Abstract

Based on the characteristics of evanescent wave moiré fringes generated from subwavelength gratings, we numerically investigated the contrast of moiré fringes for two gratings with and without a silver slab. The effect of the gratings’ geometrical parameters on the contrast of moiré fringes is analyzed in detail by using the finite-difference time domain method. Numerical results show that great enhancement of the contrast of evanescent wave moiré fringes could be achieved by surface plasmon excitations on a silver slab. These evanescent wave moiré fringes with high contrast will have potential applications in the nanofabrication field.

© 2008 Optical Society of America

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References

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  1. O. Bryngdahl, “Moiré: formation and interpretation,” J. Opt. Soc. Am. 64, 1287-1294 (1974).
    [CrossRef]
  2. O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley, 1989).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).
  6. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
    [CrossRef] [PubMed]
  7. S. A. Ramakrishna and J. B. Pendry, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747-1762 (2002).
    [CrossRef]
  8. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  9. D. R. Lide, The CRC Handbook of Chemistry and Physics, 85th ed. (CRC, 2004-2005).

2007

2005

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

2002

S. A. Ramakrishna and J. B. Pendry, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747-1762 (2002).
[CrossRef]

1974

1972

M. C. King and D. H. Berry, “Photolithographic mask alignment using moiré techniques,” Appl. Opt. 11, 2455-2459 (1972).
[CrossRef] [PubMed]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

S. A. Ramakrishna and J. B. Pendry, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747-1762 (2002).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Phys. Rev. B

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Science

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Other

D. R. Lide, The CRC Handbook of Chemistry and Physics, 85th ed. (CRC, 2004-2005).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

O. Kafri and I. Glatt, The Physics of Moiré Metrology (Wiley, 1989).

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Figures (6)

Fig. 1
Fig. 1

Generation of an evanescent wave diffracted from a grating.

Fig. 2
Fig. 2

Superposition of two gratings (a) without a silver slab and (b) with a silver slab.

Fig. 3
Fig. 3

Total magnetic field intensity distribution above the two gratings. The splitting grating is 40 nm thick, and the duty cycle is 2:1. The modulating grating is 45 nm thick, and the duty cycle is 1:2. The distance of the two gratings is 30 nm , and the thickness of the silver slab is 20 nm .

Fig. 4
Fig. 4

Amplitude curve of moiré fringes when z = 1.7 μ m in Fig. 3.

Fig. 5
Fig. 5

Relation of two gratings’ distance and evanescent wave moiré fringe contrast. The splitting grating is 40 nm thick with a 120 nm period, and the duty cycle is 2:1. The modulating grating is 45 nm thick with a 150 nm period, and the duty cycle is 1:2. The thickness of the silver slab is 0 nm and 20 nm , respectively.

Fig. 6
Fig. 6

Numerical study on the contrast of various silver slab thicknesses and modulating grating thicknesses. The splitting grating is 40 nm thick, the duty cycle is 2:1, and the modulating grating duty cycle is 1:2. (a) Modulating grating thickness fixed at 45 nm and the silver slab thickness varying. (b) Silver thickness fixed at 20 nm and the modulating grating thickness varying.

Tables (1)

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Table 1 Numerical Study on the Contrast of Various Duty Cycles of Two Gratings’ Configurations a

Equations (5)

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sin θ m = ± m λ p ,
E = n A n exp [ i ( k n r w t ) ] k n = { k k R k + i k k , k R } ,
C = A max A min ,
M = A max A min A max + A min .
p m = p 1 p 2 p 1 p 2 ,

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