Abstract

One-dimensional Fibonacci gratings are used to transform evanescent waves into propagating waves for far-field super-resolution imaging. By detecting far-field intensity distributions of light through objects in front of the Fibonacci grating in free space, we can observe the objects with nearly λ/9 spatial resolution. Analytical results are verified by numerical simulations. We also discuss the effect of sampling error on imaging resolution of the system.

© 2013 Optical Society of America

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References

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2012

D. Lu and Z. Liu, Nat. Commun. 3, 1205 (2012).
[CrossRef]

2007

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

2006

2005

2000

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

1999

R. C. Dunn, Chem. Rev. 99, 2891 (1999).
[CrossRef]

1986

D. Levine and P. J. Steinhardt, Phys. Rev. B 34, 596 (1986).
[CrossRef]

Alekseyev, L. A.

Belkebir, K.

A. Sentenac, P. C. Chaumet, and K. Belkebir, Phys. Rev. Lett. 97, 243901 (2006).
[CrossRef]

Chaumet, P. C.

A. Sentenac, P. C. Chaumet, and K. Belkebir, Phys. Rev. Lett. 97, 243901 (2006).
[CrossRef]

Dunn, R. C.

R. C. Dunn, Chem. Rev. 99, 2891 (1999).
[CrossRef]

Durant, S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005), pp. 32–95.

Jacob, Z.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Levine, D.

D. Levine and P. J. Steinhardt, Phys. Rev. B 34, 596 (1986).
[CrossRef]

Liu, Z.

D. Lu and Z. Liu, Nat. Commun. 3, 1205 (2012).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

S. Durant, Z. Liu, J. M. Steele, and X. Zhang, J. Opt. Soc. Am. B 23, 2383 (2006).
[CrossRef]

Lu, D.

D. Lu and Z. Liu, Nat. Commun. 3, 1205 (2012).
[CrossRef]

Narimanov, E. E.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985), p. 366.

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Podolskiy, V. A.

Sentenac, A.

A. Sentenac, P. C. Chaumet, and K. Belkebir, Phys. Rev. Lett. 97, 243901 (2006).
[CrossRef]

Steele, J. M.

Steinhardt, P. J.

D. Levine and P. J. Steinhardt, Phys. Rev. B 34, 596 (1986).
[CrossRef]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

S. Durant, Z. Liu, J. M. Steele, and X. Zhang, J. Opt. Soc. Am. B 23, 2383 (2006).
[CrossRef]

Chem. Rev.

R. C. Dunn, Chem. Rev. 99, 2891 (1999).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Commun.

D. Lu and Z. Liu, Nat. Commun. 3, 1205 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

D. Levine and P. J. Steinhardt, Phys. Rev. B 34, 596 (1986).
[CrossRef]

Phys. Rev. Lett.

A. Sentenac, P. C. Chaumet, and K. Belkebir, Phys. Rev. Lett. 97, 243901 (2006).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Science

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Other

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985), p. 366.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005), pp. 32–95.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Scheme of the Fibonacci grating imaging system. (b) Calculated diffraction efficiencies of 0 (red dashed line) 1 (blue solid line) and +1 (green dotted line) orders of Fibonacci grating. (c) and (d) Calculated gray intensity distributions of light through a two-line object placed in front of the Fibonacci grating and in free space, respectively.

Fig. 2.
Fig. 2.

(a) Gray intensity distributions of three two-line objects spaced by λ/9, λ/6, and λ/4, respectively, from left to right. (b) and (c) Gray intensity distributions of reconstructed objects by using the Fibonacci grating system and periodic grating system, respectively. (d) Corresponding cross sections of intensity distributions of objects (black dashed line) and their retrieved images as Fibonacci grating (red solid line) and periodic grating (blue dot line) are used, respectively.

Fig. 3.
Fig. 3.

(a) Cross sections of light field intensity at detection plane as the sampling interval is 5 nm (red solid line), 300 nm (green solid circles) and its fitted curve (blue dashed line). (b) Cross sections of the reconstructed image of a two-line object with λ/9 space as the sampling interval is 5 nm (red solid line) and 300 nm (blue dot line), respectively.

Equations (2)

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g(x)=o(x)h(x),
k=k+mΛ,

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