Abstract

On the basis of the finite-difference time-domain technique, the diffraction of the high-density grating in the near field is developed, and the gray-scale pattern of the diffraction intensity distribution of a one-dimensional grating is presented. A detailed analysis shows that the near-field diffraction of the grating is the result of the diffraction of a single slit, the interference of two evanescent waves from neighboring slits, and the interference of the homogeneous waves from the slits. Through many numerical calculations, the condition for obtaining the quasi-Talbot imaging of the grating in the near field is explored, i.e., the period of the grating d is larger than the incident wavelength λ but smaller than 4λ. The influence of the opening ratio of the grating on the quasi-Talbot imaging of the grating in the near field is also discussed. This study of the near-field diffraction of the high-density grating may be helpful for understanding the diffraction characteristics of subwavelength structures, and the quasi-Talbot imaging of the high-density grating will contribute to the application of the grating in near-field photolithography.

© 2008 Optical Society of America

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References

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    [CrossRef]
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2007 (2)

2006 (2)

2005 (1)

S. Y. Teng, L. R. Liu, and D. A. Liu, “Analytic expression of the diffraction of a circular aperture,” Optik (Stuttgart) 116, 568-572 (2005).
[CrossRef]

2000 (1)

J. G. Goodberlet, “Patterning sub-50 nm features with near-field embedded-amplitude masks,” Appl. Phys. Lett. 81, 1315-1317 (2000).
[CrossRef]

1999 (1)

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

1998 (1)

1997 (1)

J. Aizenberg, J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Imaging the irradiance distribution in the optical near field,” Appl. Phys. Lett. 71, 3773-3775 (1997).
[CrossRef]

1995 (1)

1994 (2)

L. F. Li, “Bremmer series, R-matrix propagation algorithm, and numerical modeling of diffraction gratings,” J. Opt. Soc. Am. A 11, 2829-2835 (1994).
[CrossRef]

J. F. Clauser and S. F. Li, “Talbot-von Lau atom interferometry with cold slow potassium,” Phys. Rev. A 49, 2213-2216 (1994).
[CrossRef]

1993 (1)

E. Noponen and J. Turunen, “Electromagnetic theory of Talbot imaging,” Opt. Commun. 98, 132-140 (1993).
[CrossRef]

1990 (1)

1989 (2)

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

1944 (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163-182 (1944).
[CrossRef]

1836 (1)

W. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401-407 (1836).
[CrossRef]

Aizenberg, J.

J. Aizenberg, J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Imaging the irradiance distribution in the optical near field,” Appl. Phys. Lett. 71, 3773-3775 (1997).
[CrossRef]

Avendaño, J.

Bethe, H. A.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163-182 (1944).
[CrossRef]

Chavez-Rivas, F.

Chen, X. Y.

Cheng, C. F.

Clark, C. W.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

Clauser, J. F.

J. F. Clauser and S. F. Li, “Talbot-von Lau atom interferometry with cold slow potassium,” Phys. Rev. A 49, 2213-2216 (1994).
[CrossRef]

Deng, L.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

Denschlag, J.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

Dong, Q. R.

Edwards, M.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

Goodberlet, J. G.

J. G. Goodberlet, “Patterning sub-50 nm features with near-field embedded-amplitude masks,” Appl. Phys. Lett. 81, 1315-1317 (2000).
[CrossRef]

Hagley, E. W.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

Helmerson, K.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

Ichikawa, H.

Kowarz, M. W.

Li, L. F.

Li, S. F.

J. F. Clauser and S. F. Li, “Talbot-von Lau atom interferometry with cold slow potassium,” Phys. Rev. A 49, 2213-2216 (1994).
[CrossRef]

Liu, D. A.

S. Y. Teng, L. R. Liu, and D. A. Liu, “Analytic expression of the diffraction of a circular aperture,” Optik (Stuttgart) 116, 568-572 (2005).
[CrossRef]

Liu, L.

Liu, L. R.

S. Y. Teng, L. R. Liu, and D. A. Liu, “Analytic expression of the diffraction of a circular aperture,” Optik (Stuttgart) 116, 568-572 (2005).
[CrossRef]

Lohmann, A. W.

Lu, Y.

Mata-Mendez, O.

Noponen, E.

E. Noponen and J. Turunen, “Electromagnetic theory of Talbot imaging,” Opt. Commun. 98, 132-140 (1993).
[CrossRef]

Paul, K. E.

J. Aizenberg, J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Imaging the irradiance distribution in the optical near field,” Appl. Phys. Lett. 71, 3773-3775 (1997).
[CrossRef]

Phillips, W. D.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

Rogers, J. A.

J. Aizenberg, J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Imaging the irradiance distribution in the optical near field,” Appl. Phys. Lett. 71, 3773-3775 (1997).
[CrossRef]

Rolston, S. L.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

Simsarian, J. E.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

Talbot, W. H. F.

W. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401-407 (1836).
[CrossRef]

Teng, S. Y.

Thomas, J.

Turunen, J.

E. Noponen and J. Turunen, “Electromagnetic theory of Talbot imaging,” Opt. Commun. 98, 132-140 (1993).
[CrossRef]

Wang, B.

Wang, S.

Whitesides, G. M.

J. Aizenberg, J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Imaging the irradiance distribution in the optical near field,” Appl. Phys. Lett. 71, 3773-3775 (1997).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Zhang, N. Y.

Zhou, C.

Zhou, T. J.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

J. Aizenberg, J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Imaging the irradiance distribution in the optical near field,” Appl. Phys. Lett. 71, 3773-3775 (1997).
[CrossRef]

J. G. Goodberlet, “Patterning sub-50 nm features with near-field embedded-amplitude masks,” Appl. Phys. Lett. 81, 1315-1317 (2000).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media,” IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Commun. (1)

E. Noponen and J. Turunen, “Electromagnetic theory of Talbot imaging,” Opt. Commun. 98, 132-140 (1993).
[CrossRef]

Opt. Lett. (1)

Optik (Stuttgart) (1)

S. Y. Teng, L. R. Liu, and D. A. Liu, “Analytic expression of the diffraction of a circular aperture,” Optik (Stuttgart) 116, 568-572 (2005).
[CrossRef]

Philos. Mag. (1)

W. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401-407 (1836).
[CrossRef]

Phys. Rev. (1)

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163-182 (1944).
[CrossRef]

Phys. Rev. A (1)

J. F. Clauser and S. F. Li, “Talbot-von Lau atom interferometry with cold slow potassium,” Phys. Rev. A 49, 2213-2216 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal matter-wave-dispersion Talbot effect,” Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of the diffraction of the grating.

Fig. 2
Fig. 2

Gray-scale diagrams of the diffraction intensity distributions of the grating of period (a) d = λ , (b) d = 2 λ , (c) d = 4 λ .

Fig. 3
Fig. 3

Gray-scale diagrams of the diffraction intensity distributions of the grating with opening ratio taking values of (a) 1 2 , (b) 1 3 , (c) 1 4 .

Fig. 4
Fig. 4

Gray-scale diagrams of the diffraction intensity of the single slit of width (a) 0.5 λ , (b) λ, (c) 2 λ .

Fig. 5
Fig. 5

Gray-scale diagrams of the diffraction intensity distribution through three slits with spacing λ and slit width (a) 0.5 λ , (b) λ, (c) 2 λ .

Fig. 6
Fig. 6

Gray-scale diagrams of the diffraction intensity distribution through three slits of width 0.5 λ and spacing (a) λ, (b) 2 λ , (c) 4 λ .

Fig. 7
Fig. 7

Quasi-Talbot images of the grating, where (a) shows the quasi-Talbot images at the first (solid curve) and second (dotted curve) quasi-Talbot distances of the grating with d = 1.5 λ , (b) presents the cases with d = 2 λ and opening ratios of 1 2 (solid curve), 1 3 (dashed curve) and 1 4 (dotted curve), and (c) shows the cases with d = 4 λ at the first quasi-Talbot distance (solid curve) and the half quasi-Talbot distance (dotted curve).

Fig. 8
Fig. 8

One-dimensional intensity distributions at the (a) fourth, (b) fifth, and (c) sixth Talbot distances of the grating of period d = λ .

Fig. 9
Fig. 9

Diffractions of the grating of period d = 0.8 λ ; (a) is the gray-scale diagram, and (b) and (c) are the one-dimensional distributions at different distance from the grating.

Fig. 10
Fig. 10

Diffractions of the grating of period d = 0.4 λ ; (a) is the gray-scale diagram, and (b) and (c) are the one-dimensional distributions at different distances.

Fig. 11
Fig. 11

Gray-scale diagrams of the diffraction intensity distribution through three slits of spacing (a) 0.8 λ , (b) 0.4 λ .

Equations (4)

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× E = μ 0 H t ,
× H = ε 0 ε r E t + J ,
J = σ E ,
x T = λ { [ 1 m 2 λ 2 d 2 ] 1 2 [ 1 n 2 λ 2 d 2 ] 1 2 }

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