Abstract

Nondiffracting vector Bessel beams are of considerable interest due to their nondiffracting nature and unique high-numerical-aperture focusing properties. Here we demonstrate their creation by a simple procedure requiring only a spatial light modulator and an azimuthally varying birefringent plate, known as a q-plate. We extend our control of both the geometric and dynamic phases to perform a polarization and modal decomposition on the vector field. We study both single-charged Bessel beams as well as superpositions and find good agreement with theory. Since we are able to encode nondiffracting modes with circular polarizations possessing different orbital angular momenta, we suggest these modes will be of interest in optical trapping, microscopy, and optical communication.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Q. Zhan, Adv. Opt. Photon. 1, 1 (2009).
    [CrossRef]
  2. T. G. Brown and Q. Zhan, Opt. Express 18, 10775 (2010).
    [CrossRef]
  3. E. Hasman, G. Biener, A. Niv, and V. Kleiner, Space-Variant Polarization Manipulation (Elsevier, 2005), Vol. 47, pp. 215–289.
  4. T. G. Brown, Unconventional Polarization States: Beam Propagation, Focusing and Imaging (Elsevier, 2011), Vol. 56, pp. 81–129.
  5. A. M. Beckley, T. G. Brown, and M. A. Alonso, Opt. Express 18, 10777 (2010).
    [CrossRef]
  6. G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
    [CrossRef]
  7. D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
    [CrossRef]
  8. Y. Mushiake, K. Matzumurra, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
    [CrossRef]
  9. T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun 203, 1 (2002).
    [CrossRef]
  10. M. Stalder and M. Schadt, Opt. Lett. 21, 1948 (1996).
    [CrossRef]
  11. L. Marrucci, C. Manzo, and D. Paparo, Appl. Phys. Lett. 88, 221102 (2006).
    [CrossRef]
  12. W. Han, W. Cheng, and Q. Zhan, Opt. Lett. 36, 1605 (2011).
    [CrossRef]
  13. F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, Appl. Opt. 51, C1 (2012).
    [CrossRef]
  14. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
    [CrossRef]
  15. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
    [CrossRef]
  16. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef]
  17. B. Jia, X. Gan, and M. Gu, Opt. Express 13, 6821 (2005).
    [CrossRef]
  18. B. Hao and J. Leger, Opt. Express 15, 3550 (2007).
    [CrossRef]
  19. G. M. Philip, V. Kumar, G. Milione, and N. K. Viswanathan, Opt. Lett. 37, 2667 (2012).
    [CrossRef]
  20. W. Cheng, J. W. Haus, and Q. Zhan, Opt. Express 17, 17829 (2009).
    [CrossRef]
  21. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef]
  22. R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, Opt. Express 17, 23389 (2009).
    [CrossRef]
  23. Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
    [CrossRef]
  24. J. Tervo and J. Turunen, Opt. Commun. 192, 13 (2001).
    [CrossRef]
  25. A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
    [CrossRef]
  26. G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
    [CrossRef]
  27. A. Flores-Pérez, J. Hernández-Hernández, R. Jáuregui, and K. Volke-Sepúlveda, Opt. Lett. 31, 1732 (2006).
    [CrossRef]
  28. D. W. K. Wong and G. Chen, Appl. Opt. 47, 602 (2008).
    [CrossRef]
  29. C. Lopez-Mariscal and K. Helmerson, Opt. Lett. 35, 1215 (2010).
    [CrossRef]
  30. A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
    [CrossRef]
  31. L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
    [CrossRef]
  32. S. C. McEldowney, D. M. Shemo, R. A. Chipman, and P. K. Smith, Opt. Lett. 33, 134 (2008).
    [CrossRef]
  33. Y. Li, J. Kim, and M. J. Escuti, Appl. Opt. 51, 8236 (2012).
    [CrossRef]
  34. G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, J. Appl. Phys. 98, 123102 (2005).
    [CrossRef]
  35. I. A. Litvin, A. Dudley, F. S. Roux, and A. Forbes, Opt. Express 20, 10996 (2012).
    [CrossRef]
  36. D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré, Opt. Lett. 37, 2478 (2012).
    [CrossRef]

2012

2011

W. Han, W. Cheng, and Q. Zhan, Opt. Lett. 36, 1605 (2011).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

2010

2009

2008

2007

B. Hao and J. Leger, Opt. Express 15, 3550 (2007).
[CrossRef]

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

2006

L. Marrucci, C. Manzo, and D. Paparo, Appl. Phys. Lett. 88, 221102 (2006).
[CrossRef]

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

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

2005

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

B. Jia, X. Gan, and M. Gu, Opt. Express 13, 6821 (2005).
[CrossRef]

2004

2003

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

2002

T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun 203, 1 (2002).
[CrossRef]

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

2001

J. Tervo and J. Turunen, Opt. Commun. 192, 13 (2001).
[CrossRef]

2000

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

1996

1987

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

1972

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

Y. Mushiake, K. Matzumurra, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Alfano, R. R.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Alonso, M. A.

Beckley, A. M.

Belyi, V.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Biener, G.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[CrossRef]

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Space-Variant Polarization Manipulation (Elsevier, 2005), Vol. 47, pp. 215–289.

Bomzon, Z.

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

Brown, T. G.

T. G. Brown and Q. Zhan, Opt. Express 18, 10775 (2010).
[CrossRef]

A. M. Beckley, T. G. Brown, and M. A. Alonso, Opt. Express 18, 10777 (2010).
[CrossRef]

T. G. Brown, Unconventional Polarization States: Beam Propagation, Focusing and Imaging (Elsevier, 2011), Vol. 56, pp. 81–129.

Callan-Jones, A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Cardano, F.

Chen, G.

Cheng, W.

Chipman, R. A.

Courjon, D.

T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun 203, 1 (2002).
[CrossRef]

Crawford, G. P.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

de Lisio, C.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Dudley, A.

Duparré, M.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eakin, J. N.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Escuti, M. J.

Evans, S.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

Flamm, D.

Flores-Pérez, A.

Forbes, A.

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Gan, X.

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Grosjean, T.

T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun 203, 1 (2002).
[CrossRef]

Gu, M.

Han, W.

Hao, B.

Hasman, E.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[CrossRef]

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Space-Variant Polarization Manipulation (Elsevier, 2005), Vol. 47, pp. 215–289.

Haus, J. W.

Helmerson, K.

Hernández-Hernández, J.

Jáuregui, R.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Jia, B.

Karimi, E.

Khilo, N.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, Opt. Express 17, 23389 (2009).
[CrossRef]

Kim, J.

Kleiner, V.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[CrossRef]

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Space-Variant Polarization Manipulation (Elsevier, 2005), Vol. 47, pp. 215–289.

Kumar, V.

Leger, J.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Li, Y.

Litvin, I. A.

Lopez-Mariscal, C.

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, Appl. Phys. Lett. 88, 221102 (2006).
[CrossRef]

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

Marrucci, L.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, Appl. Opt. 51, C1 (2012).
[CrossRef]

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

L. Marrucci, C. Manzo, and D. Paparo, Appl. Phys. Lett. 88, 221102 (2006).
[CrossRef]

Matzumurra, K.

Y. Mushiake, K. Matzumurra, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

McEldowney, S. C.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Milione, G.

G. M. Philip, V. Kumar, G. Milione, and N. K. Viswanathan, Opt. Lett. 37, 2667 (2012).
[CrossRef]

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Mushiake, Y.

Y. Mushiake, K. Matzumurra, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Naidoo, D.

Nakajima, N.

Y. Mushiake, K. Matzumurra, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Niv, A.

A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
[CrossRef]

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Space-Variant Polarization Manipulation (Elsevier, 2005), Vol. 47, pp. 215–289.

Nolan, D. A.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Paparo, D.

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

L. Marrucci, C. Manzo, and D. Paparo, Appl. Phys. Lett. 88, 221102 (2006).
[CrossRef]

Pelcovits, R. A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Philip, G. M.

Pohl, D.

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

Radcliffe, M. D.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Ropot, P.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Roux, F. S.

Santamato, E.

Schadt, M.

Schulze, C.

Shemo, D. M.

Slussarenko, S.

Smith, P. K.

Spajer, M.

T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun 203, 1 (2002).
[CrossRef]

Stalder, M.

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Tervo, J.

J. Tervo and J. Turunen, Opt. Commun. 192, 13 (2001).
[CrossRef]

Turunen, J.

J. Tervo and J. Turunen, Opt. Commun. 192, 13 (2001).
[CrossRef]

Vasilyeu, R.

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, Opt. Express 17, 23389 (2009).
[CrossRef]

Viswanathan, N. K.

Volke-Sepúlveda, K.

Wong, D. W. K.

Zhan, Q.

Adv. Opt. Photon.

Appl. Opt.

Appl. Phys. Lett.

D. Pohl, Appl. Phys. Lett. 20, 266 (1972).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, Appl. Phys. Lett. 88, 221102 (2006).
[CrossRef]

Z. Bomzon, A. Niv, G. Biener, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 80, 3685 (2002).
[CrossRef]

J. Appl. Phys.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

New J. Phys.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
[CrossRef]

Opt. Commun

T. Grosjean, D. Courjon, and M. Spajer, Opt. Commun 203, 1 (2002).
[CrossRef]

Opt. Commun.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
[CrossRef]

J. Tervo and J. Turunen, Opt. Commun. 192, 13 (2001).
[CrossRef]

A. Dudley, R. Vasilyeu, V. Belyi, N. Khilo, P. Ropot, and A. Forbes, Opt. Commun. 285, 5 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

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

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 108, 190401 (2012).
[CrossRef]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Proc. IEEE

Y. Mushiake, K. Matzumurra, and N. Nakajima, Proc. IEEE 60, 1107 (1972).
[CrossRef]

Other

E. Hasman, G. Biener, A. Niv, and V. Kleiner, Space-Variant Polarization Manipulation (Elsevier, 2005), Vol. 47, pp. 215–289.

T. G. Brown, Unconventional Polarization States: Beam Propagation, Focusing and Imaging (Elsevier, 2011), Vol. 56, pp. 81–129.

Supplementary Material (1)

» Media 1: MOV (715 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Schematic of the experimental setup [division 1, scalar generation; division 2, vector generation; division 3, vector decomposition; division 4, scalar (azimuthal) decomposition]. L, lens (f1=15mm, f2=150mm, f3 and f4=500mm, f5=300mm); SLM, spatial light modulator; A, aperture; Q, q-plate; PG, polarization grating; CCD, camera.

Fig. 2.
Fig. 2.

(a) Transform of a q-plate with corresponding state equations. (b) The action of a PG with the incoming polarization marked in the corresponding outputs.

Fig. 3.
Fig. 3.

Experimentally recorded near- and far-field intensity profiles of (a) and (b) the scalar single-charged Bessel beam of azimuthal index =0; (c) and (d) superposition of azimuthal indices =2 and +2. (e)–(h) Experimental near-field [(e) and (g)] and far-field [(f) and (h)] intensity profiles of the corresponding vector Bessel fields recorded after the q-plate. Insets denote the corresponding vector beams recorded with a polarizer in front of the CCD. Red (white) arrows denote the polarization direction (polarizer orientation).

Fig. 4.
Fig. 4.

(a)–(g) Experimentally recorded near-field intensity profiles of vector Bessel fields recorded after the q-plate with a polarizer in front of the CCD for initial scalar Bessel beams of =5,3,1,0,+1,+3, and +5, respectively. (h)–(n) Intensity profiles for an =0 vector Bessel beam recorded with a rotating polarizer. The full data (video) can be viewed in Media 1. White arrows mark the corresponding polarizer setting.

Fig. 5.
Fig. 5.

(a) Correlation signals for the azimuthal decomposition for both the left- (orange) and right-circular (pink) polarization components. (b) =+1 and (c) =1 Bessel beams after the q-plate associated with left- and right-circular polarization components, respectively. (d) A table summarizing the transformation of the input values after the q-plate.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

u(r,ϕ,z=0)=J(krr)exp(iϕ)(11),
(cos(Qϕ)sin(Qϕ)sin(Qϕ)cos(Qϕ))(11)exp(iϕ)exp(i(+Q)ϕ)(1i)+exp(i(Q)ϕ)(1i),
|1,R+|1,L=exp(iϕ)(1i)+exp(iϕ)(1i)=(cos(ϕ)sin(ϕ)).

Metrics