Abstract

We demonstrate experimentally and theoretically that a parabolic mirror (PM) with a high numerical aperture (NA) of 1 focuses a radially polarized laser mode to the smallest diffraction-limited spot at a fixed NA and wavelength, having an area of 0.134λ2. The measurements were performed with a confocal microscope, using the PM as a focusing and collecting element. The results stand in accordance with the theoretical calculations presented by Davidson and Bokor [Opt. Lett. 29, 1318 (2004)] , who predicted a reduction in the total focal spot size of 43% as compared with an aplanatic lens.

© 2008 Optical Society of America

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  1. S. Quabis, R. Dorn, M. Eberler, O. Glockl, and G. Leuchs, Opt. Commun. 179, 1 (2000).
    [CrossRef]
  2. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 4 (2003).
    [CrossRef]
  3. The spot size is defined as the area that is encircled by the contour line at half the maximum value of the intensity.
  4. N. Davidson and N. Bokor, Opt. Lett. 29, 1318 (2004).
    [CrossRef] [PubMed]
  5. A. Lieb and A. J. Meixner, Opt. Express 8, 458 (2001).
    [CrossRef] [PubMed]
  6. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).
  7. Radial beam profile at the mirror aperture, I(r)=I0exp(r/w0)2I1(2r/w0) with fitting parameter 2r/w0=1.2728.
  8. C. Debus, M. A. Lieb, A. Drechsler, and A. J. Meixner, J. Microsc. 210, 203 (2003).
    [CrossRef] [PubMed]
  9. B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
    [CrossRef]
  10. F. Stade, A. Heeren, M. Fleischer, and D. Kern, Microelectron. Eng. 84, 1589 (2007).
    [CrossRef]
  11. M. R. Beversluis, A. Bouhelier, and L. Novotny, Phys. Rev. B 68, 115433 (2003).
    [CrossRef]
  12. A. Bouhelier, M. R. Beversluis, and L. Novotny, Appl. Phys. Lett. 82, 4596 (2003).
    [CrossRef]
  13. N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
    [CrossRef]
  14. M.Born and E.Wolf, eds., Principles of Optics, 7th. ed. (Cambridge U. Press, 1999).

2007 (1)

F. Stade, A. Heeren, M. Fleischer, and D. Kern, Microelectron. Eng. 84, 1589 (2007).
[CrossRef]

2006 (1)

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

2004 (2)

N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

N. Davidson and N. Bokor, Opt. Lett. 29, 1318 (2004).
[CrossRef] [PubMed]

2003 (4)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 4 (2003).
[CrossRef]

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

M. R. Beversluis, A. Bouhelier, and L. Novotny, Phys. Rev. B 68, 115433 (2003).
[CrossRef]

A. Bouhelier, M. R. Beversluis, and L. Novotny, Appl. Phys. Lett. 82, 4596 (2003).
[CrossRef]

2001 (1)

2000 (1)

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

1999 (1)

M.Born and E.Wolf, eds., Principles of Optics, 7th. ed. (Cambridge U. Press, 1999).

1959 (1)

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

Beversluis, M. R.

M. R. Beversluis, A. Bouhelier, and L. Novotny, Phys. Rev. B 68, 115433 (2003).
[CrossRef]

A. Bouhelier, M. R. Beversluis, and L. Novotny, Appl. Phys. Lett. 82, 4596 (2003).
[CrossRef]

Bokor, N.

Bouhelier, A.

M. R. Beversluis, A. Bouhelier, and L. Novotny, Phys. Rev. B 68, 115433 (2003).
[CrossRef]

A. Bouhelier, M. R. Beversluis, and L. Novotny, Appl. Phys. Lett. 82, 4596 (2003).
[CrossRef]

Davidson, N.

Debus, C.

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

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 4 (2003).
[CrossRef]

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

Drechsler, A.

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

Eberler, M.

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

Fleischer, M.

F. Stade, A. Heeren, M. Fleischer, and D. Kern, Microelectron. Eng. 84, 1589 (2007).
[CrossRef]

Glockl, O.

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

Hayazawa, N.

N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

Heeren, A.

F. Stade, A. Heeren, M. Fleischer, and D. Kern, Microelectron. Eng. 84, 1589 (2007).
[CrossRef]

Kawata, S.

N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

Kern, D.

F. Stade, A. Heeren, M. Fleischer, and D. Kern, Microelectron. Eng. 84, 1589 (2007).
[CrossRef]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 4 (2003).
[CrossRef]

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

Lieb, A.

Lieb, M. A.

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

Meixner, A. J.

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

A. Lieb and A. J. Meixner, Opt. Express 8, 458 (2001).
[CrossRef] [PubMed]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

M. R. Beversluis, A. Bouhelier, and L. Novotny, Phys. Rev. B 68, 115433 (2003).
[CrossRef]

A. Bouhelier, M. R. Beversluis, and L. Novotny, Appl. Phys. Lett. 82, 4596 (2003).
[CrossRef]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 4 (2003).
[CrossRef]

S. Quabis, R. Dorn, M. Eberler, O. Glockl, 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]

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

Stade, F.

F. Stade, A. Heeren, M. Fleischer, and D. Kern, Microelectron. Eng. 84, 1589 (2007).
[CrossRef]

Wolf, E.

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

Appl. Phys. Lett. (2)

A. Bouhelier, M. R. Beversluis, and L. Novotny, Appl. Phys. Lett. 82, 4596 (2003).
[CrossRef]

N. Hayazawa, Y. Saito, and S. Kawata, Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

J. Microsc. (1)

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

Microelectron. Eng. (1)

F. Stade, A. Heeren, M. Fleischer, and D. Kern, Microelectron. Eng. 84, 1589 (2007).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

M. R. Beversluis, A. Bouhelier, and L. Novotny, Phys. Rev. B 68, 115433 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 4 (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 (4)

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge U. Press, 2006).

Radial beam profile at the mirror aperture, I(r)=I0exp(r/w0)2I1(2r/w0) with fitting parameter 2r/w0=1.2728.

M.Born and E.Wolf, eds., Principles of Optics, 7th. ed. (Cambridge U. Press, 1999).

The spot size is defined as the area that is encircled by the contour line at half the maximum value of the intensity.

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Figures (3)

Fig. 1
Fig. 1

(a) Calculated intensity distribution of a radially polarized Bessel–Gauss beam for I = 632.8 nm in the focal region of a PM with NA = 0.999 . (b) Line section through the focal region showing the total field strength E 2 , the longitudinal field strength E z 2 , and the transversal field strength E p 2 . (c) Experimental confocal scan of a 40 nm fluorescent bead.

Fig. 2
Fig. 2

Confocal fluorescence images of a gold cone rastered through the focus of (a) a radially polarized mode and (b) a horizontally polarized Gauss mode, compared with the respective theoretical E z 2 distributions. The scale bar is 633 nm .

Fig. 3
Fig. 3

(a) Confocal image of a single Nile Blue molecule scanned through the focus of a radially polarized laser beam in a PM. (b) Line section through the center of the focus, compared with the calculated E z 2 distribution. (c) PL pattern of a gold cone scanned through a radial mode. (d) Comparison between the experimental PL signal and the calculated E z 2 distribution.

Equations (1)

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E ( P ) = i k f 2 π Ω E f m ( θ , ϕ ) exp ( i ( k s r P + Δ φ ( θ , ϕ ) ) ) sin θ d θ d ϕ .

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