Abstract

Both radially polarized and azimuthally polarized beams can be decomposed into linear combinations of circularly polarized vortex beams having opposite vortex charges. We show experimental evidence for this decomposition using a specially designed vortex sensing diffraction grating that generates multiple vortex patterns having different senses of circularly polarization in the different diffracted orders. When this grating is illuminated with a radially or azimuthally polarized beam, the grating separates the components into different diffracted orders. Experimental results are shown.

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  18. http://www.arcoptix.com/
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2009 (2)

2008 (2)

A. Niv, Y. Gorodetski, V. Kleiner, and E. Hasman, “Topological spin-orbit interaction of light in anisotropic inhomogeneous subwavelength structures,” Opt. Lett. 33(24), 2910–2912 (2008).
[CrossRef] [PubMed]

A. Y. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction with embedded phase singularity,” Opt. Commun. 281(6), 1366–1374 (2008).
[CrossRef]

2007 (3)

2005 (3)

2004 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

2001 (2)

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
[CrossRef]

J. A. Davis, J. Adachi, C. R. Fernández-Pousa, and I. Moreno, “Polarization beam splitters using polarization diffraction gratings,” Opt. Lett. 26(9), 587–589 (2001).
[CrossRef]

2000 (2)

1996 (1)

1990 (2)

V. Yu Bazhenov, V. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocations in their wave-fronts,” JETP Lett. 52, 429–431 (1990).

S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29(15), 2234–2239 (1990).
[CrossRef] [PubMed]

Adachi, J.

Barnett, S. M.

Bekshaev, A. Y.

A. Y. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction with embedded phase singularity,” Opt. Commun. 281(6), 1366–1374 (2008).
[CrossRef]

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” N. J. Phys. 9(3), 78 (2007).
[CrossRef]

Bomzon, Z.

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
[CrossRef]

Bu, J.

Burge, R. E.

Cottrell, D. M.

Courjon, D.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005).
[CrossRef]

Courtial, J.

Davis, J. A.

Ding, J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Evans, G. H.

Fernández-Pousa, C. R.

Ford, D. H.

Franke-Arnold, S.

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” N. J. Phys. 9(3), 78 (2007).
[CrossRef]

Gao, B. Z.

Gibson, G.

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Gorodetski, Y.

Grosjean, T.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005).
[CrossRef]

Guo, C.-S.

Hasman, E.

A. Niv, Y. Gorodetski, V. Kleiner, and E. Hasman, “Topological spin-orbit interaction of light in anisotropic inhomogeneous subwavelength structures,” Opt. Lett. 33(24), 2910–2912 (2008).
[CrossRef] [PubMed]

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
[CrossRef]

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” N. J. Phys. 9(3), 78 (2007).
[CrossRef]

Jureller, J. E.

Karamoch, A. I.

A. Y. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction with embedded phase singularity,” Opt. Commun. 281(6), 1366–1374 (2008).
[CrossRef]

Kimura, W. D.

Kleiner, V.

A. Niv, Y. Gorodetski, V. Kleiner, and E. Hasman, “Topological spin-orbit interaction of light in anisotropic inhomogeneous subwavelength structures,” Opt. Lett. 33(24), 2910–2912 (2008).
[CrossRef] [PubMed]

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
[CrossRef]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” N. J. Phys. 9(3), 78 (2007).
[CrossRef]

McNamara, D. E.

Mitry, M. J.

Moh, K. J.

Moreno, I.

Morita, R.

Ni, W.-J.

Niv, A.

Oka, K.

Padgett, M. J.

Park, S.

Pas’ko, V.

Pascoguin, B. M. L.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” N. J. Phys. 9(3), 78 (2007).
[CrossRef]

Sabac, A.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005).
[CrossRef]

Schadt, M.

Scherer, N. F.

Sonehara, T.

Soskin, M. S.

V. Yu Bazhenov, V. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocations in their wave-fronts,” JETP Lett. 52, 429–431 (1990).

Stalder, M.

Tidwell, S. C.

Tokizane, Y.

Toussaint, K. C.

Vasnetsov, M.

Vasnetsov, V.

V. Yu Bazhenov, V. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocations in their wave-fronts,” JETP Lett. 52, 429–431 (1990).

Wang, H.-T.

Wang, X.-L.

Yu Bazhenov, V.

V. Yu Bazhenov, V. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocations in their wave-fronts,” JETP Lett. 52, 429–431 (1990).

Yuan, X.-C.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
[CrossRef]

JETP Lett. (1)

V. Yu Bazhenov, V. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocations in their wave-fronts,” JETP Lett. 52, 429–431 (1990).

N. J. Phys. (1)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” N. J. Phys. 9(3), 78 (2007).
[CrossRef]

Opt. Commun. (3)

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light into a tighter spot,” Opt. Commun. 179(1-6), 1–7 (2000).
[CrossRef]

A. Y. Bekshaev and A. I. Karamoch, “Spatial characteristics of vortex light beams produced by diffraction with embedded phase singularity,” Opt. Commun. 281(6), 1366–1374 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (6)

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Other (1)

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Figures (6)

Fig. 1
Fig. 1

(a,b) Decomposition of radially and azimuthally polarized beams as the superposition of two circularly polarized vortex beams with opposite helicity and opposite topological charge. (c) Scheme of the liquid crystal director structure of the radial polarization converter (RPC) device.

Fig. 2
Fig. 2

Experimental patterns of the beam emerging from the radial polarization converter device. (a) Azimuthally polarized beam, (b) Radially polarized beam, (c) Circularly polarized vortex beam. The left column shows the results without analyzer (polarization states has been drawn as a watermark). The central and right columns show respectively the results with a vertically and horizontally oriented analyzer.

Fig. 3
Fig. 3

Binary phase gratings with embedded singularity: (a) = + 1 , (b) = 1 .

Fig. 4
Fig. 4

Experimental patterns generated by the polarization diffraction grating. In (a-c) the pattern is analyzed through a linear polarizer oriented (a) horizontally, (b) at 45° and (c) vertically. In (d-e) the pattern is analyzed through a circular polarizer that transmits (d) both left and right circular polarizations, (e) left circular polarization, and (f) right circular polarization.

Fig. 5
Fig. 5

Experimental pattern generated when the polarization diffraction grating is illuminated with (a-c) radially polarized light and (d-f) azimuthally polarized light. In (a,d) the grating is switched off. In (b,e) the vortex grating with = + 1 is displayed. In (c,f) the vortex grating with = 1 is displayed.

Fig. 6
Fig. 6

Experimental diffraction pattern generated when the polarization diffraction grating is illuminated with the circularly polarized vortex beam. (a-c) correspond to G C, and (d-f) to G C, + . In (a,d) the grating is switched off. The displayed grating has = + 1 in (b,e), and = 1 in (c,f).

Equations (15)

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E RAD = ( cos ϕ sin ϕ ) = ( 1 2 ( e i ϕ + e i ϕ ) 1 2 i ( e i ϕ e i ϕ ) ) = 1 2 e i ϕ ( 1 i ) + 1 2 e i ϕ ( 1 + i ) .
E AZ = ( sin ϕ cos ϕ ) = ( 1 2 i ( e i ϕ e i ϕ ) 1 2 ( e i ϕ + e i ϕ ) ) = i { 1 2 e i ϕ ( 1 i ) 1 2 e i ϕ ( 1 + i ) } .
E RAD ± i E AZ = ( cos ϕ sin ϕ ) ± i ( sin ϕ cos ϕ ) = e i ϕ ( 1 ± i ) .
G L ( x , y ) = ( 1 0 0 G ( x , y ) ) = ( 1 0 0 0 ) + G ( x , y ) ( 0 0 0 1 ) .
G ( x , y ) = n = c n e i n 2 π x / D ,
G L ( x , y ) = ( 1 0 0 0 ) + 2 π ( e + i 2 π x / D + e i 2 π x / D ) ( 0 0 0 1 ) .
G C ± ( x , y ) = W λ / 4 ( ± 45 o ) G L ( x , y ) W λ / 4 ( 45 o ) = = 1 2 ( i 1 ± 1 i ) + 1 π ( e + i 2 π x / D + e i 2 π x / D ) ( i ± 1 1 i ) .
W λ / 4 ( θ ) = R ( θ ) ( 1 0 0 i ) R ( + θ ) .
R ( θ ) = ( cos θ sin θ sin θ cos θ ) .
G ( x , y ) = n = c n e i n φ e i n 2 π x / D .
G ( x , y ) = 2 π ( e i φ e i 2 π x / D + e i φ e i 2 π x / D ) .
G C, ± ( x , y ) = 1 2 ( i 1 ± 1 i ) + 1 π ( e i ϕ e i 2 π x / D + e i ϕ e + i 2 π x / D ) ( i ± 1 1 i ) .
G C, + ( x , y ) ( 0 1 ) = 1 2 ( 1 i ) + 1 π ( e i ϕ e + i 2 π x / D + e i ϕ e i 2 π x / D ) ( 1 + i ) .
G C, + ( x , y ) E RAD = i e i ϕ ( 1 i ) + 2 i π ( e i 2 π x / D + e i 2 ϕ e + i 2 π x / D ) ( 1 + i ) .
G C, = + 1 + ( x , y ) E AZ = e i ϕ ( 1 i ) 2 i π ( e i 2 ϕ e i 2 π x / D e + i 2 π x / D ) ( 1 + i ) .

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