Abstract

On the basis of the vectorial Rayleigh diffraction integrals and stationary-phase method, the analytic expression describing the vectorial field distribution of radially polarized Gaussian beams diffracted by an axicon is derived. The theoretical analysis and simulation calculation show that the radial component of the diffraction field is the propagation-invariant first-order Bessel beam when the radially polarized Gaussian beam illuminates the axicon. However, the longitudinal component possesses no such behavior because of its intrinsic r dependence, and its central intensity is the maximum. The longitudinal component is related to the open angle and index of the axicon, which has to be considered when the open angle and index are large. For a small open angle and index, the longitudinal component can be neglected, and the scalar approximation is valid.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
    [CrossRef]
  2. P. A. Bélanger, M. Rioux, “Ring pattern of a lens-axicon doublet illuminated by a Gaussian beam,” Appl. Opt. 17, 1080–1086 (1978).
    [CrossRef] [PubMed]
  3. G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
    [CrossRef]
  4. R. M. Herman, T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [CrossRef]
  5. I. Manek, Y. B. Ovchinnikov, R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
    [CrossRef]
  6. Y. Song, D. Milan, I. I.I. Hill, W. T. Long, “Narrow all-light atom guide,” Opt. Lett. 24, 1805–1807 (1999).
    [CrossRef]
  7. H. Metcalf, P. Straaten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203–286 (1994).
    [CrossRef]
  8. V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
    [CrossRef]
  9. K. A. Ameur, F. Sanchez, “Gaussian beam conversion using an axicon,” J. Mod. Opt. 46, 1537–1548 (1999).
    [CrossRef]
  10. C. Paterson, R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
    [CrossRef]
  11. M. de Angelis, L. Cacciapuoti, G. Pierattini, G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
    [CrossRef]
  12. B. Dépret, P. Verkerk, D. Hennequin, “Characteriza- tion and modeling of the hollow beam produced by a real conical lens,” Opt. Commun. 211, 31–38 (2002).
    [CrossRef]
  13. A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
    [CrossRef] [PubMed]
  14. J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
    [CrossRef]
  15. V. Jarutis, R. Paškauskas, A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
    [CrossRef]
  16. J. Arlt, R. Kuhn, K. Dholakia, “Spatial transformation of Laguerre–Gaussian laser modes,” J. Mod. Opt. 48, 783–787 (2001).
  17. M. Lei, B. Yao, “Characteristics of beam profile of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
    [CrossRef]
  18. A. Ciattoni, B. Crosignani, P. D. Porto, “Vectorial analytical description of propagation of a highly nonparaxial beam,” Opt. Commun. 202, 17–20 (2002).
    [CrossRef]
  19. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1966).
  20. P. Török, P. Varga, Z. Laczik, G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995).
    [CrossRef]
  21. M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).
  22. J. Lloydb, K. Wanga, A. Barkana, D. M. Mittleman, “Characterization of apparent superluminal effects in the focus of an axicon lens using terahertz time- domain spectroscopy,” Opt. Commun. 219, 289–294 (2003).
    [CrossRef]
  23. C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37, 565–575 (2002).
    [CrossRef]
  24. N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, S. Withington, “The quasi-optical analysis of Bessel beams in the far infrared,” Infrared Phys. Technol. 46, 233–247 (2005).
    [CrossRef]

2005 (1)

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, S. Withington, “The quasi-optical analysis of Bessel beams in the far infrared,” Infrared Phys. Technol. 46, 233–247 (2005).
[CrossRef]

2004 (1)

M. Lei, B. Yao, “Characteristics of beam profile of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[CrossRef]

2003 (2)

J. Lloydb, K. Wanga, A. Barkana, D. M. Mittleman, “Characterization of apparent superluminal effects in the focus of an axicon lens using terahertz time- domain spectroscopy,” Opt. Commun. 219, 289–294 (2003).
[CrossRef]

M. de Angelis, L. Cacciapuoti, G. Pierattini, G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

2002 (5)

B. Dépret, P. Verkerk, D. Hennequin, “Characteriza- tion and modeling of the hollow beam produced by a real conical lens,” Opt. Commun. 211, 31–38 (2002).
[CrossRef]

G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37, 565–575 (2002).
[CrossRef]

A. Ciattoni, B. Crosignani, P. D. Porto, “Vectorial analytical description of propagation of a highly nonparaxial beam,” Opt. Commun. 202, 17–20 (2002).
[CrossRef]

2001 (1)

J. Arlt, R. Kuhn, K. Dholakia, “Spatial transformation of Laguerre–Gaussian laser modes,” J. Mod. Opt. 48, 783–787 (2001).

2000 (2)

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

V. Jarutis, R. Paškauskas, A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

1999 (2)

K. A. Ameur, F. Sanchez, “Gaussian beam conversion using an axicon,” J. Mod. Opt. 46, 1537–1548 (1999).
[CrossRef]

Y. Song, D. Milan, I. I.I. Hill, W. T. Long, “Narrow all-light atom guide,” Opt. Lett. 24, 1805–1807 (1999).
[CrossRef]

1998 (1)

I. Manek, Y. B. Ovchinnikov, R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

1996 (1)

C. Paterson, R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

1995 (1)

1994 (1)

H. Metcalf, P. Straaten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203–286 (1994).
[CrossRef]

1991 (1)

1989 (1)

1978 (1)

1954 (1)

Altucci, C.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37, 565–575 (2002).
[CrossRef]

Ameur, K. A.

K. A. Ameur, F. Sanchez, “Gaussian beam conversion using an axicon,” J. Mod. Opt. 46, 1537–1548 (1999).
[CrossRef]

Arlt, J.

J. Arlt, R. Kuhn, K. Dholakia, “Spatial transformation of Laguerre–Gaussian laser modes,” J. Mod. Opt. 48, 783–787 (2001).

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

Barkana, A.

J. Lloydb, K. Wanga, A. Barkana, D. M. Mittleman, “Characterization of apparent superluminal effects in the focus of an axicon lens using terahertz time- domain spectroscopy,” Opt. Commun. 219, 289–294 (2003).
[CrossRef]

Bélanger, P. A.

Booker, G. R.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).

Bruzzese, R.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37, 565–575 (2002).
[CrossRef]

Cacciapuoti, L.

M. de Angelis, L. Cacciapuoti, G. Pierattini, G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Chávez-Cerda, S.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Ciattoni, A.

A. Ciattoni, B. Crosignani, P. D. Porto, “Vectorial analytical description of propagation of a highly nonparaxial beam,” Opt. Commun. 202, 17–20 (2002).
[CrossRef]

Crosignani, B.

A. Ciattoni, B. Crosignani, P. D. Porto, “Vectorial analytical description of propagation of a highly nonparaxial beam,” Opt. Commun. 202, 17–20 (2002).
[CrossRef]

de Angelis, M.

M. de Angelis, L. Cacciapuoti, G. Pierattini, G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

de Lisio, C.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37, 565–575 (2002).
[CrossRef]

Dépret, B.

B. Dépret, P. Verkerk, D. Hennequin, “Characteriza- tion and modeling of the hollow beam produced by a real conical lens,” Opt. Commun. 211, 31–38 (2002).
[CrossRef]

Dholakia, K.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

J. Arlt, R. Kuhn, K. Dholakia, “Spatial transformation of Laguerre–Gaussian laser modes,” J. Mod. Opt. 48, 783–787 (2001).

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

Friberg, A. T.

Garcés-Chávez, V.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Grimm, R.

I. Manek, Y. B. Ovchinnikov, R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

Hennequin, D.

B. Dépret, P. Verkerk, D. Hennequin, “Characteriza- tion and modeling of the hollow beam produced by a real conical lens,” Opt. Commun. 211, 31–38 (2002).
[CrossRef]

Herman, R. M.

Hill, I. I.I.

Indebetouw, G.

G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
[CrossRef]

Jarutis, V.

V. Jarutis, R. Paškauskas, A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

Kuhn, R.

J. Arlt, R. Kuhn, K. Dholakia, “Spatial transformation of Laguerre–Gaussian laser modes,” J. Mod. Opt. 48, 783–787 (2001).

Laczik, Z.

Lanigan, W.

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, S. Withington, “The quasi-optical analysis of Bessel beams in the far infrared,” Infrared Phys. Technol. 46, 233–247 (2005).
[CrossRef]

Lei, M.

M. Lei, B. Yao, “Characteristics of beam profile of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[CrossRef]

Lloydb, J.

J. Lloydb, K. Wanga, A. Barkana, D. M. Mittleman, “Characterization of apparent superluminal effects in the focus of an axicon lens using terahertz time- domain spectroscopy,” Opt. Commun. 219, 289–294 (2003).
[CrossRef]

Long, W. T.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1966).

Mahon, R.

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, S. Withington, “The quasi-optical analysis of Bessel beams in the far infrared,” Infrared Phys. Technol. 46, 233–247 (2005).
[CrossRef]

Manek, I.

I. Manek, Y. B. Ovchinnikov, R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

McLeod, J. H.

Metcalf, H.

H. Metcalf, P. Straaten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203–286 (1994).
[CrossRef]

Milan, D.

Mittleman, D. M.

J. Lloydb, K. Wanga, A. Barkana, D. M. Mittleman, “Characterization of apparent superluminal effects in the focus of an axicon lens using terahertz time- domain spectroscopy,” Opt. Commun. 219, 289–294 (2003).
[CrossRef]

Murphy, J. A.

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, S. Withington, “The quasi-optical analysis of Bessel beams in the far infrared,” Infrared Phys. Technol. 46, 233–247 (2005).
[CrossRef]

Ovchinnikov, Y. B.

I. Manek, Y. B. Ovchinnikov, R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

Paškauskas, R.

V. Jarutis, R. Paškauskas, A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

Paterson, C.

C. Paterson, R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

Pierattini, G.

M. de Angelis, L. Cacciapuoti, G. Pierattini, G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Porto, P. D.

A. Ciattoni, B. Crosignani, P. D. Porto, “Vectorial analytical description of propagation of a highly nonparaxial beam,” Opt. Commun. 202, 17–20 (2002).
[CrossRef]

Porzio, A.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37, 565–575 (2002).
[CrossRef]

Rioux, M.

Sanchez, F.

K. A. Ameur, F. Sanchez, “Gaussian beam conversion using an axicon,” J. Mod. Opt. 46, 1537–1548 (1999).
[CrossRef]

Sibbett, W.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Smith, R.

C. Paterson, R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

Solimeno, S.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37, 565–575 (2002).
[CrossRef]

Song, Y.

Stabinis, A.

V. Jarutis, R. Paškauskas, A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

Straaten, P.

H. Metcalf, P. Straaten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203–286 (1994).
[CrossRef]

Tino, G. M.

M. de Angelis, L. Cacciapuoti, G. Pierattini, G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

Török, P.

Tosa, V.

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37, 565–575 (2002).
[CrossRef]

Trappe, N.

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, S. Withington, “The quasi-optical analysis of Bessel beams in the far infrared,” Infrared Phys. Technol. 46, 233–247 (2005).
[CrossRef]

Turunen, J.

Varga, P.

Vasara, A.

Verkerk, P.

B. Dépret, P. Verkerk, D. Hennequin, “Characteriza- tion and modeling of the hollow beam produced by a real conical lens,” Opt. Commun. 211, 31–38 (2002).
[CrossRef]

Volke-Sepulveda, K.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Wanga, K.

J. Lloydb, K. Wanga, A. Barkana, D. M. Mittleman, “Characterization of apparent superluminal effects in the focus of an axicon lens using terahertz time- domain spectroscopy,” Opt. Commun. 219, 289–294 (2003).
[CrossRef]

Wiggins, T. A.

Withington, S.

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, S. Withington, “The quasi-optical analysis of Bessel beams in the far infrared,” Infrared Phys. Technol. 46, 233–247 (2005).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).

Yao, B.

M. Lei, B. Yao, “Characteristics of beam profile of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[CrossRef]

Appl. Opt. (1)

Infrared Phys. Technol. (1)

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, S. Withington, “The quasi-optical analysis of Bessel beams in the far infrared,” Infrared Phys. Technol. 46, 233–247 (2005).
[CrossRef]

J. Mod. Opt. (3)

G. Indebetouw, “Properties of a scanning holographic microscope: improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
[CrossRef]

K. A. Ameur, F. Sanchez, “Gaussian beam conversion using an axicon,” J. Mod. Opt. 46, 1537–1548 (1999).
[CrossRef]

J. Arlt, R. Kuhn, K. Dholakia, “Spatial transformation of Laguerre–Gaussian laser modes,” J. Mod. Opt. 48, 783–787 (2001).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Commun. (8)

I. Manek, Y. B. Ovchinnikov, R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

B. Dépret, P. Verkerk, D. Hennequin, “Characteriza- tion and modeling of the hollow beam produced by a real conical lens,” Opt. Commun. 211, 31–38 (2002).
[CrossRef]

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

V. Jarutis, R. Paškauskas, A. Stabinis, “Focusing of Laguerre–Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

J. Lloydb, K. Wanga, A. Barkana, D. M. Mittleman, “Characterization of apparent superluminal effects in the focus of an axicon lens using terahertz time- domain spectroscopy,” Opt. Commun. 219, 289–294 (2003).
[CrossRef]

M. Lei, B. Yao, “Characteristics of beam profile of Gaussian beam passing through an axicon,” Opt. Commun. 239, 367–372 (2004).
[CrossRef]

A. Ciattoni, B. Crosignani, P. D. Porto, “Vectorial analytical description of propagation of a highly nonparaxial beam,” Opt. Commun. 202, 17–20 (2002).
[CrossRef]

C. Paterson, R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

Opt. Lasers Eng. (2)

M. de Angelis, L. Cacciapuoti, G. Pierattini, G. M. Tino, “Axially symmetric hollow beams using refractive conical lenses,” Opt. Lasers Eng. 39, 283–291 (2003).
[CrossRef]

C. Altucci, R. Bruzzese, C. de Lisio, A. Porzio, S. Solimeno, V. Tosa, “Diffractionless beams and their use for harmonic generation,” Opt. Lasers Eng. 37, 565–575 (2002).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

H. Metcalf, P. Straaten, “Cooling and trapping of neutral atoms,” Phys. Rep. 244, 203–286 (1994).
[CrossRef]

Phys. Rev. A (1)

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Other (2)

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1966).

M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).

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 (3)

Fig. 1
Fig. 1

Schematic overview of the natural basis ( k ̂ , l ̂ , m ̂ ) , polarization basis ( k ̂ , s ̂ , p ̂ ) , and Cartesian basis ( x ̂ , y ̂ , z ̂ ) .

Fig. 2
Fig. 2

Intensity distribution and contour of (a) the radial component of the electric field and (b) the longitudinal component at z = 0.5 z max . The calculation parameters are n = 2 , w 0 = 5 mm , R = 30 mm , α = 10 ° , and λ = 514.5 nm .

Fig. 3
Fig. 3

Ratio of the maximum intensities of the longitudinal and radial components as a function of (a) the open angle and (b) the refractive index of the axicon. The calculation parameters are the same as shown in Fig. 2.

Equations (36)

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

E x ( r ) = 1 2 π E x ( r 0 ) z ( exp ( i k l ) l ) d x 0 d y 0 ,
E y ( r ) = 1 2 π E y ( r 0 ) z ( exp ( i k l ) l ) d x 0 d y 0 ,
E z ( r ) = 1 2 π [ E x ( r 0 ) x ( exp ( i k l ) l ) + E y ( r 0 ) y ( exp ( i k l ) l ) ] d x 0 d y 0 ,
E x ( r ) = 1 2 π E x ( r 0 ) z i k l 1 l 3 exp ( i k l ) d x 0 d y 0 ,
E y ( r ) = 1 2 π E y ( r 0 ) z i k l 1 l 3 exp ( i k l ) d x 0 d y 0 ,
E z ( r ) = 1 2 π [ E x ( r 0 ) ( x x 0 ) + E y ( r 0 ) ( y y 0 ) ] i k l 1 l 3 exp ( i k l ) d x 0 d y 0 .
l r + x 0 2 + y 0 2 2 x x 0 2 y y 0 2 r ,
E x ( ρ , β , z ) = i z exp ( i k r ) λ r 2 0 d ρ 0 0 2 π d ϕ E x ( r 0 ) exp ( i k ρ 0 2 2 r ) exp ( i k ρ ρ 0 cos ( ϕ β ) r ) ρ 0 ,
E y ( ρ , β , z ) = i z exp ( i k r ) λ r 2 0 d ρ 0 0 2 π d ϕ E y ( r 0 ) exp ( i k ρ 0 2 2 r ) exp ( i k ρ ρ 0 cos ( ϕ β ) r ) ρ 0 ,
E z ( ρ , β , z ) = i exp ( i k r ) λ r 2 0 d ρ 0 0 2 π d ϕ [ E x ( r 0 ) ( ρ cos β ρ 0 cos ϕ ) + E y ( r 0 ) ( ρ sin β ρ 0 sin ϕ ) ] × exp ( i k ρ 0 2 2 r ) exp ( i k ρ ρ 0 cos ( ϕ β ) r ) ρ 0 .
E ( r 0 ) = ( E x ( r 0 ) E y ( r 0 ) E z ( r 0 ) ) = P ( ϕ ) A ( ρ 0 , ϕ ) ,
P 0 = ( a ( ϕ ) b ( ϕ ) 0 ) .
P ( ϕ ) = R 1 L 1 ILCRP 0 ,
R = [ cos ϕ sin ϕ 0 sin ϕ cos ϕ 0 0 0 1 ] ,
C = [ cos θ 0 sin θ 0 1 0 sin θ 0 cos θ ] ,
L = [ cos α 0 sin α 0 1 0 sin α 0 cos α ] ,
I = [ t p 0 0 0 t s 0 0 0 t p ] .
P ( ϕ ) = [ a ( t p cos θ cos 2 ϕ + t s sin 2 ϕ ) + b ( t p cos θ t s ) sin ϕ cos ϕ a ( t p cos θ t s ) sin ϕ cos ϕ + b ( t p cos θ sin 2 ϕ + t s cosn 2 ϕ ) a t p sin θ cos ϕ b t p sin θ sin ϕ ] .
E ( r 0 ) = exp ( ρ 0 2 w 0 2 ) e ̂ x + exp ( ρ 0 2 w 0 2 ) e ̂ y .
P ( ϕ ) = [ t p cos θ cos ϕ t p cos θ sin ϕ t p sin θ ] .
A ( ρ 0 , ϕ ) = exp ( ρ 0 2 w 0 2 ) exp ( i k ξ ρ 0 ) rect ( ρ 0 R ) ,
rect ( ρ 0 R ) = { 1 , ρ 0 R 0 , otherwise } .
0 2 π d ϕ cos m ϕ exp [ i η cos ( ϕ β ) ] = 2 π i m J m ( η ) cos m β ,
0 2 π d ϕ sin m ϕ exp [ i η cos ( ϕ β ) ] = 2 π i m J m ( η ) sin m β ,
E x ( ρ , β , z ) = i k z t p cos θ exp ( i k r ) r 2 cos β 0 R d ρ 0 exp ( μ ) J 1 ( η ) ρ 0 ,
E y ( ρ , β , z ) = i k z t p cos θ exp ( i k r ) r 2 sin β 0 R d ρ 0 exp ( μ ) J 1 ( η ) ρ 0 ,
E z ( ρ , β , z ) = k t p cos θ exp ( i k r ) r 2 0 R d ρ 0 exp ( μ ) [ ρ 0 J 0 ( η ) i ρ J 1 ( η ) ] ρ 0 ,
μ = exp [ ρ 0 2 w 0 2 + i k ρ 0 2 2 r i k ρ 0 ξ ] , η = k ρ ρ 0 r .
E x ( ρ , β , z ) = B k z t p ξ cos θ r cos β exp ( r 2 ξ 2 w 0 2 ) J 1 ( k ρ ξ ) ,
E y ( ρ , β , z ) = B k z t p ξ cos θ r sin β exp ( r 2 ξ 2 w 0 2 ) J 1 ( k ρ ξ ) ,
E z ( ρ , β , z ) = B i k t p ξ cos θ 2 r exp ( r 2 ξ 2 w 0 2 ) [ r ξ J 0 ( k ρ ξ ) i ρ J 1 ( k ρ ξ ) ] ,
B = π 2 k exp ( i π 4 ) exp ( i k ξ 2 r 2 ) exp ( i k r ) .
E ρ ( ρ , β , z ) = k z t p ξ cos θ r exp ( r 2 ξ 2 w 0 2 ) J 1 ( k ρ ξ ) ,
E z ( ρ , β , z ) = i k t p ξ cos θ 2 r exp ( r 2 ξ 2 w 0 2 ) [ r ξ J 0 ( k ρ ξ ) i ρ J 1 ( k ρ ξ ) ] ,
I ρ ( ρ , β , z ) = E ρ ( ρ , β , z ) 2 E ρ ( ρ , β , z ) max 2 ,
I z ( ρ , β , z ) = E z ( ρ , β , z ) 2 E ρ ( ρ , β , z ) max 2 .

Metrics