Abstract

We demonstrate that the amplitude of vector-vortex beams has a Bessel–Gauss (BG) distribution through a rigorous vector electromagnetic analysis. We also investigate the intensity profiles in the focal plane of vector-vortex beams that are focused by a high numerical-aperture lens obeying the Helmholtz condition. Although the intensity of a vector-vortex BG beam with a topological charge n=1 is nonzero along the axis in the focal plane, the beams with n1 show discrete multiple spots which can be useful for optical trapping.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Express 14, 4208 (2006).
    [CrossRef] [PubMed]
  2. M. Stalder and M. Schadt, Opt. Lett. 21, 1948 (1996).
    [CrossRef] [PubMed]
  3. C. Maurer, A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, New J. Phys. 9, 78 (2007).
    [CrossRef]
  4. X. L. Wang, J. P. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, Opt. Lett. 32, 3549 (2007).
    [CrossRef] [PubMed]
  5. Q. Zhan, Adv. Opt. Photon. 1, 1 (2009).
    [CrossRef]
  6. J. T. Barreiro, T. C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 105, 030407 (2010).
    [CrossRef] [PubMed]
  7. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  8. H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
    [CrossRef]
  9. K. Huang, P. Shi, X. L. Kang, X. B. Zhang, and Y. P. Li, Opt. Lett. 35, 965 (2010).
    [CrossRef] [PubMed]
  10. M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
    [CrossRef] [PubMed]
  11. A. Niv, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 29, 238 (2004).
    [CrossRef] [PubMed]
  12. Y. Kozawa and S. Sato, J. Opt. Soc. Am. A 24, 1793 (2007).
    [CrossRef]
  13. S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, Opt. Express 15, 8619 (2007).
    [CrossRef] [PubMed]

2010 (2)

2009 (1)

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

2007 (4)

2006 (1)

2004 (1)

2003 (1)

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

2002 (1)

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

1996 (1)

Arlt, J.

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Arnold, A. S.

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 105, 030407 (2010).
[CrossRef] [PubMed]

Bernet, S.

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

Biener, G.

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Dholakia, K.

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Ding, J. P.

Dorn, R.

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

Ellinas, D.

Franke-Arnold, S.

Furhapter, S.

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

Girkin, J. M.

Guo, C. S.

Hasman, E.

Huang, K.

Jesacher, A.

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

Kang, X. L.

Kleiner, V.

Kozawa, Y.

Kwiat, P. G.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 105, 030407 (2010).
[CrossRef] [PubMed]

Leach, J.

Lembessis, V. E.

Leuchs, G.

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

Li, Y. P.

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

MacDonald, M.

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Maurer, C.

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

Ni, W. J.

Niv, A.

Ohberg, P.

Padgett, M. J.

Paterson, L.

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Quabis, S.

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

Ritsch-Marte, M.

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

Sato, S.

Schadt, M.

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Shi, P.

Sibbett, W.

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Stalder, M.

Volke-Sepulveda, K.

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

Wang, H. T.

Wang, X. L.

Wei, T. C.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 105, 030407 (2010).
[CrossRef] [PubMed]

Wright, A. J.

Zhan, Q.

Zhang, X. B.

Adv. Opt. Photon. (1)

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

Nat. Photon. (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photon. 2, 501 (2008).
[CrossRef]

New J. Phys. (1)

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

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. Lett. (2)

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, Phys. Rev. Lett. 105, 030407 (2010).
[CrossRef] [PubMed]

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

Science (1)

M. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, Science 296, 1101 (2002).
[CrossRef] [PubMed]

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

Intensity and vector plots of the vector-vortex BG beams with n = 1 , 1, 2, 3 and φ 0 = 0 in the waist plane. The beam parameters are w 0 = 2.5 mm and β = 0.5 mm 1 . (a)  n = 1 ; (b)  n = 1 , the radially polarized beam; (c)  n = 2 ; (d)  n = 3 .

Fig. 2
Fig. 2

Schematic of the vector-vortex BG beams focused by a high NA lens. The origin of the coordinate system is located in the geometric focus of the lens. The waist plane of beams and the pupil plane of the lens share the same position. θ denotes the angle between the convergent ray and the optical axis.

Fig. 3
Fig. 3

Total electric field ( | E t | 2 = | E ρ | 2 + | E ϕ | 2 + | E z | 2 ) in the focal plane of the focused vector-vortex BG beams with n = 1 , 1, 2, 3 and φ 0 = 0 . The NA of the focusing lens is 0.95 in vacuum. (a)  n = 1 . Inset, total electric field and polarization profile of the focused beam with n = 1 in the x = z plane. (b)  n = 1 , the radially polarized beam. (c)  n = 2 . Inset, normalized intensity along the dashed line A A , which indicates the on-axis intensity of the focused beam with n = 2 is nonzero. (d)  n = 3 .

Equations (10)

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

× × E k 2 E = 0 ,
E ( r , φ , z , t ) = F ( r , φ , z ) exp [ i ( k z ω t ) ] ,
1 r r ( r F r r ) 1 r 2 F r 2 r 2 F φ φ + 1 r 2 2 F r φ 2 + 2 i k F r z = 0 ,
1 r r ( r F φ r ) 1 r 2 F φ + 2 r 2 F r φ + 1 r 2 2 F φ φ 2 + 2 i k F φ z = 0.
1 r r ( r A r ) n 2 r 2 A + 2 i k A z = 0 ,
A ( r , z ) = 1 1 + i z / z 0 exp ( r 2 / w 0 2 1 + i z / z 0 ) · exp [ i β 2 z / ( 2 k ) 1 + i z / z 0 ] J n ( β r 1 + i z / z 0 ) ,
E ρ ( ρ , ϕ , z ) = C · i n + 1 cos [ ( n 1 ) ϕ + φ 0 ] 0 α P ( θ ) A ( θ ) [ cos θ ( J n J n 2 ) + ( J n + J n 2 ) ] sin θ · e i k z cos θ d θ ,
E ϕ ( ρ , ϕ , z ) = C · i n + 1 sin [ ( n 1 ) ϕ + φ 0 ] 0 α P ( θ ) A ( θ ) [ cos θ ( J n + J n 2 ) + ( J n J n 2 ) ] sin θ · e i k z cos θ d θ ,
E z ( ρ , ϕ , z ) = 2 C · i n cos [ ( n 1 ) ϕ + φ 0 ] 0 α P ( θ ) A ( θ ) J n 1 · sin 2 θ · e i k z cos θ d θ ,
P ( θ ) = exp ( γ 2 tan 2 θ tan 2 α ) J n ( β w 0 γ tan θ tan α ) ,

Metrics