Abstract

We show in this work an oblique layered system that is capable of manipulating two dimensional subwavelength images. Through properly designed planar layered system, we demonstrate analytically that lateral image shift could be achieved with subwavelength resolution, due to the asymmetry of the dispersion curve of constant frequency. Further, image rotation with arbitrary angle, as well as image magnification could be generated through a concentric geometry of the alternating layered system. In addition, we verify the image mechanism using full wave electromagnetic (EM) simulations. Utilizing the proposed layered system, optical image of an object with subwavelength features can be projected allowing for further optical processing of the image by conventional optics.

© 2011 OSA

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  6. S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101(R) (2003).
  7. T. A. Morgado and M. G. Silveirinha, “Transport of an arbitrary near-field component with an array of tilted wires,” New J. Phys. 11, 083023 (2009).
    [CrossRef]
  8. T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Experimental verification of full reconstruction of the near-field with a metamaterial lens,” Appl. Phys. Lett. 97, 144102 (2010).
    [CrossRef]
  9. A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35, 142–144 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. Y. Jin, “Improving subwavelength resolution of multilayered structures containing negative-permittivity layers by flatting the transmission curves,” Prog. Electromagn. Res. 105, 347–364 (2010).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  24. M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
    [CrossRef]
  25. H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15, 15886–15891 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  30. H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78, 054204 (2008).
    [CrossRef]

2011

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[CrossRef]

2010

B. Zeng, X. Yang, C. Wang, Q. Feng, and X. Luo, “Super-resolution imaging at different wavelengths by using a one-dimensional metamaterial structure,” J. Opt. 12, 035104 (2010).
[CrossRef]

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Experimental verification of full reconstruction of the near-field with a metamaterial lens,” Appl. Phys. Lett. 97, 144102 (2010).
[CrossRef]

Y. Jin, “Improving subwavelength resolution of multilayered structures containing negative-permittivity layers by flatting the transmission curves,” Prog. Electromagn. Res. 105, 347–364 (2010).
[CrossRef]

A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35, 142–144 (2010).
[CrossRef] [PubMed]

R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal-dielectric multilayers,” Opt. Lett. 35, 1133–1135 (2010).
[CrossRef] [PubMed]

B. Stein, J. Y. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, “Surface plasmon mode steering and negative refraction,” Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

2009

T. A. Morgado and M. G. Silveirinha, “Transport of an arbitrary near-field component with an array of tilted wires,” New J. Phys. 11, 083023 (2009).
[CrossRef]

2008

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
[CrossRef]

H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78, 054204 (2008).
[CrossRef]

B. Wang, L. Shen, and S. He, “Superlens formed by a one-dimensional dielectric photonic crystal,” J. Opt. Soc. Am. B 25, 391–395 (2008).
[CrossRef]

W. Wang, H. Xing, L. Fang, Y. Liu, J. Ma, L. Lin, C. Wang, and X. Luo, “Far-field imaging device: planar hyperlens with magnification using multi-layer metamaterial,” Opt. Express 16, 21142–21148 (2008).
[CrossRef] [PubMed]

2007

2006

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, 113110 (2006).
[CrossRef]

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

K. J. Webb and M. Yang, “Subwavelength imaging with a multilayer silver film structure,” Opt. Lett. 31, 2130–2132 (2006).
[CrossRef] [PubMed]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[CrossRef] [PubMed]

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

2005

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]

2003

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101(R) (2003).

2000

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

1873

E. Abbe, “Beitrage zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. Mikrosk. Anat. 9, 413–468 (1873).
[CrossRef]

Abbe, E.

E. Abbe, “Beitrage zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. Mikrosk. Anat. 9, 413–468 (1873).
[CrossRef]

Alekseyev, L. V.

Belov, P. A.

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[CrossRef]

A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35, 142–144 (2010).
[CrossRef] [PubMed]

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, 113110 (2006).
[CrossRef]

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71, 193105 (2005).

Chan, C. T.

H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78, 054204 (2008).
[CrossRef]

Chen, H.

H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B 78, 054204 (2008).
[CrossRef]

Devaux, E.

B. Stein, J. Y. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, “Surface plasmon mode steering and negative refraction,” Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Ebbesen, T. W.

B. Stein, J. Y. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, “Surface plasmon mode steering and negative refraction,” Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Engheta, N.

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

Fang, L.

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]

Feng, Q.

B. Zeng, X. Yang, C. Wang, Q. Feng, and X. Luo, “Super-resolution imaging at different wavelengths by using a one-dimensional metamaterial structure,” J. Opt. 12, 035104 (2010).
[CrossRef]

Genet, C.

B. Stein, J. Y. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, “Surface plasmon mode steering and negative refraction,” Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Hao, Y.

A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35, 142–144 (2010).
[CrossRef] [PubMed]

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, 113110 (2006).
[CrossRef]

He, S.

B. Wang, L. Shen, and S. He, “Superlens formed by a one-dimensional dielectric photonic crystal,” J. Opt. Soc. Am. B 25, 391–395 (2008).
[CrossRef]

X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75, 045103 (2007).
[CrossRef]

Ikonen, P.

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71, 193105 (2005).

Jacob, Z.

Jin, Y.

Y. Jin, “Improving subwavelength resolution of multilayered structures containing negative-permittivity layers by flatting the transmission curves,” Prog. Electromagn. Res. 105, 347–364 (2010).
[CrossRef]

X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75, 045103 (2007).
[CrossRef]

Kildishev, A. V.

Kivshar, Y. S.

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[CrossRef]

Kotynski, R.

R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal-dielectric multilayers,” Opt. Lett. 35, 1133–1135 (2010).
[CrossRef] [PubMed]

R. Kotynski, T. Stefaniuk, and A. Pastuszczak, “Sub-wavelength diffraction-free imaging with low-loss metal-dielectric multilayers,” arXiv:1002.0658v1.

Laluet, J. Y.

B. Stein, J. Y. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, “Surface plasmon mode steering and negative refraction,” Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Lee, H.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15, 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, 1686 (2007).
[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]

Li, X.

X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75, 045103 (2007).
[CrossRef]

Lin, L.

Liu, Y.

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 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, 15886–15891 (2007).
[CrossRef] [PubMed]

Luo, X.

B. Zeng, X. Yang, C. Wang, Q. Feng, and X. Luo, “Super-resolution imaging at different wavelengths by using a one-dimensional metamaterial structure,” J. Opt. 12, 035104 (2010).
[CrossRef]

W. Wang, H. Xing, L. Fang, Y. Liu, J. Ma, L. Lin, C. Wang, and X. Luo, “Far-field imaging device: planar hyperlens with magnification using multi-layer metamaterial,” Opt. Express 16, 21142–21148 (2008).
[CrossRef] [PubMed]

Ma, J.

Marcos, J. S.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Experimental verification of full reconstruction of the near-field with a metamaterial lens,” Appl. Phys. Lett. 97, 144102 (2010).
[CrossRef]

Maslovski, S. I.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Experimental verification of full reconstruction of the near-field with a metamaterial lens,” Appl. Phys. Lett. 97, 144102 (2010).
[CrossRef]

Morgado, T. A.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Experimental verification of full reconstruction of the near-field with a metamaterial lens,” Appl. Phys. Lett. 97, 144102 (2010).
[CrossRef]

T. A. Morgado and M. G. Silveirinha, “Transport of an arbitrary near-field component with an array of tilted wires,” New J. Phys. 11, 083023 (2009).
[CrossRef]

Narimanov, E.

Narimanov, E. E.

Orlov, A. A.

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[CrossRef]

Parini, C.

Pastuszczak, A.

R. Kotynski, T. Stefaniuk, and A. Pastuszczak, “Sub-wavelength diffraction-free imaging with low-loss metal-dielectric multilayers,” arXiv:1002.0658v1.

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, 115116 (2006).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101(R) (2003).

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

Qiu, M.

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
[CrossRef]

Rahman, A.

Ramakrishna, S. A.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101(R) (2003).

Salandrino, A.

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

Shen, L.

Silveirinha, M. G.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Experimental verification of full reconstruction of the near-field with a metamaterial lens,” Appl. Phys. Lett. 97, 144102 (2010).
[CrossRef]

T. A. Morgado and M. G. Silveirinha, “Transport of an arbitrary near-field component with an array of tilted wires,” New J. Phys. 11, 083023 (2009).
[CrossRef]

Simovski, C. R.

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71, 193105 (2005).

Stefaniuk, T.

R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal-dielectric multilayers,” Opt. Lett. 35, 1133–1135 (2010).
[CrossRef] [PubMed]

R. Kotynski, T. Stefaniuk, and A. Pastuszczak, “Sub-wavelength diffraction-free imaging with low-loss metal-dielectric multilayers,” arXiv:1002.0658v1.

Stein, B.

B. Stein, J. Y. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, “Surface plasmon mode steering and negative refraction,” Phys. Rev. Lett. 105, 266804 (2010).
[CrossRef]

Stewart, W. J.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 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, 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, 534–537 (2005).
[CrossRef] [PubMed]

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, 115116 (2006).
[CrossRef]

Voroshilov, P. M.

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[CrossRef]

Wang, B.

Wang, C.

B. Zeng, X. Yang, C. Wang, Q. Feng, and X. Luo, “Super-resolution imaging at different wavelengths by using a one-dimensional metamaterial structure,” J. Opt. 12, 035104 (2010).
[CrossRef]

W. Wang, H. Xing, L. Fang, Y. Liu, J. Ma, L. Lin, C. Wang, and X. Luo, “Far-field imaging device: planar hyperlens with magnification using multi-layer metamaterial,” Opt. Express 16, 21142–21148 (2008).
[CrossRef] [PubMed]

Wang, W.

Webb, K. J.

Wiltshire, M. C. K.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).

Wood, B.

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

Xing, H.

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 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, 15886–15891 (2007).
[CrossRef] [PubMed]

Yan, M.

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
[CrossRef]

Yan, W.

M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B 78, 125113 (2008).
[CrossRef]

Yang, M.

Yang, X.

B. Zeng, X. Yang, C. Wang, Q. Feng, and X. Luo, “Super-resolution imaging at different wavelengths by using a one-dimensional metamaterial structure,” J. Opt. 12, 035104 (2010).
[CrossRef]

Zeng, B.

B. Zeng, X. Yang, C. Wang, Q. Feng, and X. Luo, “Super-resolution imaging at different wavelengths by using a one-dimensional metamaterial structure,” J. Opt. 12, 035104 (2010).
[CrossRef]

Zhang, X.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15, 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, 1686 (2007).
[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]

Appl. Phys. Lett.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Experimental verification of full reconstruction of the near-field with a metamaterial lens,” Appl. Phys. Lett. 97, 144102 (2010).
[CrossRef]

Arch. Mikrosk. Anat.

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Figures (11)

Fig. 1
Fig. 1

(color online) (a) The geometry of the planar oblique layered system in the xy plane, the û and directions are two principal axes obtained by rotating an angle θ from the and ŷ directions, where ɛu =ɛx and ɛv =ɛy . (b) Dispersion relation between kx and ky for θ = 45°, ω = ω 0 (solid line) and ω′ = 1.05ω 0 (dashed line). The slightly variation of constant frequency contour between ω and ω′ can determine the direction of the group velocity, which therefore points towards the contour at a higher frequency ω′. The length of arrows is proportional to the magnitude of the group velocity.

Fig. 2
Fig. 2

(a) Dispersion relation with guiding bands. (b) Transmission curves of a lossless anisotropic medium at a given ω = ω 0. The permittivity of the metal is given by (8) with ɛm (∞) = 1.0. The layers are of equal width d 1 = d 2 = λ/40.

Fig. 3
Fig. 3

(color online) The distribution of magnetic energy density (a)–(e) for an effective anisotropic medium, and (f)–(j) for an oblique planar layered system in the xy plane, with θ = 0°, 15°, 30°, 45°, and 60°, respectively. Here, the permittivity of metal ɛm = −3.5 + 0.23i, and the permittivity of dielectric ɛd = 4.3. The yellow solid lines indicate the boundaries of the systems.

Fig. 4
Fig. 4

(color online) Comparison of magnetic energy density of the image plane along the y direction between (a) the effective anisotropic medium and (b) the planar layered systems for different oblique angle.

Fig. 5
Fig. 5

(color online) Transmission curves of a lossy anisotropic medium for different θ (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°.

Fig. 6
Fig. 6

(color online) The distribution of magnetic energy density (a)–(e) for an effective anisotropic medium, and (f)–(j) for an oblique planar layered system in the xy plane, with different permittivity of dielectric ɛd = 3.5, 4.0, 4.3, 4.8, and 6.0, respectively. Here, the permittivity of metal ɛm = −3.5 + 0.23i, and the oblique angle θ = 30°. The yellow solid lines indicate the boundaries of the systems.

Fig. 7
Fig. 7

(color online) Comparison of magnetic energy density of the image plane along the y direction between (a) the effective anisotropic medium and (b) the planar layered systems for different permittivity of dielectric.

Fig. 8
Fig. 8

(color online) Transmission curves of a lossy anisotropic medium for different permittivity of dielectric ɛd (a) 3.5, (b) 4.0, (c) 4.3, (d) 4.8, and (e) 6.0.

Fig. 9
Fig. 9

(color online) The distribution of magnetic energy density for an effective anisotropic medium in the xz plane. (a) θ = 30°, ɛd = 4.3, (b) θ = 30°, ɛd = 4.8, (c) θ = 45°, ɛd = 4.3, (d) θ = 45°, ɛd = 4.8. (e)–(h) the corresponding detailed distribution at the image plane along the z direction. The yellow solid lines indicate the boundaries of the systems.

Fig. 10
Fig. 10

(color online) (a) The geometry of the concentric oblique layered system in the xy plane, the û and directions are two principal axes obtained by rotating an angle θ from the and ϕ ^ directions, where ɛu =ɛx and ɛv =ɛy . (b) Schematic of the image rotator configuration. (c)(d) The distribution of magnetic energy density for an effective anisotropic medium and the concentric layered system, respectively. Here, the permittivity of metal ɛm = −3.5 + 0.23i, the permittivity of dielectric ɛd = 4.0, and the oblique angle θ = 30°. The yellow solid lines outline the interior and exterior boundaries of systems.

Fig. 11
Fig. 11

(color online) Comparison of magnetic energy density of the image plane along the ϕ direction between (a) the effective anisotropic medium and (b) the concentric layered systems for a = 0.1λ, b = 0.6λ, and θ = 30°.

Equations (12)

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ɛ x = ( d 1 + d 2 ) ɛ m ɛ d d 1 ɛ m + d 2 ɛ d , ɛ y = d 1 ɛ m + d 2 ɛ d d 1 + d 2
ɛ ¯ n o r m a l = [ ɛ x 0 0 ɛ y ]
ɛ ¯ o b l i q u e = [ ɛ x x ɛ x y ɛ y x ɛ y y ] = [ cos θ sin θ sin θ cos θ ] [ ɛ x 0 0 ɛ y ] [ cos θ sin θ sin θ cos θ ]
k x 2 ɛ x x + 2 k x k y ɛ x y + k y 2 ɛ y y = ω 2 c 2 ( ɛ x x ɛ y y ɛ x y 2 )
α = θ ± arctan ɛ y ɛ x
k x 2 + k y 2 = ω 2 c 2 ɛ
α ɛ = ± ɛ x x Λ ɛ x x ɛ y y ɛ x y 2 tan ± ( Λ d 2 )
ɛ m ( ω ) = ɛ m ( ) ω p 2 ω 2
T = 2 exp [ i d k y ɛ x y ɛ x x ] 2 cos ( Λ d ) + i sin ( Λ d ) [ ( ɛ x y 2 ɛ x x ɛ y y ) k x ɛ ɛ x x Λ + ɛ ɛ x x Λ ( ɛ x y 2 ɛ x x ɛ y y ) k x ]
ϕ = β cot ( θ ) ln ( a r )
ɛ ¯ r o t a t o r = [ cos θ sin θ sin θ cos θ ] [ cos ϕ sin ϕ sin ϕ cos ϕ ] [ ɛ x 0 0 ɛ y ] × [ cos ϕ sin ϕ sin ϕ cos ϕ ] × [ cos θ sin θ sin θ cos θ ] .
I i I j S i S j = b a ( i , j = 1 , 2 , 3 , i j )

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