Abstract

It is shown that the spatial convolution formulation offers the advantage for direct analysis in the real space of the effects of system-object feature mismatches on the resulting image quality. Imaging systems of various layered Ag-poly(methyl methacrylate) configurations and a variety of square-slit objects were considered for the analysis. The results reveal how those feature mismatches affect the image quality and clarify the previously suggested possible advantage of using a layered Ag superlens over a single-Ag slab of the same total thickness. Those mismatches may eventually be quantified to allow the optimization of a superlens appropriate for imaging a certain object.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  2. 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]
  3. D. O. S. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver lens,” Opt. Express 13, 2127-2134 (2005).
    [CrossRef] [PubMed]
  4. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  5. S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449-521 (2005).
    [CrossRef]
  6. B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
    [CrossRef]
  7. D. O. S. Melville and R. J. Blaikie, “Experimental comparison of resolution and pattern fidelity in single and double layer planar lens lithography,” J. Opt. Soc. Am. B 23, 461-467 (2006).
    [CrossRef]
  8. D. O. S. Melville and R. J. Blaikie, “Analysis and optimization of multilayer silver superlens for near-field optical lithography,” Physica B 394, 197-202 (2007).
    [CrossRef]
  9. C. P. Moore, M. D. Arnold, P. J. Bones, and R. J. Blaikie, “Image fidelity for single-layer and multi-layer silver superlens,” J. Opt. Soc. Am. A 25, 911-918 (2008).
    [CrossRef]
  10. K. Lee, Y. Jung, G. Kang, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
    [CrossRef]
  11. The result presented in Figs. 4(f) and 4(g) of seems to have a missing factor of (2π)−1 in the calculated intensity.
  12. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

2009

K. Lee, Y. Jung, G. Kang, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

2008

2007

D. O. S. Melville and R. J. Blaikie, “Analysis and optimization of multilayer silver superlens for near-field optical lithography,” Physica B 394, 197-202 (2007).
[CrossRef]

2006

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

D. O. S. Melville and R. J. Blaikie, “Experimental comparison of resolution and pattern fidelity in single and double layer planar lens lithography,” J. Opt. Soc. Am. B 23, 461-467 (2006).
[CrossRef]

2005

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449-521 (2005).
[CrossRef]

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]

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

2000

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

1968

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Arnold, M. D.

Blaikie, R. J.

Bones, P. J.

Fang, N.

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]

Jung, Y.

K. Lee, Y. Jung, G. Kang, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

Kang, G.

K. Lee, Y. Jung, G. Kang, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

Kim, K.

K. Lee, Y. Jung, G. Kang, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

Lee, H.

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]

Lee, K.

K. Lee, Y. Jung, G. Kang, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

Melville, D. O. S.

Moore, C. P.

Park, H.

K. Lee, Y. Jung, G. Kang, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

Pendry, J. B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

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

Ramakrishna, S. A.

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449-521 (2005).
[CrossRef]

Sun, C.

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]

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Zhang, X.

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]

Appl. Phys. Lett.

K. Lee, Y. Jung, G. Kang, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Express

Phys. Rev. B

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Phys. Rev. Lett.

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

Physica B

D. O. S. Melville and R. J. Blaikie, “Analysis and optimization of multilayer silver superlens for near-field optical lithography,” Physica B 394, 197-202 (2007).
[CrossRef]

Rep. Prog. Phys.

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68, 449-521 (2005).
[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]

Sov. Phys. Usp.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other

The result presented in Figs. 4(f) and 4(g) of seems to have a missing factor of (2π)−1 in the calculated intensity.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Basic layer configuration of a unit cell in a periodic layered metal-dielectric system and notations of the system parameters

Fig. 2
Fig. 2

Transmission function T ( x x ) of a superlens with 5 nm single-Ag layer and two 2.5 nm PMMAs plotted for x at the middle of (a) a slit, (b) inter-slit interval, and (c) the resulting image (dashed-dotted line) and separate contributions of the real (dashed line) and imaginary (solid line) parts for an object with w = 20   nm and p = 80   nm .

Fig. 3
Fig. 3

Transmission function T ( x x ) of a superlens with 40 nm single-Ag layer and two 20 nm PMMAs plotted for x at the middle of (a) a slit, (b) inter-slit interval, and (c) the resulting image (dashed-dotted line) and separate contributions of the real (dashed line) and imaginary (solid line) parts for the same object of Fig. 2.

Fig. 4
Fig. 4

The same T ( x x ) function as in Fig. 3 plotted with x fixed at the middle of (a) a slit, (b) inter-slit interval, and (c) the resulting image (dashed-dotted line) including the contributions of both the real (dashed line) and imaginary (solid line) parts of a two-slit object of the same p but different w ( = 60   nm ) .

Fig. 5
Fig. 5

The same T ( x x ) function as in Fig. 4 plotted with x fixed at the middle of (a) a slit, (b) inter-slit interval, and (c) the resulting image (dashed-dotted line) including the contributions of both the real (dashed line) and imaginary (solid line) parts of a two-slit object of the same w as in Fig. 4 with p = 100   nm .

Fig. 6
Fig. 6

Images of the same objects with w = 40   nm , p = 80   nm obtained by the superlens system with (a) d 1 = 20   nm , d 2 = 40   nm and (b) d 1 = 15   nm , d 2 = 40   nm ( 2 d 1 ) .

Fig. 7
Fig. 7

The real and imaginary parts of T ( x x ) function calculated for a superlens of four unit cells with d 1 = 5   nm , d 2 = 10   nm which is plotted with x at the middle of (a) the slit, (b) the pitch, and (c) the resulting image (dashed-dotted line) including the additive contributions of both the real (dashed line) and imaginary (solid line) parts of a two-slit object of the same w and p as in Fig. 3.

Fig. 8
Fig. 8

Comparison of images obtained for the same object of (a) 1 × 40   nm Ag-slab and (b) 2 × 20   nm Ag-slab superlenses.

Fig. 9
Fig. 9

The real and imaginary parts of T ( x x ) function calculated for a superlens of four unit cells with d 1 = 5   nm , d 2 = 10   nm which is plotted with x at the middle of (a) the slit, (b) the pitch, and (c) the resulting image (dashed-dotted line) including the additive contributions of both the real (dashed line) and imaginary (solid line) parts of a two-slit object with w = 30   nm and p = 60   nm .

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

T ( k x ) = E i ( k x ) E o ( k x ) ,     E i ( k x ) = T ( k x ) E o ( k x ) ,
[ m 11 m 12 m 21 m 22 ] = P 1 D 1 1 D 2 P 2 D 2 1 D 1 P 1 ,
P j = [ exp ( i k z j d ) 0 0 exp ( i k z j d ) ] ,     D j = [ 1 1 k z j / ε j k z j / ε j ] .
E i ( x ) = E o ( x ) T ( x x , d 1 , d 2 , N ) d x ,
T ( x x , d 1 , d 2 , N ) = 1 2 π T ( k x , d 1 , d 2 , N ) exp [ i k x ( x x ) ] d k x .
f = | 1 | T ( x x ) E o ( x ) d x E o ( x ) | d x | E o ( x ) | d x | ,
f = | 1 | [ T ( x x ) δ ( x x ) ] E o ( x ) d x | d x | E o ( x ) | d x | ,
H = | [ | T ( x x ) E o ( x ) d x | 2 E o ( x ) E o ( x ) ] d x E o ( x ) E o ( x ) d x | ,
T ( k x , d 1 , d 2 , N ) = 4 ε 1 ε 2 k z 1 k z 2   exp ( 2 i k z 1 d 1 ) ( ε 2 k z 1 + ε 1 k z 2 ) exp ( i k z 2 d 2 ) ( ε 2 k z 1 ε 1 k z 2 ) exp ( i k z 2 d 2 ) .

Metrics