Abstract

In response to increasing interest in the area of subdiffraction-limited near-field imaging, the performance of several different realizable and theoretical superresolving silver-based lenses is simulated for a variety of different input object profiles. A computationally-efficient T-matrix technique is used to model the lenses, which consist of layers of silver with total width of 40nm sandwiched between layers of polymethyl methacrylate and silicon dioxide. The lenses are exposed to nonperiodic bright- and dark-slit input patterns, with feature size varied between 1nm and 2.5μm. The performance of the lenses is characterized in terms of transfer function, contrast profile, error profile, and input-to-output correlation. It is shown that increasing the number of layers in a lens increases the lens’ transmission coefficients at high spatial frequencies; however, this does not always lead to better imaging performance. The main reasons for this are lens-specific resonances that distort features at certain spatial frequencies, and the increased attenuation of the DC component of transmitted images, which reduces image fidelity, particularly for dark-line features. This suggests that, to achieve optimum results, the design of the superresolving lens system should take into account the characteristics of the images that it is expected to transmit.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2007 (1)

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

2006 (2)

2005 (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]

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]

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

2003 (3)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161-163 (2003).
[CrossRef]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

2001 (1)

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Imaging, compression and Poynting vector streamlines for negative permittivity materials,” Electron. Lett. 37, 1243-1244 (2001).
[CrossRef]

2000 (2)

Appl. Opt. (1)

Appl. Phys. Lett. (2)

N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161-163 (2003).
[CrossRef]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Electron. Lett. (1)

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Imaging, compression and Poynting vector streamlines for negative permittivity materials,” Electron. Lett. 37, 1243-1244 (2001).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (1)

Phys. Rev. B (1)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

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

Physica B (1)

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

Rep. Prog. Phys. (1)

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

Science (1)

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 (4)

A. A. Michelson, Studies in Optics (U. Chicago Press, 1962).

H. Lohninger, Teach/Me Data Analysis (Springer-Verlag, 1999).

H. Abdi, “Coefficients of correlation, alienation and determination,” in Encyclopedia of Measurement and Statistics, N. Salkind, ed. (Sage, 2007), pp. 158-162.

D. O. S. Melville, “Planar lensing lithography: enhancing the optical near field,” Ph.D. thesis (University of Canterbury, New Zealand, 2006).

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Figures (12)

Fig. 1
Fig. 1

Comparison of 20 nm bright-line-pair versus dark-line-pair images for single-layer and multilayer superlenses. Note that the multilayer lens (solid) outperforms the single-layer lens (dashed) when imaging the bright features (a) but not when imaging the dark features (b).

Fig. 2
Fig. 2

Lens composition and dimensions. Top: 80 nm vacuum gap used for proximity imaging. Middle: Single-layer silver superlens with 10 nm Si O 2 final layer in accordance with practical experimental conditions [9]. Bottom: Multilayer superlens made up of eight individual 5 nm silver laminations. Total silver thickness is 40 nm , as for the single-layer lens. Input object patterns are applied from the left of the lenses and output images are retrieved from the right, as indicated.

Fig. 3
Fig. 3

Component system describing the interaction between transverse magnetic (TM)-polarized waves and a uniform, planar interface [8].

Fig. 4
Fig. 4

Transfer functions for single-layer and multilayer superlenses and an 80 nm vacuum gap. The single-layer lens is 40 nm thick, sandwiched between PMMA and Si O 2 spacers, whereas the multilayer lens consists of eight 5 nm thick silver laminations (separated by 5 nm ) with the same PMMA and Si O 2 outer layers.

Fig. 5
Fig. 5

Input (dashed) and output (solid) intensity profiles for a 75 nm feature imaged through a 20 : 40 : 10 nm PMMA : Ag : Si O 2 realizable superlens. The definitions for the maximum intensity I max , minimum intensity I min , background intensity I dc , and the intensity at the center of the dark-line feature in the object I dark are shown for use in the contrast and pseudocontrast calculations.

Fig. 6
Fig. 6

(a) Pseudocontrast profile for a dual dark-slit pattern exposed to a multilayer realizable superlens. Note prevalent ripples between 100 nm and 1 μ m . (b) Input (dashed) and output (solid) intensity profiles for a 465 nm dual dark-slit pattern imaged through such a lens.

Fig. 7
Fig. 7

(a) Single bright-, (b) single dark-, (c) dual bright-, and (d) dual dark-slit input intensity patterns used to generate contrast, error, and correlation profiles. Slit width(s) is (are) varied between 1 nm and 2.5 μ m .

Fig. 8
Fig. 8

(a) Single and (b) dual dark-slit contrast profiles for single-layer and multilayer superlenses and an 80 nm vacuum gap.

Fig. 9
Fig. 9

(a) Single and (b) dual dark-slit pseudocontrast profiles for single-layer and multilayer superlenses and an 80 nm vacuum gap.

Fig. 10
Fig. 10

Spatial-domain output for a 20 nm dark slit (dotted) projected through single-layer (dashed) and multilayer (solid) layer realizable superlenses. The pseudocontrast is 0.9997 for the single-layer lens and 0.4033 for the multilayer lens.

Fig. 11
Fig. 11

(a) Single bright-, (b) single dark-, (c) dual bright- and (d) dual dark-slit error profiles for single-layer and multilayer superlenses and an 80 nm vacuum gap.

Fig. 12
Fig. 12

(a) Single bright-, (b) single dark-, (c) dual bright- and (d) dual dark-slit correlation coefficient profiles for single-layer and multilayer superlenses and an 80 nm vacuum gap.

Equations (17)

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[ E x C E x D ] = k z 2 ϵ [ ϵ k z + ϵ k z ϵ k z ϵ k z ϵ k z ϵ k z ϵ k z + ϵ k z ] [ E x A E x B ] = T ( 0 ) [ E x A E x B ] ,
T ( d ) = [ exp ( i k z d ) 0 0 exp ( i k z d ) ] T ( 0 ) [ exp ( i k z d ) 0 0 exp ( i k z d ) ] .
[ t 0 ] = [ T 11 T 12 T 21 T 22 ] [ 1 r ]
t = T 11 T 22 T 12 T 21 T 22 .
C M = I max I min I max + I min ,
C pseudo = I DC I dark I DC + I dark
C pseudo = I bright I DC I DC + I bright .
H = [ a s ( x ) i ( x ) ] 2 d x ,
d H d a = 2 s ( x ) [ a s ( x ) i ( x ) ] d x = 0 .
a = [ s ( x ) i ( x ) ] d x s ( x ) 2 d x .
H = { [ s ( x ) i ( x ) ] d x [ s ( x ) 2 ] d x s ( x ) i ( x ) } 2 d x .
H = ( s i s 2 s i ) 2 .
r s , i = cov s , i σ s σ i ,
C I e x 0 I e x + 0 = 1 ,
r = m x + c .
r = m x ,
r = x ,

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