Abstract

We demonstrate that an annulus of light whose polarization is linear at each point, but the plane of polarization gradually rotates by π radians can be used to generate Bessel-Poincaré beams. In any transverse plane this beam exhibits concentric rings of polarization singularities in the form of L-lines, where the polarization is purely linear. Although the L-lines are invisible in terms of light intensity variations, we present a simple way to visualize them as dark rings around a sharp peak of intensity in the beam center. To do this we use a segmented polarizer whose transmission axes are oriented differently in each segment. The radius of the first L-line is always smaller than the radius of the central disk of the zero-order Bessel beam that would be produced if the annulus were homogeneously polarized and had no phase circulation along it.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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2015 (2)

2014 (1)

2013 (3)

2012 (3)

2010 (1)

2009 (2)

2007 (3)

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun. 272(2), 314–319 (2007).
[Crossref]

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[Crossref]

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

2005 (2)

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[Crossref]

2004 (2)

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
[Crossref]

C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43(22), 4322–4327 (2004).
[Crossref] [PubMed]

2002 (1)

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209(1-3), 155–165 (2002).
[Crossref]

2000 (1)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

1995 (1)

Z. Bouchal and M. Olivík, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42(8), 1555–1566 (1995).
[Crossref]

1987 (1)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

1964 (1)

P. Jacquinot and B. Roizen-Dossier, “Apodisation,” Prog. Opt. 3, 29–186 (1964).
[Crossref]

Alonso, M. A.

April, A.

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

Beckley, A. M.

Bernet, S.

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

Berry, M. V.

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[Crossref]

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[Crossref]

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
[Crossref]

Bouchal, Z.

Z. Bouchal and M. Olivík, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42(8), 1555–1566 (1995).
[Crossref]

Brown, T. G.

Campos, J.

Cardano, F.

Choudhury, A.

Courjon, D.

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun. 272(2), 314–319 (2007).
[Crossref]

de Lisio, C.

Dehez, H.

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]

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

Donegan, J. F.

Dudley, A.

Durnin, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Escuti, M.

Forbes, A.

Fürhapter, S.

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

Galvez, E. J.

Grosjean, T.

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun. 272(2), 314–319 (2007).
[Crossref]

Hnatovsky, C.

Jacquinot, P.

P. Jacquinot and B. Roizen-Dossier, “Apodisation,” Prog. Opt. 3, 29–186 (1964).
[Crossref]

Jeffrey, M. R.

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[Crossref]

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[Crossref]

Jesacher, A.

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

Kalkandjiev, T. K.

Karimi, E.

Khadka, S.

Kozawa, Y.

Krolikowski, W.

Li, Y.

Lindberg, J.

J. Lindberg, “Mathematical concepts of optical superresolution,” J. Opt. 14(8), 083001 (2012).
[Crossref]

Lizana, A.

Loiko, Y.

Loiko, Y. V.

Lunney, J. G.

Mansuripur, M.

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[Crossref]

Marrucci, L.

Maurer, C.

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

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

Mhlanga, T.

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Mompart, J.

Nomoto, S.

O’Dwyer, D. P.

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular Optics: Optical Vortices and Polarization Singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

Olivík, M.

Z. Bouchal and M. Olivík, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42(8), 1555–1566 (1995).
[Crossref]

Orlov, S.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209(1-3), 155–165 (2002).
[Crossref]

Padgett, M. J.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular Optics: Optical Vortices and Polarization Singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

Peinado, A.

Phelan, C. F.

Piché, M.

Rakovich, Y. P.

Regelskis, K.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209(1-3), 155–165 (2002).
[Crossref]

Ritsch-Marte, M.

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

Roizen-Dossier, B.

P. Jacquinot and B. Roizen-Dossier, “Apodisation,” Prog. Opt. 3, 29–186 (1964).
[Crossref]

Santamato, E.

Sato, S.

Schubert, W. H.

Sheppard, C. J. R.

Shvedov, V.

Smilgevicius, V.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209(1-3), 155–165 (2002).
[Crossref]

Stabinis, A.

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209(1-3), 155–165 (2002).
[Crossref]

Tomizawa, H.

Turpin, A.

Vyas, S.

Appl. Opt. (2)

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: Diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

J. Mod. Opt. (1)

Z. Bouchal and M. Olivík, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42(8), 1555–1566 (1995).
[Crossref]

J. Opt. (1)

J. Lindberg, “Mathematical concepts of optical superresolution,” J. Opt. 14(8), 083001 (2012).
[Crossref]

J. Opt. A, Pure Appl. Opt. (2)

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
[Crossref]

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A, Pure Appl. Opt. 7(11), 685–690 (2005).
[Crossref]

New J. Phys. (1)

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

Opt. Commun. (3)

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun. 272(2), 314–319 (2007).
[Crossref]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[Crossref]

S. Orlov, K. Regelskis, V. Smilgevičius, and A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209(1-3), 155–165 (2002).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Prog. Opt. (3)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular Optics: Optical Vortices and Polarization Singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics,” Prog. Opt. 50, 13–50 (2007).
[Crossref]

P. Jacquinot and B. Roizen-Dossier, “Apodisation,” Prog. Opt. 3, 29–186 (1964).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 The near-axis distribution of the electric field (denoted by red arrows) inside a superposition of two circularly polarized Bessel beams with (a) l1 = 0, σ1 = 1; l2 = 1, σ2 = −1 and (b) l1 = 0, σ1 = −1; l2 = 1, σ2 = 1. The instantaneous distribution of the electric field in the constituting Bessel beams is shown in the top panels of (a) and (b). The trajectories of fixed points on the wave fronts of the constituting beams are plotted using green lines. The distribution of linear polarization along the first L-line in the resulting Bessel beam is represented by black double arrows. T is the period and λ is the wavelength of the light wave.
Fig. 2
Fig. 2 Polarization maps of (a) the beam described by Eq. (4a) and (4b) the beam described by Eq. (4b). Right-handed states of polarization are in red, left-handed states of polarization are in blue. The first two L-lines shown in both (a) and (b) are in black.
Fig. 3
Fig. 3 Generation and analysis of nondiffracting Bessel-Poincaré beams (BPB). (a) Schematic of the beam synthesizer. P1 and QWP1 denote an input polarizer and input quarter-wave plate, respectively; O1 and O2 denote objectives with NA = 0.25 and NA = 0.5, respectively; BC is a ~2.8 mm long KGd(WO4)2 crystal; IP denotes the image plane where the two sharp annuli of light (see text) are formed with O2; S is a stop whose circular opening has a radius of ~5 mm; L is a plano-convex lens of focal distance f = 70 cm. The inset shows how the BPB1 given by Eq. (4a) can be converted into the BPB2 given by Eq. (4b) using a half-wave plate (HWP). (b) Experimental results on the generation of a nondiffracting BPB1 and revealing the constituting J0- and J1-beam inside it. QWP2 and P2 denote an analyzing quarter-wave plate and analyzing polarizer, respectively. The intensity distributions of the constituting J0- and J1-beam are shown at 0 and 5 meters after L.
Fig. 4
Fig. 4 Revealing the polarization structure of Bessel-Poincaré beams. (a) simulations pertaining to the BPB1. (b) simulations pertaining to the BPB2. (c) experimental data (i.e., CCD images) showing how the first L-line in the BPB1 and BPB2 can be traced using a conventional polarizer with one transmission axis and clearly observed with a segmented polarizer with four differently oriented transmission axes. The different orientations of the transmission axes in both the cases are indicated by double arrows. In (a) and (b), right-handed states of polarization are in red, left-handed states of polarization are in blue.
Fig. 5
Fig. 5 The sub-diffraction size of the first L-line inside Bessel-Poincaré beams. (a) experimental (solid lines) and calculated (dotted lines) intensity profiles of the original BPB1 (green), the BPB1 after the segmented polarizer (red), and the constituting J0-beam (blue). (b) visual comparison of the revealed first L-line and the central disk of the J0-beam, which are contained within the BPB1. The top-right image in the simulations shows the BPB1 after an ideal spatially inhomogeneous polarizer whose transmission axis continuously changes its orientation, mimicking the polarization distribution of the L-lines. The middle and right columns represent a 4-segment polarizer.

Equations (8)

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E= 1 2 E 0 ( e ρ +iσ e φ ) J | l | ( k ρ ρ)exp(i((l+σ)φ+ φ 0 + k z zωt)),
E= n=1 m E n ( e ρ +i σ n e φ ) J | l n | ( k ρ ρ)exp{ i(( l n + σ n )φ+ l n φ 0 ) } e i( k z zωt) ,
E= E 0 J | l | ( k ρ ρ)[ cos( (l+σ)φ+l φ 0 ) e ρ σsin( (l+σ)φ+l φ 0 ) e φ ] e i( k z zωt) .
E = 11 ( E 1 J 0 ( k ρ ρ)( e ρ +i e φ )exp(iφ)+ E 2 J 1 ( k ρ ρ)( e ρ i e φ ) ) e i( k z zωt) ,
E = 12 ( E 1 J 0 ( k ρ ρ)( e ρ i e φ )exp(iφ)+ E 2 J 1 ( k ρ ρ)( e ρ +i e φ )exp(2iφ) ) e i( k z zωt) .
E 21 =( E 1 J 0 ( k ρ ρ)( e ρ i e φ )exp(iφ)+ E 2 J 1 ( k ρ ρ)( e ρ +i e φ ) ) e i( k z zωt) ,
E 22 =( E 1 J 0 ( k ρ ρ)( e ρ +i e φ )exp(iφ)+ E 2 J 1 ( k ρ ρ)( e ρ i e φ )exp(2iφ) ) e i( k z zωt) .
( cos 2 (φ/2) cos(φ/2)sin(φ/2) cos(φ/2)sin(φ/2) sin 2 (φ/2) ).

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