Abstract

Diffractions by the one-dimensional high-density grating in the near field with TM and TE polarization illuminations are studied, and the diffraction intensity distributions are calculated with the finite-difference time-domain technique. The calculation results show that the diffractions of the high-density grating with different polarization illuminations are different. The quasi-Talbot image of the grating depends on the polarization of the incident wave, and the existence condition of the quasi-Talbot image of the grating in the near field also changes with the polarization of the incident wave. We present explanations based on the vector distribution of the energy flow density. These studies on the polarization dependence of the quasi-Talbot imaging of the high-density grating are helpful for the application of the grating to near-field photolithography.

© 2010 Optical Society of America

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References

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2008 (2)

2007 (2)

2006 (1)

2005 (1)

S. Y. Teng, C. F. Cheng, M. Liu, W. L. Gui, and Z. Z. Xu, “The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces,” Chin. Phys. 20, 1990-1995 (2005).

2003 (1)

Z. J. Sun, Y. S. Jung, and H. K. Kima, “Role of surface plasmons in the optical interaction in metallic gratings with narrow slits,” Appl. Phys. Lett. 83, 3021-3023 (2003).
[CrossRef]

2002 (1)

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
[CrossRef]

1998 (1)

1995 (1)

1994 (2)

L. 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-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49, 2213-2216 (1994).
[CrossRef]

1992 (1)

1990 (1)

1989 (1)

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]

1836 (1)

W. H. F. Talbot “Facts relating to optical science,” No. IV, Philos. Mag. 9, 401-407 (1836).

Chen, X. Y.

Cheng, C. F.

Clauser, J. F.

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

Crouse, R.

Dong, Q. R.

Glytsis, E. N.

Goodman,

Goodman, Introduction of Fourier Optics (McGraw-Hill, 1968).

Grann, E. B.

Gui, W. L.

S. Y. Teng, C. F. Cheng, M. Liu, W. L. Gui, and Z. Z. Xu, “The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces,” Chin. Phys. 20, 1990-1995 (2005).

Ichikawa, H.

Jung, Y. S.

Z. J. Sun, Y. S. Jung, and H. K. Kima, “Role of surface plasmons in the optical interaction in metallic gratings with narrow slits,” Appl. Phys. Lett. 83, 3021-3023 (2003).
[CrossRef]

Kima, H. K.

Z. J. Sun, Y. S. Jung, and H. K. Kima, “Role of surface plasmons in the optical interaction in metallic gratings with narrow slits,” Appl. Phys. Lett. 83, 3021-3023 (2003).
[CrossRef]

Latimer, P.

Li, L.

Li, S. F.

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

Liu, L.

Liu, M.

S. Y. Teng, C. F. Cheng, M. Liu, W. L. Gui, and Z. Z. Xu, “The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces,” Chin. Phys. 20, 1990-1995 (2005).

Lohmann, A. W.

Lu, Y.

Moharam, M. G.

Papadopoulos, A. D.

Pommet, D. A.

Sun, Z. J.

Z. J. Sun, Y. S. Jung, and H. K. Kima, “Role of surface plasmons in the optical interaction in metallic gratings with narrow slits,” Appl. Phys. Lett. 83, 3021-3023 (2003).
[CrossRef]

Talbot, W. H. F.

W. H. F. Talbot “Facts relating to optical science,” No. IV, Philos. Mag. 9, 401-407 (1836).

Tan, Y. G.

Teng, S. Y.

Thomas, J.

Treacy, M. M. J.

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
[CrossRef]

Wang, B.

Wang, S.

Xu, Z. Z.

S. Y. Teng, C. F. Cheng, M. Liu, W. L. Gui, and Z. Z. Xu, “The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces,” Chin. Phys. 20, 1990-1995 (2005).

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. (4)

Appl. Phys. Lett. (1)

Z. J. Sun, Y. S. Jung, and H. K. Kima, “Role of surface plasmons in the optical interaction in metallic gratings with narrow slits,” Appl. Phys. Lett. 83, 3021-3023 (2003).
[CrossRef]

Chin. Phys. (1)

S. Y. Teng, C. F. Cheng, M. Liu, W. L. Gui, and Z. Z. Xu, “The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces,” Chin. Phys. 20, 1990-1995 (2005).

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 (7)

Philos. Mag. (1)

W. H. F. Talbot “Facts relating to optical science,” No. IV, Philos. Mag. 9, 401-407 (1836).

Phys. Rev. A (1)

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

Phys. Rev. B (1)

M. M. J. Treacy, “Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,” Phys. Rev. B 66, 195105 (2002).
[CrossRef]

Other (1)

Goodman, Introduction of Fourier Optics (McGraw-Hill, 1968).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the diffraction of the grating in the near field and the deep Fresnel region.

Fig. 2
Fig. 2

Elementary cells of the Yee lattice for TM and TE polarizations.

Fig. 3
Fig. 3

Diffraction gray-scale diagrams of the grating: (a)–(d) for TM polarization, (e)–(h) for TE polarization. The period of the grating from (a) to (d) takes d = 0.8 λ , λ, 2 λ , and 4 λ , respectively, and so does that from (e) to (h).

Fig. 4
Fig. 4

One-dimensional intensity distributions of the high-density grating with different periods and at different distances: (a)–(c) for TM polarization, (d)–(f) for TE polarization.

Fig. 5
Fig. 5

The vector distributions of the energy flow density S: (a)–(c) for TM polarization, (d)–(f) for TE polarization. The grating period from (a) to (c) takes 0.8 λ , λ, and 2 λ , respectively, and so does that from (d) to (f).

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