Abstract

The loss and back-coupling effects on the subwavelength imaging of three-dimensional superlens are reported in this paper. The loss is added in the image region of a superlens. The back-coupling effects are considered by adding a shielded layer above the object region. (1) By adding loss in the image region, the long range plasmon mode is drastically suppressed. (2) The back-coupling shield above the objects has the effects of amplifying the higher spatial frequency components while suppressing the long range plasmon mode. Because of (1) and (2), the transfer function becomes flatter. Subsequently, the finer resolution of images is obtained. This is confirmed by the field and intensity distribution generated by the horizontal magnetic dipoles and vertical electric dipoles located in the object region and the image intensity distributions of the patterned mask structures in the lithography.

© 2012 Optical Society of America

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References

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2012 (1)

2011 (2)

2008 (1)

W. T. Lu and S. Sridhar, Phys. Rev. B 77, 233101 (2008).
[CrossRef]

2007 (2)

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, Nano Lett. 7, 403 (2007).
[CrossRef]

Y. Xiong, Z. Liu, C. Sun, and X. Zhang, Nano Lett. 7, 3360 (2007).
[CrossRef]

2006 (3)

B. Wood and J. B. Pendry, Phys. Rev. B 74, 115116 (2006).
[CrossRef]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef]

S. Durant, Z. Liu, J. M. Steele, and X. Zhang, J. Opt. Soc. Am. B 23, 2383 (2006).
[CrossRef]

2005 (2)

D. R. Smith, Science 308, 502 (2005).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, Sci. 308, 534 (2005).
[CrossRef]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

1997 (1)

J. J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 64370 (1972).
[CrossRef]

Bagley, J. Q.

Bagley, J. Quinn

Carminati, R.

J. J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 64370 (1972).
[CrossRef]

Ding, K. H.

Durant, S.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, Nano Lett. 7, 403 (2007).
[CrossRef]

S. Durant, Z. Liu, J. M. Steele, and X. Zhang, J. Opt. Soc. Am. B 23, 2383 (2006).
[CrossRef]

Fang, N.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, Nano Lett. 7, 403 (2007).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, Sci. 308, 534 (2005).
[CrossRef]

Greffet, J. J.

J. J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).
[CrossRef]

Hillenbrand, R.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef]

Huang, S.

Ishimaru, A.

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 64370 (1972).
[CrossRef]

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (Wiley, 1990).

Korobkin, D.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef]

Lee, H.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, Nano Lett. 7, 403 (2007).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, Sci. 308, 534 (2005).
[CrossRef]

Liu, Z.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, Nano Lett. 7, 403 (2007).
[CrossRef]

Y. Xiong, Z. Liu, C. Sun, and X. Zhang, Nano Lett. 7, 3360 (2007).
[CrossRef]

S. Durant, Z. Liu, J. M. Steele, and X. Zhang, J. Opt. Soc. Am. B 23, 2383 (2006).
[CrossRef]

Lu, W. T.

W. T. Lu and S. Sridhar, Phys. Rev. B 77, 233101 (2008).
[CrossRef]

Pendry, J. B.

B. Wood and J. B. Pendry, Phys. Rev. B 74, 115116 (2006).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Pikus, Y.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, Nano Lett. 7, 403 (2007).
[CrossRef]

Shvets, G.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef]

Smith, D. R.

D. R. Smith, Science 308, 502 (2005).
[CrossRef]

Sridhar, S.

W. T. Lu and S. Sridhar, Phys. Rev. B 77, 233101 (2008).
[CrossRef]

Steele, J. M.

Sun, C.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, Nano Lett. 7, 403 (2007).
[CrossRef]

Y. Xiong, Z. Liu, C. Sun, and X. Zhang, Nano Lett. 7, 3360 (2007).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, Sci. 308, 534 (2005).
[CrossRef]

Taubner, T.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef]

Tsang, L.

Urzhumov, Y.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef]

Wang, H.

Wood, B.

B. Wood and J. B. Pendry, Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Xiong, Y.

Y. Xiong, Z. Liu, C. Sun, and X. Zhang, Nano Lett. 7, 3360 (2007).
[CrossRef]

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, Nano Lett. 7, 403 (2007).
[CrossRef]

Zhang, X.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, Nano Lett. 7, 403 (2007).
[CrossRef]

Y. Xiong, Z. Liu, C. Sun, and X. Zhang, Nano Lett. 7, 3360 (2007).
[CrossRef]

S. Durant, Z. Liu, J. M. Steele, and X. Zhang, J. Opt. Soc. Am. B 23, 2383 (2006).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, Sci. 308, 534 (2005).
[CrossRef]

J. Opt. Soc. Am. B (3)

Nano Lett. (2)

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, Nano Lett. 7, 403 (2007).
[CrossRef]

Y. Xiong, Z. Liu, C. Sun, and X. Zhang, Nano Lett. 7, 3360 (2007).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (3)

P. B. Johnson and R. W. Christy, Phys. Rev. B 64370 (1972).
[CrossRef]

B. Wood and J. B. Pendry, Phys. Rev. B 74, 115116 (2006).
[CrossRef]

W. T. Lu and S. Sridhar, Phys. Rev. B 77, 233101 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Prog. Surf. Sci. (1)

J. J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).
[CrossRef]

Sci. (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, Sci. 308, 534 (2005).
[CrossRef]

Science (2)

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef]

D. R. Smith, Science 308, 502 (2005).
[CrossRef]

Other (1)

J. A. Kong, Electromagnetic Wave Theory (Wiley, 1990).

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Figures (10)

Fig. 1.
Fig. 1.

The illustration of two superlens structures. Both structures contain three layers. Region 0, 1, and 2 are the object, metal film, and image regions, respectively. (a) The superlens structure without the shield. (b) The structure with a shield.

Fig. 2.
Fig. 2.

The amplitudes of the electromagnetic fields E and H and intensity S on the image plane generated by an x-directed HMD source. (a) The case that ε0r=ε2r=1 without a shield. (b) The case that ε0r=1 and ε2r=1+1i without a shield. (c) The case that ε0r=1 and ε2r=1+1i with a chromium shield ε1r=8.55+8.96i and hm=0.025 wavelength. The color bar will be used in all the color maps throughout this paper.

Fig. 3.
Fig. 3.

The image intensity of nine HMD point sources. (a) The case without loss and shield. (b) The case with loss. (c) The case with both loss and shield.

Fig. 4.
Fig. 4.

The image intensity of nine VED point sources. (a) The case without loss and shield. (b) The case with loss. (c) The case with both loss and shield.

Fig. 5.
Fig. 5.

The superlens used for lithography. (a) Side view. (b) Top view of the mask marked with two-dimensional grids. (c) The mask marked with layout traces.

Fig. 6.
Fig. 6.

The image of a two-dimensional grid marked on the mask. (a) No loss is added. (b) Loss is added in the image region.

Fig. 7.
Fig. 7.

The image of the layout of traces marked on the mask. (a) No loss is added. (b) Loss is added in the image region.

Fig. 8.
Fig. 8.

The transfer functions of the TM waves. (a) The case for the examples of HMD and VED as in Figs. (2), (3), and (4). (b) The case for the examples of lithography as in Figs. (6) and (7).

Fig. 9.
Fig. 9.

The image intensity of nine HMD point sources with different thickness of the chromium mask. (a) 0.001, (b) 0.005; (c) 0.01, (d) 0.05; (e) 0.1.

Fig. 10.
Fig. 10.

The image intensity of nine HMD point sources with different loss permittivity in the image region: (a) 1+0.1i, (b) 1+0.5i; (c) 1+5i, (d) 1+10i.

Tables (1)

Tables Icon

Table 1. The FWHM in x and y Directions

Equations (3)

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S=12πj=12dωW(ω)Objectdsi=13GijEM(r,r;ω)A(r)Objectdsk=13Gkj*HM(r,r;ω)A*(r)(x^i×x^k)·exp[(Δk)2|ρρ|2/2].
S=12πj=12Objectdsi=13GijEM(r,r;ω)A(r)·Objectdsk=13Gkj*HM(r,r;ω)A*(r)(x^i×x^k)dωW(ω).
TbcTM(kρ;z,z)=TTM(kρ;z,z)[1+R0,1TMexp(2ik0z(hmhs))]/[1R0,1TMr0,1TMexp(2ik0z(hmhs))exp(2ik0z(0hs))].

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