Abstract

Performance parameters are presented for high-aperture radially polarized focusing systems. These can be used for comparing the focusing performance of different optical systems, including the effect of pupil filters.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. C. J. R. Sheppard and P. Török, Optik (Stuttgart) 104, 175 (1996).
  2. C. J. R. Sheppard and S. Saghafi, Opt. Lett. 24, 1543 (1999).
    [CrossRef]
  3. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
    [CrossRef]
  4. K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000).
    [CrossRef] [PubMed]
  5. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  6. E. Y. S. Yew and C. J. R. Sheppard, Opt. Lett. 32, 3417 (2007).
    [CrossRef] [PubMed]
  7. C. J. R. Sheppard and A. Choudhury, Appl. Opt. 43, 4322 (2004).
    [CrossRef] [PubMed]
  8. M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, Opt. Eng. (Bellingham) 45, 098003 (2006).
    [CrossRef]
  9. C. J. R. Sheppard and Z. S. Hegedus, J. Opt. Soc. Am. A 5, 643 (1988).
    [CrossRef]
  10. C. J. R. Sheppard, Opt. Lett. 32, 1653 (2007).
    [CrossRef] [PubMed]
  11. C. J. R. Sheppard and M. Martinez-Corral, Opt. Lett. (to be published).
  12. J. J. Stamnes, Opt. Commun. 37, 311 (1981).
    [CrossRef]
  13. C. J. R. Sheppard and H. J. Matthews, J. Opt. Soc. Am. A 4, 1354 (1987).
    [CrossRef]
  14. J. F. Nye and J. V. Hajnal, Proc. R. Soc. London, Ser. A 409, 21 (1987).
    [CrossRef]

2007 (2)

2006 (1)

M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, Opt. Eng. (Bellingham) 45, 098003 (2006).
[CrossRef]

2004 (1)

2003 (1)

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

2000 (2)

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

K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000).
[CrossRef] [PubMed]

1999 (1)

1996 (1)

C. J. R. Sheppard and P. Török, Optik (Stuttgart) 104, 175 (1996).

1988 (1)

1987 (2)

C. J. R. Sheppard and H. J. Matthews, J. Opt. Soc. Am. A 4, 1354 (1987).
[CrossRef]

J. F. Nye and J. V. Hajnal, Proc. R. Soc. London, Ser. A 409, 21 (1987).
[CrossRef]

1981 (1)

J. J. Stamnes, Opt. Commun. 37, 311 (1981).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

J. J. Stamnes, Opt. Commun. 37, 311 (1981).
[CrossRef]

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

Opt. Eng. (Bellingham) (1)

M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, Opt. Eng. (Bellingham) 45, 098003 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Optik (Stuttgart) (1)

C. J. R. Sheppard and P. Török, Optik (Stuttgart) 104, 175 (1996).

Phys. Rev. Lett. (1)

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

Proc. R. Soc. London, Ser. A (1)

J. F. Nye and J. V. Hajnal, Proc. R. Soc. London, Ser. A 409, 21 (1987).
[CrossRef]

Other (1)

C. J. R. Sheppard and M. Martinez-Corral, Opt. Lett. (to be published).

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 (2)

Fig. 1
Fig. 1

Behavior of the parameters (a) F, the normalized ratio of the electric energy density at the focus to the focused power and, (b) F I , the normalized ratio of the electric energy density at the focus to the integrated intensity (electric energy density) for an axially oriented electric dipole field (ADW) and some other special cases (ALG, AU). ADW is shown in bold.

Fig. 2
Fig. 2

Behavior of the axial, transverse, and polar gains G A , G T , and G P for various different cases. ADW Q ( c ) = 1 c 2 is shown in bold.

Equations (17)

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

E z = i k f I z ,
E ρ = k f I ρ ,
I z = Q ( c ) J 0 ( k ρ 1 c 2 ) exp ( i k z c ) d c ,
I ρ = Q ( c ) c 1 c 2 J 1 ( k ρ 1 c 2 ) exp ( i k z c ) d c .
I z = Q ( c ) 1 ( k ρ ) 2 4 ( 1 c 2 ) + i k z c 1 2 ( k z ) 2 c 2 d c ,
I ρ = Q ( c ) c k ρ 2 ( 1 + i k z c ) d c .
q n = Q ( c ) c n d c ,
I z = q 0 + i k z q 1 ( k z ) 2 2 q 2 ( k ρ ) 2 4 ( q 0 q 2 ) ,
I ρ = k ρ 2 q 1 + i ( k ρ ) ( k z ) 2 q 2 .
E = Q ( c ) 2 1 c 2 d c .
F = 3 q 0 2 4 E ,
W EInt = Q ( c ) 2 c ( 1 c 2 ) d c ,
F I = q 0 2 Q ( c ) 2 c ( 1 c 2 ) d c ,
W E = q 0 2 [ 1 ( k z ) 2 ( q 0 q 2 q 1 2 ) q 0 2 ( k ρ ) 2 4 2 q 0 2 2 q 0 q 2 q 1 2 q 0 2 ] .
W E = q 0 2 [ 1 G A 3 ( k z ) 2 G T 3 ( k ρ ) 2 ] ,
G A = 3 ( q 0 q 2 q 1 2 ) q 0 2 ,
G T = 3 ( 2 q 0 2 2 q 0 q 2 q 1 2 ) 4 q 0 2 .

Metrics