Abstract

Reflection can significantly improve the quality of subwavelength near-field images, which is explained by appropriate interference between forward and reflected waves. Plasmonic slabs may form approximate super-mirrors. This paper develops general theory in both spectral and spatial representations that allows the reflector position and permittivity to be determined for optimum image uniformity. This elucidates previous observations and predicts behaviour for some other interesting regimes, including interferometric lithography.

© 2007 Optical Society of America

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References

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  1. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  2. J. S. Wei and F. X. Gan, "Dynamic readout of subdiffraction-limited pit arrays with a silver superlens," Appl. Phys. Lett. 87, 211101 (2005).
    [CrossRef]
  3. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
    [CrossRef] [PubMed]
  4. D. O. S. Melville and R. J. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127-2134 (2005)
    [CrossRef] [PubMed]
  5. N. Fang, H. Lee, C. Sun, X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 308, 534-537 (2005).
    [CrossRef] [PubMed]
  6. R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. O. S. Melville, "Nanoscale optical patterning using evanescent fields and surface plasmons," Int. J. Nanoscience 3, 405-417 (2004)
    [CrossRef]
  7. D. B. Shao and S. C. Chen, "Surface-plasmon-assisted nanoscale photolithography by polarized light," Appl. Phys. Lett. 86, 253107 (2005)
    [CrossRef]
  8. D. B. Shao and S. C. Chen, "Numerical simulation of surface-plasmon-assisted nanolithography," Opt. Express 13, 6964-6973 (2005).
    [CrossRef] [PubMed]
  9. M. D. Arnold and R. J. Blaikie, "Using surface-plasmon effects to improve process latitude in near-field optical lithography," in Proceedings of the International Conference on Nanoscience and Nanotechnology, Brisbane, Australia, IEEE Press 06EX1411C, 548-551 (2006).
  10. M. Schrader, M. Kozubek, S. W. Hell, T. Wilson, "Optical transfer functions of 4Pi confocal microscopes: theory and experiment," Opt. Lett. 22, 436-438 (1997).
    [CrossRef] [PubMed]
  11. B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, A. Estroff, "Evanescent wave imaging in optical lithography," Proc. SPIE 6154 (2006)

2006 (2)

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
[CrossRef] [PubMed]

B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, A. Estroff, "Evanescent wave imaging in optical lithography," Proc. SPIE 6154 (2006)

2005 (5)

D. O. S. Melville and R. J. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127-2134 (2005)
[CrossRef] [PubMed]

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

J. S. Wei and F. X. Gan, "Dynamic readout of subdiffraction-limited pit arrays with a silver superlens," Appl. Phys. Lett. 87, 211101 (2005).
[CrossRef]

D. B. Shao and S. C. Chen, "Surface-plasmon-assisted nanoscale photolithography by polarized light," Appl. Phys. Lett. 86, 253107 (2005)
[CrossRef]

D. B. Shao and S. C. Chen, "Numerical simulation of surface-plasmon-assisted nanolithography," Opt. Express 13, 6964-6973 (2005).
[CrossRef] [PubMed]

2004 (1)

R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. O. S. Melville, "Nanoscale optical patterning using evanescent fields and surface plasmons," Int. J. Nanoscience 3, 405-417 (2004)
[CrossRef]

2000 (1)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1997 (1)

Appl. Phys. Lett. (2)

J. S. Wei and F. X. Gan, "Dynamic readout of subdiffraction-limited pit arrays with a silver superlens," Appl. Phys. Lett. 87, 211101 (2005).
[CrossRef]

D. B. Shao and S. C. Chen, "Surface-plasmon-assisted nanoscale photolithography by polarized light," Appl. Phys. Lett. 86, 253107 (2005)
[CrossRef]

Int. J. Nanoscience (1)

R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. O. S. Melville, "Nanoscale optical patterning using evanescent fields and surface plasmons," Int. J. Nanoscience 3, 405-417 (2004)
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Proc. SPIE (1)

B. W. Smith, Y. Fan, J. Zhou, N. Lafferty, A. Estroff, "Evanescent wave imaging in optical lithography," Proc. SPIE 6154 (2006)

Science (2)

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

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595-1595 (2006).
[CrossRef] [PubMed]

Other (1)

M. D. Arnold and R. J. Blaikie, "Using surface-plasmon effects to improve process latitude in near-field optical lithography," in Proceedings of the International Conference on Nanoscience and Nanotechnology, Brisbane, Australia, IEEE Press 06EX1411C, 548-551 (2006).

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Figures (8)

Fig. 1.
Fig. 1.

Imaging situation under consideration here. An object at x=d is illuminated from the right, and the effects of a reflector at x=0 are studied in the imaging region 0<x<d.

Fig. 2.
Fig. 2.

Image geometry in two-dimensions, the third being invariant. A hypothetical (but representative) image with no reflection is shown in (a) and with reflection (b). The medial longitudinal profiles I 0 and I 1 as marked in (a),(b) are shown in (c),(d). Limited depth-of-field D is indicated in (c).

Fig. 3.
Fig. 3.

Movement of optimized parameters as a function of β : (a) optimized reflector permittivity for various object-mirror separations d and (b) optimized object-mirror separations for various permittivities. All reflections “negative” except as noted.

Fig. 4.
Fig. 4.

Comparison of scaled widths (width/d) for the LSF GEy versus image thickness d for various reflectors. Widths are maximums over the imaging region, corresponding to LSF contours at intensity I 0=min(I 1).

Fig. 5.
Fig. 5.

An example of an image of a binary absorber of width a using a plasmonic reflector. The full image is shown in (a), with field line direction confirming dominant tangential fields. A cross-section of the object field at the exit of the absorber (green line) is shown in (b), with model contributions overlaid (edge diffraction blue and geometric transmission cyan).

Fig. 6.
Fig. 6.

Modeling of optimal absorber object tuning. (a) shows an example LSF for a case with d=0.125λ, where the grayscale runs linearly from low (dark) to high (white). (b) shows a grayscale map of real absorber image quality (dark being high contrast) as a function of absorber half-width a/2 and image thickness d, overlaid with the optimum curve for the edge-diffraction model (solid blue) and for geometric diffraction (dashed cyan curve).

Fig. 7.
Fig. 7.

Examples of evanescent interferometric images for different perfect reflectors (“+r” left and “-r”right) compared to the no reflection case (center). Note the rotation of the axes compared with the rest of the article. The incident waves shown result in near-evanescent condition β/k=1.2, and equation (6) was used to choose permittivities for perfect symmetry.

Fig. 8.
Fig. 8.

Comparison of depth-of-field for interference imaging as a function of β: (main graph) absolute values and (inset) relative improvement of perfect positive (+r) and negative reflectors (-r) against no-reflection (r=0).

Equations (18)

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H ( x , y ) = β = [ e i α ( x + d ) + r e i α ( x + d ) ] [ h f ( d ) ] e i β y d β = G H f ( d , x , y ) * H f ( d , y ) .
g H f = e i α ( d X ) [ e i α ( x + X ) ± e i α ( x X ) ] .
X = ln r + i [ arg ( ± r ) + m 2 π ] 2 i α ,
g Ey f = e i α ( x + d ) + r e i α ( x + d )
g Ex f = e i α ( x + d ) r e i α ( x + d ) .
r = ε r α ε α r ε r α + ε α r .
ε r ε = 1 ± 1 4 ( β k ) 2 f 2 2 f 2 ,
f = α ( 1 r ) k ( 1 + r ) = 2 α tan ( α X ) ik .
G f = i π j = 1 2 [ H 1 ( 1 ) ( x j 2 + y 2 ) x j x j 2 + y 2 ]
x 1 = x + d
x 2 = + x + d 2 X .
e i α d ω ε E ( x ) h f = { α ( e i α x + r e i α x ) , β y = ( 2 m + 0 ) π 2 β ( e i α x r e i α x ) , β y = ( 2 m + 1 ) π 2 .
E ( x ) { α cos [ α ( x X ) ] , β y = ( 2 m + 0 ) π 2 β sin [ α ( x X ) ] , β y = ( 2 m + 1 ) π 2
1 = cot [ α D 2 ] α β , β < k
1 = csc [ α D 2 ] α β , β > k .
1 = cot [ α D 2 ] β α , β < k
1 = csc [ α D 2 ] β α , β > k ,
1 = exp [ Im ( α ) D ] α β .

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