Abstract

We present a method for the realization of radially and azimuthally polarized nonparaxial Bessel beams in a rigorous but simple manner. This result is achieved by using the concept of Hertz vector potential to generate exact vector solutions of Maxwell’s equations from scalar Bessel beams. The scalar part of the Hertz potential is built by analogy with the paraxial case as a linear combination of Bessel beams carrying a unit of orbital angular momentum. In this way we are able to obtain spatial and polarization patterns analogous to the ones exhibited by the standard cylindrically polarized paraxial beams. Applications of these beams are discussed.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013

T. Fedayeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt.15, 044020 (2013).
[CrossRef]

2012

2011

2010

T. Fedayeva, V. Shvedov, N. Shostka, C. Alexeyev, and A. Volyar, “Natural shaping of the cylindrically polarized beams,” Opt. Lett35, 3787–3789 (2010).
[CrossRef]

2008

A. April, “Nonparaxial TM and TE beams in free space,” Opt. Lett33, 1563–1565 (2008).
[CrossRef] [PubMed]

2007

2006

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A86, 329–334 (2006).
[CrossRef]

Y. I. Salamin, “Accurate fields of a radially polarized Gaussian laser beam,” N. J. Phys.8, 133 (2006).
[CrossRef]

2005

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solutions: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett.94, 073902 (2005).
[CrossRef] [PubMed]

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, 12–21 (2005).
[CrossRef]

K. C. Toussaint, S. Park, J. E. Jureller, and N. F. Scherer, “Generation of optical vector beams with a diffractive optical element interferoments,” Opt. Lett.30, 2846–2848 (2005).
[CrossRef] [PubMed]

2004

G. Volpe, G. D. Singh, and D. Petrov, “Optical tweezers with cylindrical vector beams produced by optical fibers,” Proc. of SPIE, 5514, 283–292 (2004).
[CrossRef]

2003

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett91, 233901 (2003).
[CrossRef] [PubMed]

G. Cincotti, A. Ciattoni, and C. Sapia, “Radially and azimuthally polarized vortices in uniaxial crystals,” Opt. Commun.220, 33–44 (2003).
[CrossRef]

2002

2001

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt.6, 480–484 (2001).
[CrossRef]

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

S. J. van Enk and H. J. Kimble, “Strongly focused light beams interacting with single atoms in free space,” Phys. Rev. A63, 023809 (2001).
[CrossRef]

R. Borghi, M. Santarsiero, and M. A. Porras, “Nonparaxial Bessel-Gauss beams,” J. Opt. Soc. Am. A,18, 1618–1624 (2001).
[CrossRef]

2000

B. Sich, B. Hecht, and L. Novotny, “Orientational imagine of single molecules by annular illumination,” Phys. Rev. Lett.85, 4482 (2000).
[CrossRef]

C. J. R. Sheppard, “Polarization of almost-plane waves,” J. Opt. Soc. Am. A17, 335–341 (2000).
[CrossRef]

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

1999

1996

1995

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

1993

H. A. Haus and J. L. Pan, “Photon spin and the paraxial wave equation,” Am. J. Phys, 61, 818–821 (1993).
[CrossRef]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8190 (1992).
[CrossRef] [PubMed]

1990

Aiello, A.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

A. Holleczek, A. Aiello, C. Gabriel, Ch. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express19, 9714–9736 (2011).
[CrossRef] [PubMed]

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts for nondiffracting Bessel beams,” Opt. Lett.36, 543–545 (2011).
[CrossRef] [PubMed]

F. Töppel, M. Ornigotti, and A. Aiello, in preparation

M. Ornigotti and A. Aiello, “Incompleteness of spin and orbital angular momentum separation for light beams,” arXiv:1304:5012 [physics.optics].

Alexeyev, C.

T. Fedayeva, V. Shvedov, N. Shostka, C. Alexeyev, and A. Volyar, “Natural shaping of the cylindrically polarized beams,” Opt. Lett35, 3787–3789 (2010).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8190 (1992).
[CrossRef] [PubMed]

Andersen, U. L.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

Aolita, L.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communications,” Nat. Commun.3, 961 (2012).
[CrossRef]

April, A.

Banzer, P.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8190 (1992).
[CrossRef] [PubMed]

Bernet, S.

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

Borghi, R.

R. Borghi, M. Santarsiero, and M. A. Porras, “Nonparaxial Bessel-Gauss beams,” J. Opt. Soc. Am. A,18, 1618–1624 (2001).
[CrossRef]

Bosmon, Z.

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

Bouchal, Z.

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

Bu, J.

Burge, R. E.

Cardano, F.

Chemmos, I. D.

Chen, Z.

Christodoulides, D. N.

Ciattoni, A.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solutions: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett.94, 073902 (2005).
[CrossRef] [PubMed]

G. Cincotti, A. Ciattoni, and C. Sapia, “Radially and azimuthally polarized vortices in uniaxial crystals,” Opt. Commun.220, 33–44 (2003).
[CrossRef]

Cincotti, G.

G. Cincotti, A. Ciattoni, and C. Sapia, “Radially and azimuthally polarized vortices in uniaxial crystals,” Opt. Commun.220, 33–44 (2003).
[CrossRef]

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, 12–21 (2005).
[CrossRef]

Courtial, J.

Crosignani, B.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solutions: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett.94, 073902 (2005).
[CrossRef] [PubMed]

D’Ambrosio, V.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communications,” Nat. Commun.3, 961 (2012).
[CrossRef]

de Lisio, C.

Di Porto, P.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solutions: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett.94, 073902 (2005).
[CrossRef] [PubMed]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett91, 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 (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 (2000).
[CrossRef]

Efremidis, N. K.

Elser, D.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

Euser, T.G.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

Fedayeva, T.

T. Fedayeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt.15, 044020 (2013).
[CrossRef]

T. Fedayeva, V. Shvedov, N. Shostka, C. Alexeyev, and A. Volyar, “Natural shaping of the cylindrically polarized beams,” Opt. Lett35, 3787–3789 (2010).
[CrossRef]

Feurer, T.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A86, 329–334 (2006).
[CrossRef]

Förtsch, M.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

Fürhapter, S.

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

Gabriel, C.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

A. Holleczek, A. Aiello, C. Gabriel, Ch. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express19, 9714–9736 (2011).
[CrossRef] [PubMed]

Gao, B. Z.

Glöckl, O.

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

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, 12–21 (2005).
[CrossRef]

Hasman, E.

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

Haus, H. A.

H. A. Haus and J. L. Pan, “Photon spin and the paraxial wave equation,” Am. J. Phys, 61, 818–821 (1993).
[CrossRef]

Hecht, B.

B. Sich, B. Hecht, and L. Novotny, “Orientational imagine of single molecules by annular illumination,” Phys. Rev. Lett.85, 4482 (2000).
[CrossRef]

Hell, S. W.

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt.6, 480–484 (2001).
[CrossRef]

Holleczek, A.

Huse, N.

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt.6, 480–484 (2001).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical electrodynamics (Wiley, 1999).

Jesacher, A.

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

Joly, N. Y.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

Jureller, J. E.

Karimi, E.

Kimble, H. J.

S. J. van Enk and H. J. Kimble, “Strongly focused light beams interacting with single atoms in free space,” Phys. Rev. A63, 023809 (2001).
[CrossRef]

Kleiner, V.

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

Leuchs, G.

A. Holleczek, A. Aiello, C. Gabriel, Ch. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express19, 9714–9736 (2011).
[CrossRef] [PubMed]

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett91, 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 (2000).
[CrossRef]

Marquardt, Ch.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

A. Holleczek, A. Aiello, C. Gabriel, Ch. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express19, 9714–9736 (2011).
[CrossRef] [PubMed]

Marrucci, L.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization patterns of vector vortex beams generated by q-plateswith different topological charges,” Appl. Opt.51, C1–C6 (2012).
[CrossRef]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communications,” Nat. Commun.3, 961 (2012).
[CrossRef]

Martinez-Herrero, R.

R. Martinez-Herrero, P. M. Mejias, and G. Piquero, Characterization of Partially Polarized Light Fields (Springer, 2009).
[CrossRef]

Maurer, C.

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

Meier, M.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A86, 329–334 (2006).
[CrossRef]

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R. Martinez-Herrero, P. M. Mejias, and G. Piquero, Characterization of Partially Polarized Light Fields (Springer, 2009).
[CrossRef]

Moh, K. J.

Nagali, E.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communications,” Nat. Commun.3, 961 (2012).
[CrossRef]

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Niziev, V. G.

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B. Sich, B. Hecht, and L. Novotny, “Orientational imagine of single molecules by annular illumination,” Phys. Rev. Lett.85, 4482 (2000).
[CrossRef]

Olivik, M.

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

Ornigotti, M.

F. Töppel, M. Ornigotti, and A. Aiello, in preparation

M. Ornigotti and A. Aiello, “Incompleteness of spin and orbital angular momentum separation for light beams,” arXiv:1304:5012 [physics.optics].

Padgett, M. J.

Pan, J. L.

H. A. Haus and J. L. Pan, “Photon spin and the paraxial wave equation,” Am. J. Phys, 61, 818–821 (1993).
[CrossRef]

Park, S.

Petrov, D.

G. Volpe, G. D. Singh, and D. Petrov, “Optical tweezers with cylindrical vector beams produced by optical fibers,” Proc. of SPIE, 5514, 283–292 (2004).
[CrossRef]

Piquero, G.

R. Martinez-Herrero, P. M. Mejias, and G. Piquero, Characterization of Partially Polarized Light Fields (Springer, 2009).
[CrossRef]

Porras, M. A.

R. Borghi, M. Santarsiero, and M. A. Porras, “Nonparaxial Bessel-Gauss beams,” J. Opt. Soc. Am. A,18, 1618–1624 (2001).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett91, 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 (2000).
[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, 78 (2007).
[CrossRef]

Romano, V.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A86, 329–334 (2006).
[CrossRef]

Rubass, A. F.

T. Fedayeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt.15, 044020 (2013).
[CrossRef]

Russel, P. St. J.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

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, 12–21 (2005).
[CrossRef]

Saghafi, S.

Salamin, Y. I.

Y. I. Salamin, “Accurate fields of a radially polarized Gaussian laser beam,” N. J. Phys.8, 133 (2006).
[CrossRef]

Santamato, E.

Santarsiero, M.

R. Borghi, M. Santarsiero, and M. A. Porras, “Nonparaxial Bessel-Gauss beams,” J. Opt. Soc. Am. A,18, 1618–1624 (2001).
[CrossRef]

Sapia, C.

G. Cincotti, A. Ciattoni, and C. Sapia, “Radially and azimuthally polarized vortices in uniaxial crystals,” Opt. Commun.220, 33–44 (2003).
[CrossRef]

Schadt, M.

Scherer, N. F.

Schönle, A.

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt.6, 480–484 (2001).
[CrossRef]

Sciarrino, F.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communications,” Nat. Commun.3, 961 (2012).
[CrossRef]

Shepard, C. J. R.

Sheppard, C. J. R.

Shostka, N.

T. Fedayeva, V. Shvedov, N. Shostka, C. Alexeyev, and A. Volyar, “Natural shaping of the cylindrically polarized beams,” Opt. Lett35, 3787–3789 (2010).
[CrossRef]

Shvedov, V.

T. Fedayeva, V. Shvedov, N. Shostka, C. Alexeyev, and A. Volyar, “Natural shaping of the cylindrically polarized beams,” Opt. Lett35, 3787–3789 (2010).
[CrossRef]

Sich, B.

B. Sich, B. Hecht, and L. Novotny, “Orientational imagine of single molecules by annular illumination,” Phys. Rev. Lett.85, 4482 (2000).
[CrossRef]

Singh, G. D.

G. Volpe, G. D. Singh, and D. Petrov, “Optical tweezers with cylindrical vector beams produced by optical fibers,” Proc. of SPIE, 5514, 283–292 (2004).
[CrossRef]

Slussarenko, S.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communications,” Nat. Commun.3, 961 (2012).
[CrossRef]

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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8190 (1992).
[CrossRef] [PubMed]

Stalder, M.

Svelto, O.

O. Svelto, Principles of Lasers (Academic Press, 1998).
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Töppel, F.

F. Töppel, M. Ornigotti, and A. Aiello, in preparation

Toussaint, K. C.

Valkov, I. S.

T. Fedayeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt.15, 044020 (2013).
[CrossRef]

van Enk, S. J.

S. J. van Enk and H. J. Kimble, “Strongly focused light beams interacting with single atoms in free space,” Phys. Rev. A63, 023809 (2001).
[CrossRef]

Volpe, G.

G. Volpe, G. D. Singh, and D. Petrov, “Optical tweezers with cylindrical vector beams produced by optical fibers,” Proc. of SPIE, 5514, 283–292 (2004).
[CrossRef]

Volyar, A.

T. Fedayeva, V. Shvedov, N. Shostka, C. Alexeyev, and A. Volyar, “Natural shaping of the cylindrically polarized beams,” Opt. Lett35, 3787–3789 (2010).
[CrossRef]

Volyar, A. V.

T. Fedayeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt.15, 044020 (2013).
[CrossRef]

Walborn, S. P.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communications,” Nat. Commun.3, 961 (2012).
[CrossRef]

Woerdman, J. P.

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts for nondiffracting Bessel beams,” Opt. Lett.36, 543–545 (2011).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8190 (1992).
[CrossRef] [PubMed]

Yakunin, V. P.

Yariv, A.

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solutions: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett.94, 073902 (2005).
[CrossRef] [PubMed]

Yuan, X.-C.

Zhong, W.

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

Zurita-Sanchez, J. R.

Am. J. Phys

H. A. Haus and J. L. Pan, “Photon spin and the paraxial wave equation,” Am. J. Phys, 61, 818–821 (1993).
[CrossRef]

Appl. Opt.

Appl. Phys. A

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys. A86, 329–334 (2006).
[CrossRef]

Appl. Phys. Lett.

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

J. Biomed. Opt.

N. Huse, A. Schönle, and S. W. Hell, “Z-polarized confocal microscopy,” J. Biomed. Opt.6, 480–484 (2001).
[CrossRef]

J. Mod. Opt.

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

J. Opt.

T. Fedayeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt.15, 044020 (2013).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. A,

R. Borghi, M. Santarsiero, and M. A. Porras, “Nonparaxial Bessel-Gauss beams,” J. Opt. Soc. Am. A,18, 1618–1624 (2001).
[CrossRef]

J. Opt. Soc. Am. B

N. J. Phys.

Y. I. Salamin, “Accurate fields of a radially polarized Gaussian laser beam,” N. J. Phys.8, 133 (2006).
[CrossRef]

Nat. Commun.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communications,” Nat. Commun.3, 961 (2012).
[CrossRef]

New J. Phys.

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

Opt. Commun.

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

G. Cincotti, A. Ciattoni, and C. Sapia, “Radially and azimuthally polarized vortices in uniaxial crystals,” Opt. Commun.220, 33–44 (2003).
[CrossRef]

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, 12–21 (2005).
[CrossRef]

Opt. Express

Opt. Lett

T. Fedayeva, V. Shvedov, N. Shostka, C. Alexeyev, and A. Volyar, “Natural shaping of the cylindrically polarized beams,” Opt. Lett35, 3787–3789 (2010).
[CrossRef]

A. April, “Nonparaxial TM and TE beams in free space,” Opt. Lett33, 1563–1565 (2008).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

S. J. van Enk and H. J. Kimble, “Strongly focused light beams interacting with single atoms in free space,” Phys. Rev. A63, 023809 (2001).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A45, 8185–8190 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett91, 233901 (2003).
[CrossRef] [PubMed]

Phys. Rev. Lett.

B. Sich, B. Hecht, and L. Novotny, “Orientational imagine of single molecules by annular illumination,” Phys. Rev. Lett.85, 4482 (2000).
[CrossRef]

C. Gabriel, A. Aiello, W. Zhong, T.G. Euser, N. Y. Joly, P. Banzer, M. Förtsch, D. Elser, U. L. Andersen, Ch. Marquardt, P. St. J. Russel, and G. Leuchs, “Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes,” Phys. Rev. Lett.106, 060502 (2011).
[CrossRef] [PubMed]

A. Ciattoni, B. Crosignani, P. Di Porto, and A. Yariv, “Azimuthally polarized spatial dark solutions: exact solutions of Maxwell’s equations in a Kerr medium,” Phys. Rev. Lett.94, 073902 (2005).
[CrossRef] [PubMed]

Proc. of SPIE

G. Volpe, G. D. Singh, and D. Petrov, “Optical tweezers with cylindrical vector beams produced by optical fibers,” Proc. of SPIE, 5514, 283–292 (2004).
[CrossRef]

Other

R. Martinez-Herrero, P. M. Mejias, and G. Piquero, Characterization of Partially Polarized Light Fields (Springer, 2009).
[CrossRef]

M. Ornigotti and A. Aiello, “Incompleteness of spin and orbital angular momentum separation for light beams,” arXiv:1304:5012 [physics.optics].

O. Svelto, Principles of Lasers (Academic Press, 1998).
[CrossRef]

J. D. Jackson, Classical electrodynamics (Wiley, 1999).

F. Töppel, M. Ornigotti, and A. Aiello, in preparation

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Figures (4)

Fig. 1
Fig. 1

(a) Contour plot of the scalar function Ψ10(r) close to the propagation axis. (b) Contour plot of the Hermite-Gauss beam ψ10. (c) Three dimensional intensity profile of the scalar function Ψ10. A direct comparison between panels (a) and (b) shows that in the paraxial domain Ψ10 correctly reproduces the behavior of the Hermite-Gauss beam ψ10. Note moreover that from panel (c) for x/w0 ≥ 4 and y/w0 ≥ 4, the scalar function Ψ10(r) shows some ripples, whose intensity is much smaller than the central lobes.

Fig. 2
Fig. 2

Complex polarization patterns of (a) co-rotating radially polarized electric field E R + and (b) counter-rotating radially polarized electric field E R , with superimposed the donut-shaped intensity distribution. The axes of both graphs span the interval [−5, 5] in units of the beams waist w0.

Fig. 3
Fig. 3

Complex polarization patterns of (a) co-rotating azimuthally polarized electric field E A + and (b) counter-rotating azimuthally polarized electric field E A ,with superimposed the donut-shaped intensity distribution. The axes of both graphs span the interval [−5, 5] in units of the beams waist w0.

Fig. 4
Fig. 4

Normalized intensity distributions for the longitudinal component Ez of the radially (upper row) and azimuthally (lower row) polarized nonparaxial fields. Panels (a)–(c) and (b)–(d) display the co-rotating and counter-rotating fields respectively.

Equations (35)

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u ^ R ± = 1 2 ( ± ψ 10 x ^ + ψ 01 y ^ ) ,
u ^ A ± = 1 2 ( ψ 01 x ^ + ψ 10 y ^ ) ,
ψ m B ( r ) = J m ( K 0 R ) exp ( i m ϕ ) exp ( i z k 2 K 0 2 ) ,
Ψ 10 ( r ) = 1 2 [ ψ 1 B ( r ) + ψ 1 B ( r ) ] ,
Ψ 01 ( r ) = i 2 [ ψ 1 B ( r ) ψ 1 B ( r ) ] .
Ψ 10 ( r ) 2 x w 0 e i k z ( 1 x 2 + y 2 2 w 0 2 + 𝒪 ( θ 0 4 ) ) 2 x w 0 e i k z e x 2 + y 2 2 w 0 2 ,
Ψ 01 ( r ) 2 y w 0 e i k z ( 1 x 2 + y 2 2 w 0 2 + 𝒪 ( θ 0 4 ) ) 2 y w 0 e i k z e x 2 + y 2 2 w 0 2 .
U ^ R ± = 1 2 ( ± Ψ 10 x ^ + Ψ 01 y ^ ) ,
U ^ A ± = 1 2 ( Ψ 01 x ^ + Ψ 01 y ^ ) .
E ( r , t ) = × ( × Π ) ,
B ( r , t ) = 1 c 2 t ( × Π ) .
E R + r ( r ) = k z 2 J 1 ( K 0 R ) e i k z z ,
E R + θ ( r ) = 0 ,
E R + z ( r ) = i k z K 0 J 0 ( K 0 R ) e i k z z ,
E R r ( r ) = cos ( 2 θ ) R 2 [ 2 K 0 R J 0 ( K 0 R ) J 1 ( K 0 R ) ( 4 + k z 2 R 2 ) ] e i k z z ,
E R θ ( r ) = sin ( 2 θ ) R 2 [ 2 K 0 R J 0 ( K 0 R ) J 1 ( K 0 R ) ( 4 k 2 R 2 ) ] e i k z z ,
E R z ( r ) = i k z K 0 cos ( 2 θ ) J 0 ( K 0 R ) e i k z z ,
E A + r ( r ) = 0 ,
E A + θ ( r ) = k 2 J 1 ( K 0 R ) e i k z z ,
E A + z ( r ) = 0 ,
E A r ( r ) = sin ( 2 θ ) R 2 [ 2 K 0 R J 0 ( K 0 R ) + J 1 ( K 0 R ) ( 4 + k z 2 R 2 ) ] e i k z z ,
E A θ ( r ) = cos ( 2 θ ) R 2 [ 2 K 0 R J 0 ( K 0 R ) J 1 ( K 0 R ) ( 4 k 2 R 2 ) ] e i k z z ,
E A z ( r ) = i k z K 0 sin ( 2 θ ) J 2 ( K 0 R ) e i k z z ,
c B R + r ( r ) = 0 ,
c B R + θ ( r ) = k k z J 1 ( K 0 R ) e i k z z ,
c B R + z ( r ) = 0 ,
c B R r ( r ) = k k z sin ( 2 θ ) J 1 ( K 0 R ) e i k z z ,
c B R θ ( r ) = k k z cos ( 2 θ ) J 1 ( K 0 R ) e i k z z ,
c B R z ( r ) = i k K 0 sin ( 2 θ ) J 2 ( K 0 R ) e i k z z ,
c B A + r ( r ) = k k z J 1 ( K 0 R ) e i k z z ,
c B A + θ ( r ) = 0 ,
c B A + z ( r ) = i k K 0 J 0 ( K 0 R ) e i k z z ,
c B A r ( r ) = k k z cos ( 2 θ ) J 1 ( K 0 R ) e i k z z ,
c B A θ ( r ) = k k z sin ( 2 θ ) J 1 ( K 0 R ) e i k z z ,
c B A z ( r ) = i k K 0 cos ( 2 θ ) J 2 ( K 0 R ) e i k z z ,

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