvartzlander, “Quadrefringence of optical vortices in a uniaxial crystal,” J. Opt. Soc. Am. A 25, 1634–1641 (2008).
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A. Rubass, T. Fadeyeva, Yu. Egorov, V. Shvedov, A. Volyar, A. S. Desyatnikov, and Yu. S. Kivshar, “Spiral-like singular beams in gyrotropic crystals,” Proc. SPIE 624, 62540H-1–8 (2006).

A. Volyar, Yu. Egorov, A. Rybas, and T. Fadeyeva, “The fine structure of “white” optical vortices in crystals,” Tech. Phys. Lett. 30, 82–89 (2004).
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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).

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T. Fadeyeva and A. Volyar, “Nondiffracting vortex-beams in a birefringent chiral crystal,” J. Opt. Soc. Am. A 27, 13–20 (2010).
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T. Fadeyeva and A. Volyar, “Extreme spin-orbit coupling in crystal-travelling paraxial beams,” J. Opt. Soc. Am. A 27, 381–389 (2010).
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T. Fadeyeva, A. Rubass, Yu. Egorov, A. Volyar, and G. Shvartzlander, “Quadrefringence of optical vortices in a uniaxial crystal,” J. Opt. Soc. Am. A 25, 1634–1641 (2008).
[CrossRef]

A. Volyar, V. Shvedov, T. Fadeyeva, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Generation of single-charge optical vortices with an uniaxial crystal,” Opt. Express 14, 3724–3729 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3724.
[CrossRef]

A. Rubass, T. Fadeyeva, Yu. Egorov, V. Shvedov, A. Volyar, A. S. Desyatnikov, and Yu. S. Kivshar, “Spiral-like singular beams in gyrotropic crystals,” Proc. SPIE 624, 62540H-1–8 (2006).

A. Volyar and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 297–304 (2006).
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A. Volyar, Yu. Egorov, A. Rybas, and T. Fadeyeva, “The fine structure of “white” optical vortices in crystals,” Tech. Phys. Lett. 30, 82–89 (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).

A. Volyar and T. Fadeyeva, “Decay and fusion of polarization umbilics of singular beam in crystal,” Opt. Spectrosc. 95, 285-29 (2003).
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A. Volyar and T. Fadeyeva, “Generation of singular beams in uniaxial crystals,” Opt. Spectrosc. 94, 264–274 (2003).
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T. Fadeyeva, K. Kotlyarov, and A. Volyar, “Extreme spin-orbit coupling in Hermite-Gaussian beams in a uniaxial crystal,” arXiv:0902.3716 (2009).

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T. A. Fadeyeva, A. F. Rubass, B. V. Sokolenko, and A. V. Volyar, “The vortex-beam ’precession’ in a rotating uniaxial crystal,” J. Opt. A 11, 094008 (2009).

Floc’h, V. Le

F. Treussart, R. Alleaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, and J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
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F. Flossman, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901 (2005).
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R. Oron, S. Blit, N. Davidson, and A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
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S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B. 72, 109–113 (2001).

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E. Brasselet, Ya. Izdebskaya, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of optical spin-orbit coupling in uniaxial crystals,” Opt. Lett. 34, 1021–1023 (2009).
[CrossRef] [PubMed]

V. Denisenko, V. Shvedov, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, A. Volyar, M. Soskin, and Yu. S. Kivshar, “Determination of topological charges of polychromatic optical vortices,” Opt. Express 17, 23374–23379 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23374.
[CrossRef]

Ya. Izdebskaya, E. Brasselet, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of linear polarization conversion in uniaxial crystals,” Opt. Express 20, 18196–18208 (2009), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-18196.
[CrossRef]

D. Neshev, A. Dreischuh, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Observation of polychromatic vortex solitons,” Opt. Lett. 33, 1851–1853 (2008).
[CrossRef] [PubMed]

V. Shvedov, Ya. Izdebskaya, A. Rode, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Generation of optical bottle beams by incoherent white-light vortices,” Opt. Express 16, 20902–20907 (2008), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20902.
[CrossRef] [PubMed]

A. Volyar, V. Shvedov, T. Fadeyeva, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Generation of single-charge optical vortices with an uniaxial crystal,” Opt. Express 14, 3724–3729 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3724.
[CrossRef]

A. Rubass, T. Fadeyeva, Yu. Egorov, V. Shvedov, A. Volyar, A. S. Desyatnikov, and Yu. S. Kivshar, “Spiral-like singular beams in gyrotropic crystals,” Proc. SPIE 624, 62540H-1–8 (2006).

V. Shvedov, W. Krolikowski, A. Volyar, D. N. Neshev, A. S. Desyatnikov, and Yu. S. Kivshar, “Focusing and correlation properties of white-light optical vortices,” Opt. Express 13, 7393–7398 (2005), http: //www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-19-7393.
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Krolikowski, W.

E. Brasselet, Ya. Izdebskaya, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of optical spin-orbit coupling in uniaxial crystals,” Opt. Lett. 34, 1021–1023 (2009).
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V. Denisenko, V. Shvedov, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, A. Volyar, M. Soskin, and Yu. S. Kivshar, “Determination of topological charges of polychromatic optical vortices,” Opt. Express 17, 23374–23379 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23374.
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Ya. Izdebskaya, E. Brasselet, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of linear polarization conversion in uniaxial crystals,” Opt. Express 20, 18196–18208 (2009), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-18196.
[CrossRef]

V. Shvedov, Ya. Izdebskaya, A. Rode, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Generation of optical bottle beams by incoherent white-light vortices,” Opt. Express 16, 20902–20907 (2008), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20902.
[CrossRef] [PubMed]

D. Neshev, A. Dreischuh, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Observation of polychromatic vortex solitons,” Opt. Lett. 33, 1851–1853 (2008).
[CrossRef] [PubMed]

A. Volyar, V. Shvedov, T. Fadeyeva, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Generation of single-charge optical vortices with an uniaxial crystal,” Opt. Express 14, 3724–3729 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3724.
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V. Shvedov, W. Krolikowski, A. Volyar, D. N. Neshev, A. S. Desyatnikov, and Yu. S. Kivshar, “Focusing and correlation properties of white-light optical vortices,” Opt. Express 13, 7393–7398 (2005), http: //www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-19-7393.
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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).
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R. Oron, S. Blit, N. Davidson, and A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
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M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
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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).
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T. Fadeyeva, A. Rubass, Yu. Egorov, A. Volyar, and G. Shvartzlander, “Quadrefringence of optical vortices in a uniaxial crystal,” J. Opt. Soc. Am. A 25, 1634–1641 (2008).
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A. Rubass, T. Fadeyeva, Yu. Egorov, V. Shvedov, A. Volyar, A. S. Desyatnikov, and Yu. S. Kivshar, “Spiral-like singular beams in gyrotropic crystals,” Proc. SPIE 624, 62540H-1–8 (2006).

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T. A. Fadeyeva, A. F. Rubass, B. V. Sokolenko, and A. V. Volyar, “The vortex-beam ’precession’ in a rotating uniaxial crystal,” J. Opt. A 11, 094008 (2009).

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Ya. Izdebskaya, E. Brasselet, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of linear polarization conversion in uniaxial crystals,” Opt. Express 20, 18196–18208 (2009), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-18196.
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N. Passilly, R. de Saint Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” J. Opt. Soc. Am. A 22, 984–991 (2005).
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F. Treussart, R. Alleaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, and J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
[CrossRef] [PubMed]

Vander, R.

Varin, C.

C. Varin and M. Piche, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
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Vasnetsov, M.

M. Soskin and M. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219 (2001).
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M. Vasnetsov and K. Staliunas, Optical Vortices, in Horizons of World Physics 228 (Nova Science, 1999).

Visser, T. D.

Volyar, A.

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

T. Fadeyeva and A. Volyar, “Nondiffracting vortex-beams in a birefringent chiral crystal,” J. Opt. Soc. Am. A 27, 13–20 (2010).
[CrossRef]

V. Denisenko, V. Shvedov, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, A. Volyar, M. Soskin, and Yu. S. Kivshar, “Determination of topological charges of polychromatic optical vortices,” Opt. Express 17, 23374–23379 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23374.
[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]

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, A. Rubass, Yu. Egorov, A. Volyar, and G. Shvartzlander, “Quadrefringence of optical vortices in a uniaxial crystal,” J. Opt. Soc. Am. A 25, 1634–1641 (2008).
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A. Volyar, V. Shvedov, T. Fadeyeva, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Generation of single-charge optical vortices with an uniaxial crystal,” Opt. Express 14, 3724–3729 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3724.
[CrossRef]

A. Rubass, T. Fadeyeva, Yu. Egorov, V. Shvedov, A. Volyar, A. S. Desyatnikov, and Yu. S. Kivshar, “Spiral-like singular beams in gyrotropic crystals,” Proc. SPIE 624, 62540H-1–8 (2006).

A. Volyar and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 297–304 (2006).
[CrossRef]

V. Shvedov, W. Krolikowski, A. Volyar, D. N. Neshev, A. S. Desyatnikov, and Yu. S. Kivshar, “Focusing and correlation properties of white-light optical vortices,” Opt. Express 13, 7393–7398 (2005), http: //www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-19-7393.
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Y. Izdebskaya, V. Shvedov, and A. Volyar, “Generation of higher-order optical vortices by a dielectric wedge,” Opt. Lett. 30, 2472–2474 (2005).
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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).

A. Volyar, Yu. Egorov, A. Rybas, and T. Fadeyeva, “The fine structure of “white” optical vortices in crystals,” Tech. Phys. Lett. 30, 82–89 (2004).
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A. Volyar and T. Fadeyeva, “Generation of singular beams in uniaxial crystals,” Opt. Spectrosc. 94, 264–274 (2003).
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A. Volyar and T. Fadeyeva, “Decay and fusion of polarization umbilics of singular beam in crystal,” Opt. Spectrosc. 95, 285-29 (2003).
[CrossRef]

T. Fadeyeva, K. Kotlyarov, and A. Volyar, “Extreme spin-orbit coupling in Hermite-Gaussian beams in a uniaxial crystal,” arXiv:0902.3716 (2009).

C. Alexeyev, A. Volyar, and M. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research Trends, ed. L. I. Chen(Nova Science Pub., 2007) pp. 131–223.

Volyar, A. V.

T. A. Fadeyeva, A. F. Rubass, B. V. Sokolenko, and A. V. Volyar, “The vortex-beam ’precession’ in a rotating uniaxial crystal,” J. Opt. A 11, 094008 (2009).

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F. Treussart, R. Alleaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, and J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
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Yavorsky, M.

C. Alexeyev, A. Volyar, and M. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research Trends, ed. L. I. Chen(Nova Science Pub., 2007) pp. 131–223.

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Zhan, Q.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. B (1)

C. Varin and M. Piche, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74, S83–S88 (2002).
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Appl. Phys. B. (1)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, “The focus of light-theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B. 72, 109–113 (2001).

Appl. Phys. Lett. (2)

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
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Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using spacevariant subwavelength metal strip grating,” Appl. Phys. Lett. 79, 1587–1589 (2001).
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J. Opt. A (3)

Y. Luo and B. Lü, “Phase singularities of high numerical aperture radially and azimuthally polarized beams in the focal region,” J. Opt. A 11, 015707 (2009).

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).

T. A. Fadeyeva, A. F. Rubass, B. V. Sokolenko, and A. V. Volyar, “The vortex-beam ’precession’ in a rotating uniaxial crystal,” J. Opt. A 11, 094008 (2009).

J. Opt. Soc Am. A (2)

A. Ciattoni, G. Cincotti, and C. Palma, “Circular polarized beams and vortex generation in uniaxial media,” J. Opt. Soc Am. A 20, 163–171 (2003).
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R. Borghi, M. Santarsiero, and M. A. Alonso, “Highly focused spirally polarized beams,” J. Opt. Soc Am. A 22, 1420–1431 (2005).
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J. Opt. Soc. Am. A (7)

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

I. Buinyi, V. Denisenko, and M. Soskin, “Topological structure in polarization resolved conoscopic patterns for nematic liquid crystal cells,” Opt. Commun. 282, 143–155 (2009).
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A. Ciattoni and C. Palma, “Anisotropic beam spreading in uniaxial crystals,” Opt. Commun. 231, 79–92 (2004).
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Opt. Express (9)

Ya. Izdebskaya, E. Brasselet, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of linear polarization conversion in uniaxial crystals,” Opt. Express 20, 18196–18208 (2009), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-18196.
[CrossRef]

V. Shvedov, W. Krolikowski, A. Volyar, D. N. Neshev, A. S. Desyatnikov, and Yu. S. Kivshar, “Focusing and correlation properties of white-light optical vortices,” Opt. Express 13, 7393–7398 (2005), http: //www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-19-7393.
[CrossRef] [PubMed]

A. Volyar, V. Shvedov, T. Fadeyeva, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Generation of single-charge optical vortices with an uniaxial crystal,” Opt. Express 14, 3724–3729 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3724.
[CrossRef]

V. Denisenko, V. Shvedov, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, A. Volyar, M. Soskin, and Yu. S. Kivshar, “Determination of topological charges of polychromatic optical vortices,” Opt. Express 17, 23374–23379 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23374.
[CrossRef]

V. Shvedov, Ya. Izdebskaya, A. Rode, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Generation of optical bottle beams by incoherent white-light vortices,” Opt. Express 16, 20902–20907 (2008), http://www. opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20902.
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K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express 7, 77–87 (2000), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-2-77.
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Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10, 324–331 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-7-324.
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D. W. Diehl, R. W. Schoonover, and T. D. Visser, “The structure of focused, radially polarized fields,” Opt. Express 14, 3030–3038 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI= oe-14-7-3030.
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R. W. Schoonover and T. D. Visser, “Polarization singularities of focused, radially polarized fields,” Opt. Express 14, 5733–5745 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI= oe-14-12-5733.
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Opt. Lett. (9)

C. Loussert and E. Brasselet, “Efficient scalar and vectorial singular beam shaping using homogeneous anisotropic media,” Opt. Lett. 35, 7–9 (2010).
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A. Shoham, R. Vander, and S. G. Lipson, “Production of radially and azimuthally polarized polychromatic beams,” Opt. Lett. 31, 3405–3407 (2006).
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A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt. Lett. 29, 238–240 (2004).
[CrossRef] [PubMed]

Y. Izdebskaya, V. Shvedov, and A. Volyar, “Generation of higher-order optical vortices by a dielectric wedge,” Opt. Lett. 30, 2472–2474 (2005).
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M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21, 1948–1950 (1996).
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H. Kawauchi, Yu. Kozawa, and Sh. Sato, “Generation of radially polarized Ti:sapphire laser beam using a c-cut crystal,” Opt. Lett. 33, 1984–1986 (2008).
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Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002).
[CrossRef]

D. Neshev, A. Dreischuh, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Observation of polychromatic vortex solitons,” Opt. Lett. 33, 1851–1853 (2008).
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E. Brasselet, Ya. Izdebskaya, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Dynamics of optical spin-orbit coupling in uniaxial crystals,” Opt. Lett. 34, 1021–1023 (2009).
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Opt. Spectrosc. (3)

A. Volyar and T. Fadeyeva, “Laguerre-Gaussian beams with complex and real arguments in uniaxial crystals,” Opt. Spectrosc. 101, 297–304 (2006).
[CrossRef]

A. Volyar and T. Fadeyeva, “Generation of singular beams in uniaxial crystals,” Opt. Spectrosc. 94, 264–274 (2003).
[CrossRef]

A. Volyar and T. Fadeyeva, “Decay and fusion of polarization umbilics of singular beam in crystal,” Opt. Spectrosc. 95, 285-29 (2003).
[CrossRef]

Phys. Rev. (1)

R. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Phys. Rev. A. (1)

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. E (1)

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. (4)

F. Flossman, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901 (2005).
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E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103, 103903 (2009).
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F. Treussart, R. Alleaume, V. Le Floc’h, L. T. Xiao, J. M. Courty, and J.-F. Roch, “Direct measurement of the photon statistics of a triggered single photon source,” Phys. Rev. Lett. 89, 093601 (2002).
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Proc. SPIE (1)

A. Rubass, T. Fadeyeva, Yu. Egorov, V. Shvedov, A. Volyar, A. S. Desyatnikov, and Yu. S. Kivshar, “Spiral-like singular beams in gyrotropic crystals,” Proc. SPIE 624, 62540H-1–8 (2006).

Prog. Opt. (2)

M. Soskin and M. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219 (2001).
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M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: Optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
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Tech. Phys. Lett. (1)

A. Volyar, Yu. Egorov, A. Rybas, and T. Fadeyeva, “The fine structure of “white” optical vortices in crystals,” Tech. Phys. Lett. 30, 82–89 (2004).
[CrossRef]

Other (7)

G. N. Ramachandran and S. Ramaseshan, “Crystal optics” in Handbuch der Physik (Springer, Berlin, 1961).

J. F. Nye, Natural focusing and fine structure of light (Inst. of Phys. Pub., Bristol, 1999).

M. Vasnetsov and K. Staliunas, Optical Vortices, in Horizons of World Physics 228 (Nova Science, 1999).

L. Allen, S. M. Barnet, and M. J. Padgett, “Optical Angular Momentum” (IOP Publishing, Bristol, 2003).

C. Alexeyev, A. Volyar, and M. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research Trends, ed. L. I. Chen(Nova Science Pub., 2007) pp. 131–223.

M. Born and E. Wolf, Principles of Optics (Pergaman, Oxfod, 1975).

T. Fadeyeva, K. Kotlyarov, and A. Volyar, “Extreme spin-orbit coupling in Hermite-Gaussian beams in a uniaxial crystal,” arXiv:0902.3716 (2009).

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Figures (8)

Fig. 1.
Fig. 1.

(a) On-axis propagation of a Gaussian beam; c is a unit vector that defines optical axis z. (b) Shaping of the TE and TM eigen-modes; corresponding directions of the electric field are indicated in (c) with arrows.

Fig. 2.
Fig. 2.

Optical arrangement used for polarization shaping of an incident beam with uniform circular polarization and two kinds of combination for a c-cut crystal and a phase plate, which introduce a phase delay δ between direction at ±45° from the x and y axis. The spatial distribution of the polarization state is made in the observation plane after the two anisotropic optical elements. The geometries shown in (a) and (b) correspond to polarization distributions in (c) and (d), respectively, with the values of phase difference δ indicated. The ellipses of RCP (red) and LCP (blue) are shown by their main axes.

Fig. 3.
Fig. 3.

(a) Degenerated white optical vortex; (b) splintered white optical vortices; (c) color distributions in the vicinity of the shifted vortex core [43].

Fig. 4.
Fig. 4.

(a) The spin (SAM) and orbital (OAM) angular momenta for the circularly polarized components of the Gaussian beam with waist 4.6 μm (dashed lines) and 11 μm (solid lines) [54]. (b) Intensity distributions of the circularly polarized field components and (c) spin momentum of the Bessel-Gaussian beam of the lowest order l = 0 in LiNbO3 crystal [20].

Fig. 5.
Fig. 5.

(a) Maps of the polarization states on the background of the intensity distribution of a Bessel beam; the curves show the directions of the major axes of polarization ellipses [35]. (b) Theoretical and (c) experimental maps of the polarization states, and (d) the theoretical edge dislocation lines for the monochromatic light. (e) Experimental intensity distribution of the polychromatic light from a halogen lamp for the Gaussian beam after the system of two SiO2 birefringent chiral crystals with opposite signs of chirality [56].

Fig. 6.
Fig. 6.

Output polarization (a) and intensity (b) distributions of the circularly polarized field component orthogonal to the incident circularly polarized Gaussian beam impinging at oblique incidence onto a c-cut crystal. (c) Splitting of the left-handed beam component at the inclination angle α = 10° [59].

Fig. 7.
Fig. 7.

Numerically calculated (a) intensity and (b) phase profiles of the on-axis x-polarized field component at 6 mm propagation length; white lines in (b) show intensity contours [46]. (c) The polarization map of the total transmitted field with ellipses of the left-hand (red) and right-hand (blue) polarizations indicated by their main axes. Blue ellipse and red triangle indicate the monstar and star polarization singularities and black lines show the phase contours in (b). (d) Experimentally measured output white-light intensity profiles with optimal input angle α for different propagation distances, as indicated [55].

Fig. 8.
Fig. 8.

(a) Intensity and (b, c) polarization distributions in the splintered partial beams in the LiNbO3 crystal on the background of the distribution of the ellipticity (gray scale from -1 to 1) of the polarization states. The initial beam has the right-hand polarization and the centered optical vortex with the topological charge l = −3. (d) The key fragment of the vortex trajectories in the LCP component for the initial triple-charge vortex beam [59].

Equations (1)

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Φ̂=(cos(δ/2)isin(δ/2)exp(i2ϕ)isin(δ/2)exp(i2ϕ)cos(δ/2)).

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