Abstract

The properties of the focal spot for 4π focusing with radially polarized light are presented for various apodization factors. With a focusing system satisfying the Herschel condition, sharp focal spots with almost-perfect spherical symmetry (leading to equal axial and transverse resolution) and extremely low sidelobes are achieved.

© 2004 Optical Society of America

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References

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  1. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
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  2. N. Davidson and N. Bokor, Opt. Lett. 29, 1318 (2004).
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  3. M. A. Lieb and A. J. Meixner, Opt. Express 8, 458 (2001), http://www.opticsexpress.org .
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  4. C. Debus, M. A. Lieb, A. Dreschler, and A. J. Meixner, J. Microsc. (Oxford) 210, 203 (2003).
    [CrossRef]
  5. S. Hell and E. H. K. Stelzer, J. Opt. Soc. Am. A 9, 2159 (1992).
    [CrossRef]
  6. S. Hell and E. H. K. Stelzer, Opt. Commun. 93, 277 (1992).
    [CrossRef]
  7. C. M. Blanca, J. Bewersdorf, and S. Hell, Appl. Phys. Lett. 79, 2321 (2001).
    [CrossRef]
  8. M. Martínez-Corral, M. T. Caballero, A. Pons, and P. Andrés, Micron. 34, 319 (2003).
    [CrossRef]
  9. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
    [CrossRef]
  10. C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
    [CrossRef]
  11. F. T. S. Yu and I. C. Khoo, Principles of Optical Engineering (Wiley, New York, 1990), pp. 140–142.
  12. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 167–169.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2004 (2)

2003 (3)

C. Debus, M. A. Lieb, A. Dreschler, and A. J. Meixner, J. Microsc. (Oxford) 210, 203 (2003).
[CrossRef]

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

M. Martínez-Corral, M. T. Caballero, A. Pons, and P. Andrés, Micron. 34, 319 (2003).
[CrossRef]

2002 (1)

2001 (2)

C. M. Blanca, J. Bewersdorf, and S. Hell, Appl. Phys. Lett. 79, 2321 (2001).
[CrossRef]

M. A. Lieb and A. J. Meixner, Opt. Express 8, 458 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

2000 (2)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

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

1993 (1)

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

1992 (2)

S. Hell and E. H. K. Stelzer, J. Opt. Soc. Am. A 9, 2159 (1992).
[CrossRef]

S. Hell and E. H. K. Stelzer, Opt. Commun. 93, 277 (1992).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Andrés, P.

M. Martínez-Corral, M. T. Caballero, A. Pons, and P. Andrés, Micron. 34, 319 (2003).
[CrossRef]

Bewersdorf, J.

C. M. Blanca, J. Bewersdorf, and S. Hell, Appl. Phys. Lett. 79, 2321 (2001).
[CrossRef]

Blanca, C. M.

C. M. Blanca, J. Bewersdorf, and S. Hell, Appl. Phys. Lett. 79, 2321 (2001).
[CrossRef]

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Bokor, N.

Bomzon, Z.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 167–169.

Caballero, M. T.

M. Martínez-Corral, M. T. Caballero, A. Pons, and P. Andrés, Micron. 34, 319 (2003).
[CrossRef]

Davidson, N.

Debus, C.

C. Debus, M. A. Lieb, A. Dreschler, and A. J. Meixner, J. Microsc. (Oxford) 210, 203 (2003).
[CrossRef]

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]

Dreschler, A.

C. Debus, M. A. Lieb, A. Dreschler, and A. J. Meixner, J. Microsc. (Oxford) 210, 203 (2003).
[CrossRef]

Eberler, M.

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

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Glöckl, O.

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

Gu, M.

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

Hasman, E.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Hell, S.

C. M. Blanca, J. Bewersdorf, and S. Hell, Appl. Phys. Lett. 79, 2321 (2001).
[CrossRef]

S. Hell and E. H. K. Stelzer, Opt. Commun. 93, 277 (1992).
[CrossRef]

S. Hell and E. H. K. Stelzer, J. Opt. Soc. Am. A 9, 2159 (1992).
[CrossRef]

Khoo, I. C.

F. T. S. Yu and I. C. Khoo, Principles of Optical Engineering (Wiley, New York, 1990), pp. 140–142.

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]

Lieb, M. A.

C. Debus, M. A. Lieb, A. Dreschler, and A. J. Meixner, J. Microsc. (Oxford) 210, 203 (2003).
[CrossRef]

M. A. Lieb and A. J. Meixner, Opt. Express 8, 458 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Martínez-Corral, M.

M. Martínez-Corral, M. T. Caballero, A. Pons, and P. Andrés, Micron. 34, 319 (2003).
[CrossRef]

Meixner, A. J.

C. Debus, M. A. Lieb, A. Dreschler, and A. J. Meixner, J. Microsc. (Oxford) 210, 203 (2003).
[CrossRef]

M. A. Lieb and A. J. Meixner, Opt. Express 8, 458 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Pons, A.

M. Martínez-Corral, M. T. Caballero, A. Pons, and P. Andrés, Micron. 34, 319 (2003).
[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]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

Stelzer, E. H. K.

S. Hell and E. H. K. Stelzer, J. Opt. Soc. Am. A 9, 2159 (1992).
[CrossRef]

S. Hell and E. H. K. Stelzer, Opt. Commun. 93, 277 (1992).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 167–169.

Yu, F. T. S.

F. T. S. Yu and I. C. Khoo, Principles of Optical Engineering (Wiley, New York, 1990), pp. 140–142.

Appl. Phys. Lett. (2)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

C. M. Blanca, J. Bewersdorf, and S. Hell, Appl. Phys. Lett. 79, 2321 (2001).
[CrossRef]

J. Microsc. (Oxford) (1)

C. Debus, M. A. Lieb, A. Dreschler, and A. J. Meixner, J. Microsc. (Oxford) 210, 203 (2003).
[CrossRef]

J. Mod. Opt. (1)

C. J. R. Sheppard and M. Gu, J. Mod. Opt. 40, 1631 (1993).
[CrossRef]

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

Micron. (1)

M. Martínez-Corral, M. T. Caballero, A. Pons, and P. Andrés, Micron. 34, 319 (2003).
[CrossRef]

Opt. Commun. (2)

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

S. Hell and E. H. K. Stelzer, Opt. Commun. 93, 277 (1992).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

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

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

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Other (2)

F. T. S. Yu and I. C. Khoo, Principles of Optical Engineering (Wiley, New York, 1990), pp. 140–142.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993), pp. 167–169.

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of a 4π focusing system with principal surfaces RΘ and focal length F, illuminated by two counterpropagating radially polarized doughnut beams with a relative π phase shift, as indicated by the dotted arrows that show the instantaneous directions of the radial polarization vectors.

Fig. 2
Fig. 2

Calculated logarithmic contour map of the electric field intensity near the focus in the R,Z plane for (a) an aplanatic, (b) an inverse-dipole, and (c) a Herschel-type 4π focusing system. Distances are normalized to the wavelength.

Fig. 3
Fig. 3

Calculated normalized intensity profiles near the focus, along the R axis [(a), (c) and (e)] and along the Z axis [(b), (d) and (f)], for (a), (b), an aplanatic, (c), (d), an inverse-dipole, and (e), (f), a Herschel-type 4π focusing system. Distances are normalized to the wavelength.

Fig. 4
Fig. 4

Calculated normalized axial sidelobe heights as a function of ΘMAX for an aplanatic (dashed curve), an inverse-dipole (dotted curve), and a Herschel-type (solid curve) 4π focusing system.

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