Abstract

Sub-diffraction-limit imaging by the surface plasmon polariton (SPP) induced in thin metal film lenses has been analyzed numerically. The SPP images are deteriorated by interference of plasmon fields in layered metal-dielectric structures. To obtain a clear imaging capability, the reflection and the transmission property of evanescent waves in the layered structures has been investigated by the finite-difference time-domain (FDTD) method. For verification, a full 3-dimensional analysis of large-scale layered structures demonstrated sub-wavelength images similar to those obtained in the recently reported experiments. The analysis has been extended further to a lithography of nano-scale images to predict the minimum possible size of the images resolved by the silver thin film lenses.

© 2008 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. 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 layer," Opt. Express 13, 2127-2134 (2005).
    [CrossRef]
  4. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, "Near-field microscopy through a SiC superlens," Science 313, 1595 (2006).
    [CrossRef]
  5. B. Wood, J. B. Pendry, and D. P. Tsai, "Directed subwavelength imaging using a layered metal-dielectric system," Phys. Rev. B 74, 115,116 (2006).
    [CrossRef]
  6. T. Xu, Y. Zhao, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, "Sub-diffraction-limited interference photo lithography with metamaterials," Opt. Express 16, 13,579-13,584 (2008).
  7. A. D. Rakić, A. B. Djurisić, J. M. Dlazar, and M. L. Majewski, "Optical properties of metallic films for verticalcavity optoelectronic devices," Appl. Opt. 37, 5271-5283 (1998).
  8. A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 3rd ed. (Artech House, 2005) Chap. 9, pp. 361-383.
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    [CrossRef]
  10. P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113,110 (2006).
    [CrossRef]
  11. H. Raether, Surface plasmons on smooth and rough surfaces and on gratings (Springer-Verlag, Berlin, 1988).
  12. M. Fujii and P. Russer, "A Nonlinear and Dispersive APML ABC for the FD-TD Methods," IEEE Microw. Compon. Lett. 12, 444-446 (2002).
    [CrossRef]
  13. N. Fang, Z. Liu, T.-J. Yen, and X. Zhang, "Regenerating evanescent waves from a silver superlens," Opt. Express 11, 682-687 (2003).
    [CrossRef]

2008

T. Xu, Y. Zhao, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, "Sub-diffraction-limited interference photo lithography with metamaterials," Opt. Express 16, 13,579-13,584 (2008).

2006

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

B. Wood, J. B. Pendry, and D. P. Tsai, "Directed subwavelength imaging using a layered metal-dielectric system," Phys. Rev. B 74, 115,116 (2006).
[CrossRef]

P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113,110 (2006).
[CrossRef]

2005

2003

2002

M. Fujii and P. Russer, "A Nonlinear and Dispersive APML ABC for the FD-TD Methods," IEEE Microw. Compon. Lett. 12, 444-446 (2002).
[CrossRef]

2000

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1998

Belov, P. A.

P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113,110 (2006).
[CrossRef]

Blaikie, R. J.

Chen, S. C.

Cui, J.

T. Xu, Y. Zhao, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, "Sub-diffraction-limited interference photo lithography with metamaterials," Opt. Express 16, 13,579-13,584 (2008).

Djurisic, A. B.

Dlazar, J. M.

Du, C.

T. Xu, Y. Zhao, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, "Sub-diffraction-limited interference photo lithography with metamaterials," Opt. Express 16, 13,579-13,584 (2008).

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]

N. Fang, Z. Liu, T.-J. Yen, and X. Zhang, "Regenerating evanescent waves from a silver superlens," Opt. Express 11, 682-687 (2003).
[CrossRef]

Fujii, M.

M. Fujii and P. Russer, "A Nonlinear and Dispersive APML ABC for the FD-TD Methods," IEEE Microw. Compon. Lett. 12, 444-446 (2002).
[CrossRef]

Hao, Y.

P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113,110 (2006).
[CrossRef]

Hillenbrand, R.

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

Korobkin, D.

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

Liu, Z.

Luo, X.

T. Xu, Y. Zhao, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, "Sub-diffraction-limited interference photo lithography with metamaterials," Opt. Express 16, 13,579-13,584 (2008).

Ma, J.

T. Xu, Y. Zhao, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, "Sub-diffraction-limited interference photo lithography with metamaterials," Opt. Express 16, 13,579-13,584 (2008).

Majewski, M. L.

Melville, D. O. S.

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, 115,116 (2006).
[CrossRef]

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Rakic, A. D.

Russer, P.

M. Fujii and P. Russer, "A Nonlinear and Dispersive APML ABC for the FD-TD Methods," IEEE Microw. Compon. Lett. 12, 444-446 (2002).
[CrossRef]

Shao, D. B.

Shvets, G.

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

Taubner, T.

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

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, 115,116 (2006).
[CrossRef]

Urzhumov, Y.

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

Wang, C.

T. Xu, Y. Zhao, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, "Sub-diffraction-limited interference photo lithography with metamaterials," Opt. Express 16, 13,579-13,584 (2008).

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, "Directed subwavelength imaging using a layered metal-dielectric system," Phys. Rev. B 74, 115,116 (2006).
[CrossRef]

Xu, T.

T. Xu, Y. Zhao, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, "Sub-diffraction-limited interference photo lithography with metamaterials," Opt. Express 16, 13,579-13,584 (2008).

Yen, T.-J.

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]

N. Fang, Z. Liu, T.-J. Yen, and X. Zhang, "Regenerating evanescent waves from a silver superlens," Opt. Express 11, 682-687 (2003).
[CrossRef]

Zhao, Y.

T. Xu, Y. Zhao, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, "Sub-diffraction-limited interference photo lithography with metamaterials," Opt. Express 16, 13,579-13,584 (2008).

Appl. Opt.

IEEE Microw. Compon. Lett.

M. Fujii and P. Russer, "A Nonlinear and Dispersive APML ABC for the FD-TD Methods," IEEE Microw. Compon. Lett. 12, 444-446 (2002).
[CrossRef]

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, 115,116 (2006).
[CrossRef]

P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113,110 (2006).
[CrossRef]

Phys. Rev. Lett.

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

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]

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

Other

H. Raether, Surface plasmons on smooth and rough surfaces and on gratings (Springer-Verlag, Berlin, 1988).

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 3rd ed. (Artech House, 2005) Chap. 9, pp. 361-383.

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Figures (18)

Fig. 1.
Fig. 1.

The Lorentz-Drude model of the complex relative permittivity of silver.

Fig. 2.
Fig. 2.

Dispersion relation of SPP on Ag film. The horizontal dash-dotted line indicates the plasma frequency at 925.5 THz. The inset shows the cross section of the analyzed layered structure.

Fig. 3.
Fig. 3.

The layer structure of the experiment by Fang. et.al. [2] considered also in this paper.

Fig. 4.
Fig. 4.

Imaging of a grating (60 nm wide slit and 60 nm wide Cr mask). Top: a linear scale profile of the grating image obtained by integrating the energy dissipation W in the photo-resist layer observed at height 180 nm. The image profile for the case of no silver layer is plotted for comparison. Bottom: the distribution of W on the cross section in a logarithmic magnitude color scale. The black solid lines indicate the boundaries of the Ag film (140 nm to 175 nm in height) and Cr mask of the grating (50 nm to 100 nm in height).

Fig. 5.
Fig. 5.

Imaging of a 40 nm wide single slit. The plots has been prepared similarly as in Fig. 4. Top: comparison of normalized W for the three cases of 35 nm thick Ag layer (FWHM 161 nm), 25 nm thick Ag layer (FWHM 111 nm), and without Ag layer (FWHM 135 nm). Bottom: the distribution of W in a logarithmic magnitude color scale for 35 nm thick Ag layer system.

Fig. 6.
Fig. 6.

Splitting field in the 3-layered structure of ε r =2 for the top, -1.5 for the metal, and 1 for the bottom layers. Top figure: normalized W detected at height 155 nm. Bottom figure: the distribution of W plotted in a logarithmic magnitude color scale. An excitation source of 40 nm in width locates at height 60 nm. The black solid lines indicate the boundaries of the metal layer.

Fig. 7.
Fig. 7.

Focusing field in the layered structure of ε r =1 for top, -1.5 for metal, and 2 for bottom. Top figure: normalized W detected at height 155 nm. Bottom figure: the distribution of W in logarithmic magnitude color scale. Same excitation source as in Fig. 6.

Fig. 8.
Fig. 8.

Comparison of the single slit image profiles by energy dissipation W for four types of layered systems. The thickness of the Drude metal is 50 or 30 nm, and the layered structures are ε r =1 for the top, -1.5 for the metal and 2 for the bottom layers, or ε r opposite in order, i.e. 2, -1.5, and 1, respectively. The plots are normalized by the largest W for 30 nm thick ε r =2, -1.5, 1. The profiles were detected at 5 nm above the metal surface.

Fig. 9.
Fig. 9.

Overall Fresnel reflection and transmission coefficients R and T, for the layered structures of ε r =2 for top,-1.5 for the metal, and 1 for bottom. Real, imaginary and absolute values are plotted.

Fig. 10.
Fig. 10.

Overall Fresnel reflection and transmission coefficients R and T, for the layered structures of ε r =1 for top, -1.5 for the metal, and 2 for bottom. Real, imaginary and absolute values are plotted. Total reflection is observed at the incident angle of 45 degrees.

Fig. 11.
Fig. 11.

Mask pattern of letter ‘T’. The purple part is chromium, and the yellow is the slit filled with PMMA (ε r =2.4.)

Fig. 12.
Fig. 12.

Electric fields of letter ‘T’ obtained with silver thin film. Top:E x , bottom left;E y and bottom right:E z .

Fig. 13.
Fig. 13.

Image of letter ‘T’ obtained by calculating W in the photo-resist layer with the silver layer. Left figure is obtained by integrating |E|2=E 2 x +E 2 y +E 2 z , and right figure obtained by modified field |E|2=E 2 x +E 2 y /4+E 2 z .

Fig. 14.
Fig. 14.

Image of letter ‘T’ obtained without the silver layer. Left and right figures obtained similarly as in Fig. 13.

Fig. 15.
Fig. 15.

Mask pattern (left) of a 40 nm diameter hole, and the images obtained with (center) and without (right) a silver thin layer.

Fig. 16.
Fig. 16.

Mask pattern (left) of two 40 nm diameter holes, and the images obtained with (center) and without (right) a silver thin layer.

Fig. 17.
Fig. 17.

Mask pattern (left) of a ring of 60 nm inner radius and 100 nm outer radius, and the images obtained with (center) and without (right) a silver thin layer.

Fig. 18.
Fig. 18.

Mask pattern (left) of 40 nm wide plus shaped slits, and the images obtained with (center) and without (right) a silver thin layer.

Equations (7)

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

W = 0 T σ E 2 dt ,
ε r = 1 ω p 2 ω o 2 ,
r mn = k z , m ε r , m k z , n ε r , n k z , m ε r , m + k z , n ε r , n ,
t mn = 1 + r mn
R = r 12 t 12 2 r 23 exp ( 2 i k z , 2 d ) 1 + r 12 r 23 exp ( 2 i k z , 2 d ) ,
T = t 12 r 23 exp ( i k z , 2 d ) 1 + r 12 r 23 exp ( 2 i k z , 2 d ) ,
k z , m = { ε r , m μ r , m ω 2 c 2 k x 2 , for m = 1 , 3 i k x 2 ε r , m μ r , m ω 2 c 2 , for m = 2 .

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