Abstract

We experimentally demonstrated the generation of orthogonally circular polarized states embedded in nonplanar geometric beams. Experimental results revealed that the production of circularly polarized beams, induced by crystal birefringence, is quantized. Numerical analyses of the polarization and the spatial morphology are consistent with the experimental results.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2015 (1)

2014 (2)

2012 (2)

X. Lu and L. Chen, “Spin-orbit interactions of a Gaussian light propagating in biaxial crystals,” Opt. Express 20(11), 11753–11766 (2012).
[Crossref] [PubMed]

T. H. Lu and L. H. Lin, “Observation of a superposition of orthogonally polarized geometric beams with a c-cut Nd:YVO4 crystal,” Appl. Phys. B 106(4), 863–866 (2012).
[Crossref]

2010 (5)

2009 (1)

2008 (1)

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-Dimensional Coherent Optical Waves Localized on Trochoidal Parametric Surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

2007 (2)

Y. Kozawa, K. Yonezawa, and S. Sato, “Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal,” Appl. Phys. B 88(1), 43–46 (2007).
[Crossref]

T. H. Lu, Y. F. Chen, and K. F. Huang, “Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026614 (2007).
[Crossref] [PubMed]

2006 (2)

K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31(14), 2151–2153 (2006).
[Crossref] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

2004 (1)

2003 (1)

Brasselet, E.

Chen, H.

Chen, L.

Chen, Y. F.

Y. T. Yu, P. H. Tuan, K. F. Huang, and Y. F. Chen, “Exploring the influence of boundary shapes on emission angular distributions and polarization states of broad-area vertical-cavity surface-emitting lasers,” Opt. Express 22(22), 26939–26946 (2014).
[Crossref] [PubMed]

T. H. Lu, Y. C. Lin, H. C. Liang, Y. J. Huang, Y. F. Chen, and K. F. Huang, “Observation of lasing modes with exotic localized wave patterns from astigmatic large-Fresnel-number cavities,” Opt. Lett. 35(3), 345–347 (2010).
[Crossref] [PubMed]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-Dimensional Coherent Optical Waves Localized on Trochoidal Parametric Surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

T. H. Lu, Y. F. Chen, and K. F. Huang, “Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026614 (2007).
[Crossref] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

Ciattoni, A.

Cincotti, G.

Clarkson, W. A.

Crespi, A.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization Entangled State Measurement on a Chip,” Phys. Rev. Lett. 105(20), 200503 (2010).
[Crossref] [PubMed]

Desyatnikov, A.

Desyatnikov, A. S.

Ding, J.

Fadeyeva, T. A.

Huang, K. F.

Y. T. Yu, P. H. Tuan, K. F. Huang, and Y. F. Chen, “Exploring the influence of boundary shapes on emission angular distributions and polarization states of broad-area vertical-cavity surface-emitting lasers,” Opt. Express 22(22), 26939–26946 (2014).
[Crossref] [PubMed]

T. H. Lu, Y. C. Lin, H. C. Liang, Y. J. Huang, Y. F. Chen, and K. F. Huang, “Observation of lasing modes with exotic localized wave patterns from astigmatic large-Fresnel-number cavities,” Opt. Lett. 35(3), 345–347 (2010).
[Crossref] [PubMed]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-Dimensional Coherent Optical Waves Localized on Trochoidal Parametric Surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

T. H. Lu, Y. F. Chen, and K. F. Huang, “Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026614 (2007).
[Crossref] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

Huang, Y. J.

Izdebskaya, Y.

Izdebskaya, Y. V.

Kivshar, Y. S.

Klimov, A. B.

A. B. Klimov, J. L. Romere, and S. Wallentowitz, “Quantum-state tomography for optical polarization with arbitrary photon numbers,” Phys. Rev. A 89(2), 020101 (2014).
[Crossref]

Kozawa, Y.

Y. Kozawa, K. Yonezawa, and S. Sato, “Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal,” Appl. Phys. B 88(1), 43–46 (2007).
[Crossref]

K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31(14), 2151–2153 (2006).
[Crossref] [PubMed]

Krolikowski, W.

Lerman, G. M.

Levy, U.

Liang, H. C.

Lin, D.

Lin, L. H.

T. H. Lu and L. H. Lin, “Observation of a superposition of orthogonally polarized geometric beams with a c-cut Nd:YVO4 crystal,” Appl. Phys. B 106(4), 863–866 (2012).
[Crossref]

Lin, Y. C.

T. H. Lu, Y. C. Lin, H. C. Liang, Y. J. Huang, Y. F. Chen, and K. F. Huang, “Observation of lasing modes with exotic localized wave patterns from astigmatic large-Fresnel-number cavities,” Opt. Lett. 35(3), 345–347 (2010).
[Crossref] [PubMed]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-Dimensional Coherent Optical Waves Localized on Trochoidal Parametric Surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

Lu, T. H.

T. H. Lu and L. H. Lin, “Observation of a superposition of orthogonally polarized geometric beams with a c-cut Nd:YVO4 crystal,” Appl. Phys. B 106(4), 863–866 (2012).
[Crossref]

T. H. Lu, Y. C. Lin, H. C. Liang, Y. J. Huang, Y. F. Chen, and K. F. Huang, “Observation of lasing modes with exotic localized wave patterns from astigmatic large-Fresnel-number cavities,” Opt. Lett. 35(3), 345–347 (2010).
[Crossref] [PubMed]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-Dimensional Coherent Optical Waves Localized on Trochoidal Parametric Surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

T. H. Lu, Y. F. Chen, and K. F. Huang, “Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026614 (2007).
[Crossref] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

Lu, X.

Mataloni, P.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization Entangled State Measurement on a Chip,” Phys. Rev. Lett. 105(20), 200503 (2010).
[Crossref] [PubMed]

Neshev, D. N.

Osellame, R.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization Entangled State Measurement on a Chip,” Phys. Rev. Lett. 105(20), 200503 (2010).
[Crossref] [PubMed]

Palma, C.

Ramponi, R.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization Entangled State Measurement on a Chip,” Phys. Rev. Lett. 105(20), 200503 (2010).
[Crossref] [PubMed]

Romere, J. L.

A. B. Klimov, J. L. Romere, and S. Wallentowitz, “Quantum-state tomography for optical polarization with arbitrary photon numbers,” Phys. Rev. A 89(2), 020101 (2014).
[Crossref]

Sansoni, L.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization Entangled State Measurement on a Chip,” Phys. Rev. Lett. 105(20), 200503 (2010).
[Crossref] [PubMed]

Sato, S.

Y. Kozawa, K. Yonezawa, and S. Sato, “Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal,” Appl. Phys. B 88(1), 43–46 (2007).
[Crossref]

K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31(14), 2151–2153 (2006).
[Crossref] [PubMed]

Sciarrino, F.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization Entangled State Measurement on a Chip,” Phys. Rev. Lett. 105(20), 200503 (2010).
[Crossref] [PubMed]

Shvedov, V.

Shvedov, V. G.

Stern, L.

Su, K. W.

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

Tuan, P. H.

Vallone, G.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization Entangled State Measurement on a Chip,” Phys. Rev. Lett. 105(20), 200503 (2010).
[Crossref] [PubMed]

Volyar, A. V.

Wallentowitz, S.

A. B. Klimov, J. L. Romere, and S. Wallentowitz, “Quantum-state tomography for optical polarization with arbitrary photon numbers,” Phys. Rev. A 89(2), 020101 (2014).
[Crossref]

Wang, H. T.

Yonezawa, K.

Y. Kozawa, K. Yonezawa, and S. Sato, “Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal,” Appl. Phys. B 88(1), 43–46 (2007).
[Crossref]

K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31(14), 2151–2153 (2006).
[Crossref] [PubMed]

Yu, Y. T.

Zhan, Q.

Zhang, B. F.

Zheng, Z.

Appl. Phys. B (2)

Y. Kozawa, K. Yonezawa, and S. Sato, “Radially polarized laser beam from a Nd:YAG laser cavity with a c-cut YVO4 crystal,” Appl. Phys. B 88(1), 43–46 (2007).
[Crossref]

T. H. Lu and L. H. Lin, “Observation of a superposition of orthogonally polarized geometric beams with a c-cut Nd:YVO4 crystal,” Appl. Phys. B 106(4), 863–866 (2012).
[Crossref]

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

Opt. Express (5)

Opt. Lett. (5)

Phys. Rev. A (1)

A. B. Klimov, J. L. Romere, and S. Wallentowitz, “Quantum-state tomography for optical polarization with arbitrary photon numbers,” Phys. Rev. A 89(2), 020101 (2014).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

T. H. Lu, Y. F. Chen, and K. F. Huang, “Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(2), 026614 (2007).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization Entangled State Measurement on a Chip,” Phys. Rev. Lett. 105(20), 200503 (2010).
[Crossref] [PubMed]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-Dimensional Coherent Optical Waves Localized on Trochoidal Parametric Surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Experimental setup and 3D trajectory of the circular geometric mode from the near field to the far field. Experimental transverse patterns of the 3D geometric mode at (a) z=0 , (b) z=1.15mm , (c) z=2.48mm , (d) z=4.27mm , (e) z=7.39mm , and (f) far field.
Fig. 2
Fig. 2 (a) Side view of the nonplanar geometric mode with left and right circularly polarized states. (b) Experimental far field pattern. (c) Enlargement of the beam at an angle θ from the z axis, and the corresponding refractive indices.
Fig. 3
Fig. 3 Phase retardation values related to different m values. Dot: experimental result. Line: numerical result.
Fig. 4
Fig. 4 Numerical results of superposed LG modes according to Eqs. (4) and (5) with ( p 0 , l 0 )=( 0,60 ) and M=4 from z=0 to the far field corresponding to experimental results in Fig. 1. The scale bars represent 100μm in (a)-(e) and 30cm in (f).
Fig. 5
Fig. 5 Phase distribution of the superposed LG modes corresponding to Fig. 4.

Equations (5)

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n eff = n o n e n e 2 cos 2 θ+ n o 2 sin 2 θ .
δ=( 2πd λ )( n eff cos( θ eff ) n o cos( θ o ) )
Φ p,l,s ( ρ,z )= 2p! π( p+| l | )! 1 w( z ) ( 2 ρ w( z ) ) | l | L p | l | ( 2 ρ 2 w ( z ) 2 )exp[ ρ 2 w ( z ) 2 ], ×exp{ i k p,l,s z[ 1+ ρ 2 2( z 2 + z R 2 ) ] }exp[ i( 2p+| l |+1 ) θ G ( z ) ]
E R ( ρ,ϕ,z )= k=M M C k M e ilϕ Φ p 0 , l 0 +3k, s 0 k ( ρ,z ),
E L ( ρ,ϕ,z )= k=M M C k M e ilϕ Φ p 0 , l 0 +3k, s 0 k ( ρ,z ),

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