Abstract

The dispersion of a hyperbolic anisotropic metamaterial (HAM) and the chromatic aberration of light focusing in this kind of HAM are studied. The HAM is formed by alternately stacking metal and dielectric layers. The rules of materials and filling factors affecting the optical property of HAM are given. The chromatic aberration of light focusing is demonstrated both theoretically and numerically. By comparing the theory with the simulation results, the factors influencing the focal length, including the heat loss of material and low spatial frequency modes, are discussed. The investigation emphasizes the anomalous properties, such as chromatic aberration and low spatial frequency modes influencing focus position, of HAM compared with that in conventional lens. Based on the analysis, the possibility of using HAM to focus light with two different wavelengths at the same point is studied.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2012

2011

G. Li, J. Li, and K. W. Cheah, “Subwavelength focusing using a hyperbolic medium with a single slit,” Appl. Opt. 50(31), G27–G30 (2011).
[CrossRef] [PubMed]

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[CrossRef]

2010

2009

S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009).
[CrossRef] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902(2009).
[CrossRef] [PubMed]

2008

2007

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

2006

X. Fan, G. P. Wang, J. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[CrossRef]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

2005

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]

2000

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

1972

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

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902(2009).
[CrossRef] [PubMed]

Chan, C. T.

X. Fan, G. P. Wang, J. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

Cheah, K. W.

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]

Costa, J. T.

Du, C.

Durant, S.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[CrossRef] [PubMed]

Engheta, N.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[CrossRef]

Escobar, M. A.

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[CrossRef]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902(2009).
[CrossRef] [PubMed]

Fan, X.

X. Fan, G. P. Wang, J. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

Fang, N.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[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]

Feng, Q.

Gan, D.

Gao, Y.

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]

Lai, Z.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[CrossRef] [PubMed]

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[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]

Lee, J.

X. Fan, G. P. Wang, J. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

Li, G.

Li, J.

Liu, J.

Liu, K.

Liu, L.

Liu, S.

Liu, Z.

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[CrossRef]

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7, 435–441 (2008).
[CrossRef] [PubMed]

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[CrossRef] [PubMed]

Luo, X.

Ma, C.

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[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(11), 115116 (2006).
[CrossRef]

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

Pikus, Y.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[CrossRef] [PubMed]

Podolskiy, V. A.

Ren, G.

Salandrino, A.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[CrossRef]

Silveirinha, M. G.

Song, Y.

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[CrossRef] [PubMed]

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[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]

Thongrattanasiri, S.

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(11), 115116 (2006).
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902(2009).
[CrossRef] [PubMed]

Wang, C.

Wang, G. P.

X. Fan, G. P. Wang, J. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

Wang, Y.

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

Xiong, Y.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[CrossRef] [PubMed]

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902(2009).
[CrossRef] [PubMed]

Zhang, X.

Y. Gao, J. Liu, X. Zhang, Y. Wang, Y. Song, S. Liu, and Y. Zhang, “Analysis of focal-shift effect in planar metallic nanoslit lenses,” Opt. Express 20(2), 1320–1329 (2012).
[CrossRef] [PubMed]

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7, 435–441 (2008).
[CrossRef] [PubMed]

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[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]

Zhang, Y.

Zhao, Y.

Appl. Opt.

Nano Lett.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[CrossRef] [PubMed]

Nat. Mater.

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7, 435–441 (2008).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

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

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[CrossRef]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[CrossRef]

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[CrossRef]

Phys. Rev. Lett.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902(2009).
[CrossRef] [PubMed]

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

X. Fan, G. P. Wang, J. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

Science

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]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

Other

E. Palik, ed., “Handbook of optical constants of solids,” (AP, 1985).

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Figures (7)

Fig. 1
Fig. 1

(a) and (d): Dispersion relation of two types of ideal HAM; (b) and (e): focusing behavior; (c) and (f): normalized magnetic field distribution in focus plane.

Fig. 2
Fig. 2

Schematic of single aperture and HAM which are formed by alternately stacking metal and dielectric layers.

Fig. 3
Fig. 3

Real parts of εx and εz, as functions of λ, for a multilayered metamaterial with (a) εm = εAg, εd = 7 and η = 0.5 (green), η = 1 (blue) and η = 2 (red); (b) εm = εAg, η = 1 and εd = 4 (green), εd = 7 (blue). Solid and dashed lines plot εx and εz, respectively.

Fig. 4
Fig. 4

Distribution of the intensity of |Hy|2 for the ideal HAM (a)–(c) and the silver-SiC multilayered structure (d)–(f) with incident wavelength of 350, 370, 390 nm, respectively.

Fig. 5
Fig. 5

Distribution of the intensity of |Hy|2 for the ideal HAM (a)–(c) and the silver-SiC multilayered structure (d)–(f) with incident wavelength of 550, 650, 850 nm, respectively.

Fig. 6
Fig. 6

Relation between the incident wavelength λ and the focal length. The plots express the theoretical focal length (blue solid line), simulation results of lossy (red circle), lossless (black asterisk) ideal medium and silver-SiC structures (green square).

Fig. 7
Fig. 7

(a) Relation between εm/εd +εd /εm and the wavelength for silver-SiC structure. (b) Focal length varies with thickness ratio under λ = 365 nm and λ = 673 nm.

Tables (1)

Tables Icon

Table 1 Focusing property of HAM in different region

Equations (9)

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

k x 2 ε z + k z 2 ε x = k 0 2
θ ( k x ) = arctan ( ε x k x ε z k z )
θ = arctan ( ε x ε z )
f = w 2 | tan θ | = w 2 ε z ε x
ε x = ε d + η ε m 1 + η , 1 ε z = 1 1 + η ( 1 ε d + η ε m )
η = d m d d
tan θ k x = ε x ε z k z + ε x 2 k x 2 / k z ε z k z 2
k = ε x ( k 0 2 k x 2 / ε z )
tan θ = ε x ε z = 1 ( 1 + η 2 ) ( 1 + η 2 + ε η )

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