Abstract

Spatial structures created by pulsed field interactions with surface-bound two-level systems are considered. Superresolved pattern formation is possible by the use of extra degrees of freedom programmed in the time-domain field.

© 1994 Optical Society of America

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References

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  1. I. J. Cox, C. J. R. Sheppard, J. Opt. Soc. Am. A 3, 1152 (1986).
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    [CrossRef]
  6. S. H. Zaidi, S. R. J. Brueck, J. Vac. Sci. Tech. B 11, 658 (1993).
    [CrossRef]
  7. T. Basche, W. E. Moerner, Nature (London) 355, 335 (1992).
    [CrossRef]
  8. A. M. Weiner, D. E. Leaird, Opt. Lett. 15, 51 (1990).
    [CrossRef] [PubMed]
  9. D. Brady, G.-S. Chen, G. Rodriguez, Opt. Lett. 17, 610 (1992).
    [CrossRef] [PubMed]
  10. K. B. Hill, K. Purchase, D. Brady, in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 211.
  11. W. S. Warren, H. Rabitz, M. Dehleh, Science 259, 1581 (1993).
    [CrossRef] [PubMed]
  12. G. P. Brivio, Surf. Sci. Rep. 17, 1 (1993).
    [CrossRef]
  13. L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).
  14. W. S. Warren, M. S. Silver, in Advances in Magnetic Resonance, J. S. Waugh (Academic, San Diego, Calif., 1988), Vol. 12, pp. 247.
  15. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).
  16. X. L. Lou, P. Xu, R. Freeman, Magn. Res. Med. 20, 165 (1991).
    [CrossRef]

1993 (4)

W. S. Warren, H. Rabitz, M. Dehleh, Science 259, 1581 (1993).
[CrossRef] [PubMed]

G. P. Brivio, Surf. Sci. Rep. 17, 1 (1993).
[CrossRef]

H. M. Phillips, R. A Sauerbrey, Opt. Eng. 32, 2424 (1993).
[CrossRef]

S. H. Zaidi, S. R. J. Brueck, J. Vac. Sci. Tech. B 11, 658 (1993).
[CrossRef]

1992 (4)

1991 (1)

X. L. Lou, P. Xu, R. Freeman, Magn. Res. Med. 20, 165 (1991).
[CrossRef]

1990 (1)

1986 (1)

1967 (1)

Allen, L.

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).

Basche, T.

T. Basche, W. E. Moerner, Nature (London) 355, 335 (1992).
[CrossRef]

Betzig, E.

E. Betzig, J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Brady, D.

D. Brady, G.-S. Chen, G. Rodriguez, Opt. Lett. 17, 610 (1992).
[CrossRef] [PubMed]

K. B. Hill, K. Purchase, D. Brady, in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 211.

Brivio, G. P.

G. P. Brivio, Surf. Sci. Rep. 17, 1 (1993).
[CrossRef]

Brueck, S. R. J.

S. H. Zaidi, S. R. J. Brueck, J. Vac. Sci. Tech. B 11, 658 (1993).
[CrossRef]

Chen, G.-S.

Cox, I. J.

Dehleh, M.

W. S. Warren, H. Rabitz, M. Dehleh, Science 259, 1581 (1993).
[CrossRef] [PubMed]

Eberly, J. H.

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).

Freeman, R.

X. L. Lou, P. Xu, R. Freeman, Magn. Res. Med. 20, 165 (1991).
[CrossRef]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Hill, K. B.

K. B. Hill, K. Purchase, D. Brady, in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 211.

Leaird, D. E.

Leith, E. N.

Lou, X. L.

X. L. Lou, P. Xu, R. Freeman, Magn. Res. Med. 20, 165 (1991).
[CrossRef]

Lukosz, W.

Moerner, W. E.

T. Basche, W. E. Moerner, Nature (London) 355, 335 (1992).
[CrossRef]

Phillips, H. M.

H. M. Phillips, R. A Sauerbrey, Opt. Eng. 32, 2424 (1993).
[CrossRef]

Purchase, K.

K. B. Hill, K. Purchase, D. Brady, in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 211.

Rabitz, H.

W. S. Warren, H. Rabitz, M. Dehleh, Science 259, 1581 (1993).
[CrossRef] [PubMed]

Rodriguez, G.

Sauerbrey, R. A

H. M. Phillips, R. A Sauerbrey, Opt. Eng. 32, 2424 (1993).
[CrossRef]

Sheppard, C. J. R.

Silver, M. S.

W. S. Warren, M. S. Silver, in Advances in Magnetic Resonance, J. S. Waugh (Academic, San Diego, Calif., 1988), Vol. 12, pp. 247.

Sun, P. C.

Trautman, J. K.

E. Betzig, J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Warren, W. S.

W. S. Warren, H. Rabitz, M. Dehleh, Science 259, 1581 (1993).
[CrossRef] [PubMed]

W. S. Warren, M. S. Silver, in Advances in Magnetic Resonance, J. S. Waugh (Academic, San Diego, Calif., 1988), Vol. 12, pp. 247.

Weiner, A. M.

Xu, P.

X. L. Lou, P. Xu, R. Freeman, Magn. Res. Med. 20, 165 (1991).
[CrossRef]

Zaidi, S. H.

S. H. Zaidi, S. R. J. Brueck, J. Vac. Sci. Tech. B 11, 658 (1993).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

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

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

S. H. Zaidi, S. R. J. Brueck, J. Vac. Sci. Tech. B 11, 658 (1993).
[CrossRef]

Magn. Res. Med. (1)

X. L. Lou, P. Xu, R. Freeman, Magn. Res. Med. 20, 165 (1991).
[CrossRef]

Nature (1)

T. Basche, W. E. Moerner, Nature (London) 355, 335 (1992).
[CrossRef]

Opt. Eng. (1)

H. M. Phillips, R. A Sauerbrey, Opt. Eng. 32, 2424 (1993).
[CrossRef]

Opt. Lett. (2)

Science (2)

E. Betzig, J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

W. S. Warren, H. Rabitz, M. Dehleh, Science 259, 1581 (1993).
[CrossRef] [PubMed]

Surf. Sci. Rep. (1)

G. P. Brivio, Surf. Sci. Rep. 17, 1 (1993).
[CrossRef]

Other (4)

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).

W. S. Warren, M. S. Silver, in Advances in Magnetic Resonance, J. S. Waugh (Academic, San Diego, Calif., 1988), Vol. 12, pp. 247.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

K. B. Hill, K. Purchase, D. Brady, in Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 211.

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Figures (3)

Fig. 1
Fig. 1

The sine function, the spatial profile excited by a sech-modulated sine, and the profile excited by an optimized 40-pulse sequence as functions of spatial displacement.

Fig. 2
Fig. 2

Optimized excitation profiles for (I) target peaks at x1x = −1, x2x = 0.04, x3x = 0.56 and (II) identical, except that x2x = −0.6.

Fig. 3
Fig. 3

Excitation profiles optimized for Δ = π/2τ at Δ = π/2τ, Δ = 1.01(π/2τ), and Δ = 1.03(π/2τ).

Equations (8)

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d ρ ( x , t ) d t = Ω ( x , t ) × ρ ( x , t ) ,
Ω ( x , t ) = [ κ E ( x , t ) , 0 , Δ ] ,
ρ ( x , t ) = [ u ( x , t ) , ν ( x , t ) , w ( x , t ) ] .
E ( x , t ) = i = 1 N a i κ τ sech ( b i t t i τ ) sinc ( x c i Δ x ) ,
t i t i 1 + τ ( 1 b i 1 + 1 b i ) * log ( 2 / ) i = 2 , , N = 0 i = 1 .
C = j = 1 N x | w ( x j / Δ x , ) w d ( x / Δ x ) | α f x ( j ) .
E ( x , t ) = ( 1 / κ τ ) sinc ( x / Δ x ) sech ( t / τ ) ,
w ( x , t = + ) = cos { π [ 1 + sinc ( x / Δ x ) ] } ,

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