Abstract

The use of transfer-matrix analyses for characterizing planar optical superlensing systems is studied here, and the simple model of the planar superlens as an isolated imaging element is shown to be defective in certain situations. These defects arise due to neglected interactions between the superlens and the spatially varying shadow masks that are normally used as scattering objects for imaging, and which are held in near-field proximity to the superlenses. An extended model is proposed that improves the accuracy of the transfer-matrix analysis, without adding significant complexity, by approximating the reflections from the shadow mask by those from a uniform metal layer. Results obtained using both forms of the transfer matrix model are compared to finite element models and two example superlenses, one with a silver monolayer and the other with three silver sublayers, are characterized. The modified transfer matrix model gives much better agreement in both cases.

© 2009 OSA

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  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]
  2. S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49(10), 1747–1762 (2002).
    [CrossRef]
  3. S. A. Ramakrishna and ., “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).
  4. D. O. S. Melville and R. J. Blaikie, “Analysis and optimization of multilayer silver superlenses for near-field optical lithography,” Phys. Rev. B 394, 197–202 (2007).
  5. 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(10), 1506–1508 (2003).
    [CrossRef]
  6. C. P. Moore, M. D. Arnold, P. J. Bones, and R. J. Blaikie, “Image fidelity for single-layer and multi-layer silver superlenses,” J. Opt. Soc. Am. A 25(4), 911–918 (2008).
    [CrossRef]
  7. 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(10), 101113 (2009).
    [CrossRef]
  8. P. Andrew and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306(5698), 1002–1005 (2004).
    [CrossRef] [PubMed]
  9. D. O. S. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
    [CrossRef] [PubMed]
  10. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
    [CrossRef] [PubMed]
  11. 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(3), 461–467 (2006).
    [CrossRef]
  12. O. S. Heavens, Optical properties of thin solid films (Butterworths Scientific Publications, London, 1955), Chap. 4.
  13. P. Pereyra, “Resonant tunneling and band mixing in multichannel superlattices,” Phys. Rev. Lett. 80(12), 2677–2680 (1998).
    [CrossRef]
  14. J. Jia, The finite element method for electromagnetics (Wiley, New York, 1993).
  15. P. Pereyra, A. Robledo-Martinez, and M. Morales-Luna, “The effect of complex and negative indices in the transmission of electromagnetic waves through superlattices,” Microelectron. J. 39(3-4), 394–397 (2008).
    [CrossRef]
  16. COMSOL is a registered trademark of COMSOL A.B., (1997–2009).
  17. P. Bienstman, Rigorous and efficient modelling of wavelength scale photonic components, PhD. Thesis (Ghent University, Belgium, 2001), Chap. 4.
  18. C. P. Moore, R. J. Blaikie, and M. D. Arnold, “Improved analytical models for single- and multi-layer silver superlenses,” Proc. 2009 MRS Spring Meeting 1182, in press (2009).
  19. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  20. J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69(19), 2772–2775 (1992).
    [CrossRef] [PubMed]
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  22. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995).
    [CrossRef]
  23. S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68(2), 449–521 (2005).
    [CrossRef]
  24. A. Z. Ultra-i, TM 123 data sheet © 2005 Rohm and Haas Electronic Materials. http://www.microresist.de/products/room_haas/pdf/ULTRA-i_123_Serie.pdf , retrieved on 18 July 2009.

2009 (1)

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(10), 101113 (2009).
[CrossRef]

2008 (2)

C. P. Moore, M. D. Arnold, P. J. Bones, and R. J. Blaikie, “Image fidelity for single-layer and multi-layer silver superlenses,” J. Opt. Soc. Am. A 25(4), 911–918 (2008).
[CrossRef]

P. Pereyra, A. Robledo-Martinez, and M. Morales-Luna, “The effect of complex and negative indices in the transmission of electromagnetic waves through superlattices,” Microelectron. J. 39(3-4), 394–397 (2008).
[CrossRef]

2007 (1)

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

2006 (1)

2005 (3)

D. O. S. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 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(5721), 534–537 (2005).
[CrossRef] [PubMed]

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68(2), 449–521 (2005).
[CrossRef]

2004 (1)

P. Andrew and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306(5698), 1002–1005 (2004).
[CrossRef] [PubMed]

2003 (2)

S. A. Ramakrishna and ., “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).

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(10), 1506–1508 (2003).
[CrossRef]

2002 (1)

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49(10), 1747–1762 (2002).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1998 (1)

P. Pereyra, “Resonant tunneling and band mixing in multichannel superlattices,” Phys. Rev. Lett. 80(12), 2677–2680 (1998).
[CrossRef]

1995 (1)

1992 (1)

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69(19), 2772–2775 (1992).
[CrossRef] [PubMed]

1981 (1)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “Highly conducting lamellar diffraction gratings,” J. Mod. Opt. 28(8), 1087–1102 (1981).

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Adams, J. L.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “Highly conducting lamellar diffraction gratings,” J. Mod. Opt. 28(8), 1087–1102 (1981).

Andrew, P.

P. Andrew and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306(5698), 1002–1005 (2004).
[CrossRef] [PubMed]

Andrewartha, J. R.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “Highly conducting lamellar diffraction gratings,” J. Mod. Opt. 28(8), 1087–1102 (1981).

Arnold, M. D.

Barnes, W. L.

P. Andrew and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306(5698), 1002–1005 (2004).
[CrossRef] [PubMed]

Blaikie, R. J.

Bones, P. J.

Botten, L. C.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “Highly conducting lamellar diffraction gratings,” J. Mod. Opt. 28(8), 1087–1102 (1981).

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Craig, M. S.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “Highly conducting lamellar diffraction gratings,” J. Mod. Opt. 28(8), 1087–1102 (1981).

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Gaylord, T. K.

Grann, E. B.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

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(10), 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(10), 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(10), 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(5721), 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(10), 101113 (2009).
[CrossRef]

MacKinnon, A.

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69(19), 2772–2775 (1992).
[CrossRef] [PubMed]

McPhedran, R. C.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “Highly conducting lamellar diffraction gratings,” J. Mod. Opt. 28(8), 1087–1102 (1981).

Melville, D. O. S.

Moharam, M. G.

Moore, C. P.

Morales-Luna, M.

P. Pereyra, A. Robledo-Martinez, and M. Morales-Luna, “The effect of complex and negative indices in the transmission of electromagnetic waves through superlattices,” Microelectron. J. 39(3-4), 394–397 (2008).
[CrossRef]

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(10), 101113 (2009).
[CrossRef]

Pendry, J. B.

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(10), 1506–1508 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49(10), 1747–1762 (2002).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69(19), 2772–2775 (1992).
[CrossRef] [PubMed]

Pereyra, P.

P. Pereyra, A. Robledo-Martinez, and M. Morales-Luna, “The effect of complex and negative indices in the transmission of electromagnetic waves through superlattices,” Microelectron. J. 39(3-4), 394–397 (2008).
[CrossRef]

P. Pereyra, “Resonant tunneling and band mixing in multichannel superlattices,” Phys. Rev. Lett. 80(12), 2677–2680 (1998).
[CrossRef]

Pommet, D. A.

Ramakrishna, S. A.

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68(2), 449–521 (2005).
[CrossRef]

S. A. Ramakrishna and ., “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).

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(10), 1506–1508 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49(10), 1747–1762 (2002).
[CrossRef]

Robledo-Martinez, A.

P. Pereyra, A. Robledo-Martinez, and M. Morales-Luna, “The effect of complex and negative indices in the transmission of electromagnetic waves through superlattices,” Microelectron. J. 39(3-4), 394–397 (2008).
[CrossRef]

Rosenbluth, M.

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(10), 1506–1508 (2003).
[CrossRef]

Schultz, S.

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(10), 1506–1508 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49(10), 1747–1762 (2002).
[CrossRef]

Schurig, D.

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(10), 1506–1508 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49(10), 1747–1762 (2002).
[CrossRef]

Smith, D. R.

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(10), 1506–1508 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49(10), 1747–1762 (2002).
[CrossRef]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

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(10), 1506–1508 (2003).
[CrossRef]

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(10), 101113 (2009).
[CrossRef]

J. Mod. Opt. (3)

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49(10), 1747–1762 (2002).
[CrossRef]

S. A. Ramakrishna and ., “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “Highly conducting lamellar diffraction gratings,” J. Mod. Opt. 28(8), 1087–1102 (1981).

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

J. Opt. Soc. Am. B (1)

Microelectron. J. (1)

P. Pereyra, A. Robledo-Martinez, and M. Morales-Luna, “The effect of complex and negative indices in the transmission of electromagnetic waves through superlattices,” Microelectron. J. 39(3-4), 394–397 (2008).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (2)

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

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett. (3)

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69(19), 2772–2775 (1992).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

P. Pereyra, “Resonant tunneling and band mixing in multichannel superlattices,” Phys. Rev. Lett. 80(12), 2677–2680 (1998).
[CrossRef]

Rep. Prog. Phys. (1)

S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68(2), 449–521 (2005).
[CrossRef]

Science (2)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

P. Andrew and W. L. Barnes, “Energy transfer across a metal film mediated by surface plasmon polaritons,” Science 306(5698), 1002–1005 (2004).
[CrossRef] [PubMed]

Other (6)

J. Jia, The finite element method for electromagnetics (Wiley, New York, 1993).

O. S. Heavens, Optical properties of thin solid films (Butterworths Scientific Publications, London, 1955), Chap. 4.

COMSOL is a registered trademark of COMSOL A.B., (1997–2009).

P. Bienstman, Rigorous and efficient modelling of wavelength scale photonic components, PhD. Thesis (Ghent University, Belgium, 2001), Chap. 4.

C. P. Moore, R. J. Blaikie, and M. D. Arnold, “Improved analytical models for single- and multi-layer silver superlenses,” Proc. 2009 MRS Spring Meeting 1182, in press (2009).

A. Z. Ultra-i, TM 123 data sheet © 2005 Rohm and Haas Electronic Materials. http://www.microresist.de/products/room_haas/pdf/ULTRA-i_123_Serie.pdf , retrieved on 18 July 2009.

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Figures (10)

Fig. 1.
Fig. 1.

Spatial-frequency transfer functions for the dielectric gap (dashed) and superlens (solid) described in Table 1. Both curves are generated from full-vector FEM simulations. The spatial frequency modes are evanescent to the right of the vertical line at 4.2 μm-1.

Fig. 2.
Fig. 2.

TMM (dashed) and FEM (solid) generated transfer functions for the superlens described in Table 1.

Fig. 3.
Fig. 3.

Output profiles predicted by TMM (dashed) and FEM (solid) for a sub-wavelength mask (dotted) with 20-nm wide apertures on a 100-nm centre-to-centre spacing.

Fig. 4.
Fig. 4.

Spatial-frequency-dependent reflection function for a 40-nm thick tungsten slab.

Fig. 5.
Fig. 5.

Recursive mask-lens interactions.

Fig. 6.
Fig. 6.

M-TMM (dotted), TMM (dashed) and FEM (solid) transfer functions for the superlens described in Table 1.

Fig. 7.
Fig. 7.

Output profiles predicted by M-TMM (dashed) and FEM (solid) for a sub-wavelength double- slit mask (dotted).

Fig. 8.
Fig. 8.

FEM modeling results for different detector-layer media: lossless SiO2, ε = 2.368 (solid); AZ ultra-i123 photoresist [24] in its unexposed state, ε = 2.729 + 0.024i (dashed); and the same resist in its fully-bleached state, ε = 2.729 + 0.001i (dotted).

Fig. 9.
Fig. 9.

Modified TMM (dotted), TMM (dashed) and FEM (solid) transfer functions for the multilayer superlens described in Table 1.

Fig. 10.
Fig. 10.

Output profiles predicted by TMM (dashed), Modified TMM (dot-dashed) and FEM (solid) for a sub-wavelength mask (dotted).

Tables (2)

Tables Icon

Table 1. Materials and dimensions of systems studied. Illumination wavelength is 365 nm and a 40-nm thick tungsten mask layer (ε r W = -1.497 + 7.690i) has been used in all cases.

Tables Icon

Table 2. Superlens characterization metrics

Equations (2)

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

op=ip·t1rL·rM.
t'=opip=t1rL·rM.

Metrics