Abstract

A wave propagation analysis carried out in two kinds of q-plates having topological unit charge (1-plates), one plate with a radial orientation of the optical axis and the other with an azimuthal one, reveals that these devices admit nondiffracting Bessel beams as exact solutions of the vector Helmholtz’s equation. The phase shifts between the ordinary and the extraordinary waves in both structures were found to be different. The polarization-scrambling term in the Helmholtz equation is responsible for such differences, emphasizing that this term cannot be dropped in radial plates, contrary to the azimuthal case. A phase shift analysis suggests that these plates are relevant for the control of nonconventional polarization states of light. In this way, a novel redistribution of the spin-orbital angular momentum of these nondiffracting beams passing by the 1-plate is demonstrated, which could be useful for applications in classic and quantum regimes.

© 2009 Optical Society of America

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References

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2009 (3)

E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, Opt. Lett. 34, 1225 (2009).
[Crossref] [PubMed]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, Appl. Phys. Lett. 94, 231124 (2009).
[Crossref]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

2007 (3)

2006 (2)

2005 (1)

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005), and references therein.
[Crossref]

2002 (1)

K. Volke-Sepulveda, V. Garccés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, 82 (2002).
[Crossref]

1995 (1)

Z. Bouchal and M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[Crossref]

1974 (1)

M. J. Stephen and J. P. Straley, Rev. Mod. Phys. 46, 617 (1974).
[Crossref]

Arlt, J.

K. Volke-Sepulveda, V. Garccés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, 82 (2002).
[Crossref]

Bouchal, Z.

Z. Bouchal and M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[Crossref]

Calvo, G. F.

Chávez-Cerda, S.

K. Volke-Sepulveda, V. Garccés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, 82 (2002).
[Crossref]

de Gennes, P. G.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Oxford U. Press, 1993).

De Martini, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

Dholakia, K.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005), and references therein.
[Crossref]

K. Volke-Sepulveda, V. Garccés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, 82 (2002).
[Crossref]

Flores-Pérez, A.

Garccés-Chávez, V.

K. Volke-Sepulveda, V. Garccés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, 82 (2002).
[Crossref]

Hernández-Hernández, J.

Jáuregui, R.

Karimi, E.

E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, Opt. Lett. 34, 1225 (2009).
[Crossref] [PubMed]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, Appl. Phys. Lett. 94, 231124 (2009).
[Crossref]

Lencina, A.

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Marrucci, L.

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, Appl. Phys. Lett. 94, 231124 (2009).
[Crossref]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, Opt. Lett. 34, 1225 (2009).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

McGloin, D.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005), and references therein.
[Crossref]

Moret, M. A.

Nagali, E.

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, Appl. Phys. Lett. 94, 231124 (2009).
[Crossref]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

Olivik, M.

Z. Bouchal and M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[Crossref]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

Piccirillo, B.

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, Appl. Phys. Lett. 94, 231124 (2009).
[Crossref]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, Opt. Lett. 34, 1225 (2009).
[Crossref] [PubMed]

Picón, A.

Prost, J.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Oxford U. Press, 1993).

Ruiz, B.

Santamato, E.

E. Karimi, B. Piccirillo, L. Marrucci, and E. Santamato, Opt. Lett. 34, 1225 (2009).
[Crossref] [PubMed]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, Appl. Phys. Lett. 94, 231124 (2009).
[Crossref]

Sciarrino, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

Stephen, M. J.

M. J. Stephen and J. P. Straley, Rev. Mod. Phys. 46, 617 (1974).
[Crossref]

Straley, J. P.

M. J. Stephen and J. P. Straley, Rev. Mod. Phys. 46, 617 (1974).
[Crossref]

Vaveliuk, P.

Volke-Sepulveda, K.

A. Flores-Pérez, J. Hernández-Hernández, R. Jáuregui, and K. Volke-Sepulveda, Opt. Lett. 31, 1732 (2006).
[Crossref] [PubMed]

K. Volke-Sepulveda, V. Garccés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, 82 (2002).
[Crossref]

Zebende, G. F.

Appl. Phys. Lett. (1)

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, Appl. Phys. Lett. 94, 231124 (2009).
[Crossref]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005), and references therein.
[Crossref]

J. Mod. Opt. (1)

Z. Bouchal and M. Olivik, J. Mod. Opt. 42, 1555 (1995).
[Crossref]

J. Opt. B (1)

K. Volke-Sepulveda, V. Garccés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, 82 (2002).
[Crossref]

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

Opt. Lett. (4)

Phys. Rev. Lett. (2)

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref] [PubMed]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, Phys. Rev. Lett. 103, 013601 (2009).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

M. J. Stephen and J. P. Straley, Rev. Mod. Phys. 46, 617 (1974).
[Crossref]

Other (1)

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Oxford U. Press, 1993).

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Figures (3)

Fig. 1
Fig. 1

Director lines in a cross section of both radially and azimuthally symmetric 1-plates.

Fig. 2
Fig. 2

Differences between e and o longitudinal wavenumbers as a function of β (in units of k 0 ) for two different values of n o 2 = n e 2 n o 2 .

Fig. 3
Fig. 3

AMR obtained by using radially and circularly polarized nondiffracting Bessel beam. The 1-plate must be made a quarter-wave retarder by tuning β, d, n o , and n e .

Equations (5)

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E a = E a ( φ ) + E a ( r ) = E a 0 ( φ ) e i k a ( φ ) z J 1 ( β a ( φ ) r ) φ ̂ + E a 0 ( r ) e i k a ( r ) z [ J 1 ( β a ( r ) r ) r ̂ + i ( β a ( r ) k a ( r ) ) J 0 ( β a ( r ) r ) z ̂ ] ,
E b = E b ( φ ) + E b ( r ) = E b 0 ( φ ) e i k b ( φ ) z J 1 ( β b ( φ ) r ) φ ̂ + E b 0 ( r ) e i k b ( r ) z [ J 1 ( β b ( r ) r ) r ̂ + i ( n e 2 β b ( r ) n o 2 k b ( r ) ) J 0 ( β b ( r ) r ) z ̂ ] .
E ( z < 0 ) = E 0 J 1 ( β r ) e i k z z ( φ ̂ + r ̂ ) ,
E a = E a 0 J 1 ( β r ) [ e i k a ( r ) z r ̂ + e i k a ( φ ) z φ ̂ ] .
E ( z > d ) = E 0 J 1 ( β r ) e i k z z e i φ ( x ̂ ± i y ̂ ) .

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