Abstract

We have used a Gaussian standing-wave atom-optical lens to focus a thermal atomic beam. We examine the effect of variations in the intensity profile along the direction of the atomic beam on the performance of our atom-optical lens. For a constant focal-length atom-optical lens, we find that the resolution and contrast of the standing-wave lens are independent of the intensity profile.

© 1997 Optical Society of America

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References

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  1. G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham, M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636 (1992).
    [Crossref] [PubMed]
  2. J. J. McClelland, R. E. Sholten, E. C. Palm, and R. J. Cellota, Science 262, 877 (1993).
    [Crossref] [PubMed]
  3. R. W. McGowan, D. M. Giltner, and S. A. Lee, Opt. Lett. 20, 2535 (1995).
    [Crossref]
  4. We define throughput as the time required for making a pattern of a given area and thickness.
  5. V. Natarajan, R. E. Behringer, and G. Timp, Phys. Rev. A 53, 4381 (1996).
    [Crossref] [PubMed]
  6. V. Natarajan, R. E. Behringer, G. Timp, and D. M. Tennant, J. Vac. Sci. Technol. B 13, 2823 (1995).
    [Crossref]
  7. G. Timp, R. E. Behringer, V. Natarajan, and D. Tennant, “Focusing a thermal atomic beam to nanometer resolution using a laser,” submitted to Phys. Rev. A.
  8. J. J. McClelland, J. Opt. Soc. Am. B 12, 1761 (1995).
    [Crossref]
  9. J. P. Gordon and A. Ashkin, Phys. Rev. A 21, 1601 (1980).
    [Crossref]
  10. C. Tanguy, S. Reynaud, M. Matsuoka, and C. Cohen-Tannoudji, Opt. Commun. 44, 294 (1983).
    [Crossref]
  11. K. K. Berggren, M. Prentiss, G. Timp, and R. E. Behringer, J. Opt. Soc. Am. B 11, 1166 (1994).
    [Crossref]
  12. J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1701 (1985).
    [Crossref]
  13. This saturation intensity is a weighted average for δmf=0 over the mf sublevels of the 3S1/2→3P3/2 transition.
  14. See the feature on laser cooling and trapping of atoms, J. Opt. Soc. Am. B 6, 2023–2278 (1989).

1996 (1)

V. Natarajan, R. E. Behringer, and G. Timp, Phys. Rev. A 53, 4381 (1996).
[Crossref] [PubMed]

1995 (3)

1994 (1)

1993 (1)

J. J. McClelland, R. E. Sholten, E. C. Palm, and R. J. Cellota, Science 262, 877 (1993).
[Crossref] [PubMed]

1992 (1)

G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham, M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636 (1992).
[Crossref] [PubMed]

1989 (1)

1985 (1)

J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1701 (1985).
[Crossref]

1983 (1)

C. Tanguy, S. Reynaud, M. Matsuoka, and C. Cohen-Tannoudji, Opt. Commun. 44, 294 (1983).
[Crossref]

1980 (1)

J. P. Gordon and A. Ashkin, Phys. Rev. A 21, 1601 (1980).
[Crossref]

Ashkin, A.

J. P. Gordon and A. Ashkin, Phys. Rev. A 21, 1601 (1980).
[Crossref]

Behringer, R. E.

V. Natarajan, R. E. Behringer, and G. Timp, Phys. Rev. A 53, 4381 (1996).
[Crossref] [PubMed]

V. Natarajan, R. E. Behringer, G. Timp, and D. M. Tennant, J. Vac. Sci. Technol. B 13, 2823 (1995).
[Crossref]

K. K. Berggren, M. Prentiss, G. Timp, and R. E. Behringer, J. Opt. Soc. Am. B 11, 1166 (1994).
[Crossref]

G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham, M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636 (1992).
[Crossref] [PubMed]

G. Timp, R. E. Behringer, V. Natarajan, and D. Tennant, “Focusing a thermal atomic beam to nanometer resolution using a laser,” submitted to Phys. Rev. A.

Berggren, K. K.

K. K. Berggren, M. Prentiss, G. Timp, and R. E. Behringer, J. Opt. Soc. Am. B 11, 1166 (1994).
[Crossref]

G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham, M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636 (1992).
[Crossref] [PubMed]

Cellota, R. J.

J. J. McClelland, R. E. Sholten, E. C. Palm, and R. J. Cellota, Science 262, 877 (1993).
[Crossref] [PubMed]

Cohen-Tannoudji, C.

J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1701 (1985).
[Crossref]

C. Tanguy, S. Reynaud, M. Matsuoka, and C. Cohen-Tannoudji, Opt. Commun. 44, 294 (1983).
[Crossref]

Cunningham, J. E.

G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham, M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636 (1992).
[Crossref] [PubMed]

Dalibard, J.

J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1701 (1985).
[Crossref]

Giltner, D. M.

Gordon, J. P.

J. P. Gordon and A. Ashkin, Phys. Rev. A 21, 1601 (1980).
[Crossref]

Lee, S. A.

Matsuoka, M.

C. Tanguy, S. Reynaud, M. Matsuoka, and C. Cohen-Tannoudji, Opt. Commun. 44, 294 (1983).
[Crossref]

McClelland, J. J.

J. J. McClelland, J. Opt. Soc. Am. B 12, 1761 (1995).
[Crossref]

J. J. McClelland, R. E. Sholten, E. C. Palm, and R. J. Cellota, Science 262, 877 (1993).
[Crossref] [PubMed]

McGowan, R. W.

Natarajan, V.

V. Natarajan, R. E. Behringer, and G. Timp, Phys. Rev. A 53, 4381 (1996).
[Crossref] [PubMed]

V. Natarajan, R. E. Behringer, G. Timp, and D. M. Tennant, J. Vac. Sci. Technol. B 13, 2823 (1995).
[Crossref]

G. Timp, R. E. Behringer, V. Natarajan, and D. Tennant, “Focusing a thermal atomic beam to nanometer resolution using a laser,” submitted to Phys. Rev. A.

Palm, E. C.

J. J. McClelland, R. E. Sholten, E. C. Palm, and R. J. Cellota, Science 262, 877 (1993).
[Crossref] [PubMed]

Prentiss, M.

K. K. Berggren, M. Prentiss, G. Timp, and R. E. Behringer, J. Opt. Soc. Am. B 11, 1166 (1994).
[Crossref]

G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham, M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636 (1992).
[Crossref] [PubMed]

Reynaud, S.

C. Tanguy, S. Reynaud, M. Matsuoka, and C. Cohen-Tannoudji, Opt. Commun. 44, 294 (1983).
[Crossref]

Sholten, R. E.

J. J. McClelland, R. E. Sholten, E. C. Palm, and R. J. Cellota, Science 262, 877 (1993).
[Crossref] [PubMed]

Tanguy, C.

C. Tanguy, S. Reynaud, M. Matsuoka, and C. Cohen-Tannoudji, Opt. Commun. 44, 294 (1983).
[Crossref]

Tennant, D.

G. Timp, R. E. Behringer, V. Natarajan, and D. Tennant, “Focusing a thermal atomic beam to nanometer resolution using a laser,” submitted to Phys. Rev. A.

Tennant, D. M.

V. Natarajan, R. E. Behringer, G. Timp, and D. M. Tennant, J. Vac. Sci. Technol. B 13, 2823 (1995).
[Crossref]

G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham, M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636 (1992).
[Crossref] [PubMed]

Timp, G.

V. Natarajan, R. E. Behringer, and G. Timp, Phys. Rev. A 53, 4381 (1996).
[Crossref] [PubMed]

V. Natarajan, R. E. Behringer, G. Timp, and D. M. Tennant, J. Vac. Sci. Technol. B 13, 2823 (1995).
[Crossref]

K. K. Berggren, M. Prentiss, G. Timp, and R. E. Behringer, J. Opt. Soc. Am. B 11, 1166 (1994).
[Crossref]

G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham, M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636 (1992).
[Crossref] [PubMed]

G. Timp, R. E. Behringer, V. Natarajan, and D. Tennant, “Focusing a thermal atomic beam to nanometer resolution using a laser,” submitted to Phys. Rev. A.

J. Opt. Soc. Am. B (4)

J. Vac. Sci. Technol. B (1)

V. Natarajan, R. E. Behringer, G. Timp, and D. M. Tennant, J. Vac. Sci. Technol. B 13, 2823 (1995).
[Crossref]

Opt. Commun. (1)

C. Tanguy, S. Reynaud, M. Matsuoka, and C. Cohen-Tannoudji, Opt. Commun. 44, 294 (1983).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (2)

J. P. Gordon and A. Ashkin, Phys. Rev. A 21, 1601 (1980).
[Crossref]

V. Natarajan, R. E. Behringer, and G. Timp, Phys. Rev. A 53, 4381 (1996).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

G. Timp, R. E. Behringer, D. M. Tennant, J. E. Cunningham, M. Prentiss, and K. K. Berggren, Phys. Rev. Lett. 69, 1636 (1992).
[Crossref] [PubMed]

Science (1)

J. J. McClelland, R. E. Sholten, E. C. Palm, and R. J. Cellota, Science 262, 877 (1993).
[Crossref] [PubMed]

Other (3)

We define throughput as the time required for making a pattern of a given area and thickness.

G. Timp, R. E. Behringer, V. Natarajan, and D. Tennant, “Focusing a thermal atomic beam to nanometer resolution using a laser,” submitted to Phys. Rev. A.

This saturation intensity is a weighted average for δmf=0 over the mf sublevels of the 3S1/2→3P3/2 transition.

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Figures (4)

Fig. 1
Fig. 1

Results of numerical simulations of power to focus, P˜ (solid curve), and deposited linewidth L˜ (dashed curve), plotted as a function of focused position within the Gaussian zf (in units of σ). P˜ and L˜ have been normalized to the power and linewidth found when zf=0. The filled circles represent measurements of L˜ from experimental data of depositions at three different zf and constant σ.

Fig. 2
Fig. 2

Intensity profiles in the z direction with the center of the Gaussian placed (a) at the sample, zf=0, with σ=120 µm and an input power of 8 mW, (b) 0.5σ above the sample, zf=-σ/2, with σ=120 µm and an input power of 40 mW, and (c) σ below the sample, zf=+σ, with σ=60 µm and an input power of 1.5 mW.

Fig. 3
Fig. 3

(a), (b), (c) STM micrographs of sodium gratings focused on silicon substrates with the intensity profiles shown in Figs. 2(a), 2(b), and 2(c), respectively. The height of the features in the gratings is 20 nm, and the period of the gratings is 294.5 nm.

Fig. 4
Fig. 4

(a), (b), (c) Averaged line profiles (solid curves) taken from the images in Figs. 3(a), 3(b), and 3(c), respectively, and numerical simulation (dashed curves) of the experimental conditions used in Fig. 3. The average widths of the data and the simulations are (a) 39 and 35 nm, (b) 36 and 29 nm, and (c) 40 and 36 nm.

Equations (2)

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Ux,t=Δ21+Ix,tIs21+Δ2/Γ/221/2,
fσ2π1/2pkPsPΔΓ11-½Φ2zf/σ,

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