Abstract

A circular cylindrical and an oblate cylindrical perfect lens are designed by using coordinate transformation theory. Theoretical analyses are performed to give an insight into the variant angular magnification in the oblate cylindrical perfect lens. We further take advantage of the oblate cylindrical coordinate system to make the object surface flat for future practical imaging and lithography applications. We also for the first time make systematical simulations of various kinds of perfect lens, including numerical confirmation of Mankei Tsang’s statement about the magnification of the planar perfect lens and the imaging and magnifying performance beyond the diffraction limit of our designed perfect lens. All the calculated results agree well with our mathematical derivations, thus verifying the coordinate transformation method in designing perfect lenses.

© 2008 Optical Society of America

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys.-Usp. 10, 509-514 (1968).
    [CrossRef]
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    [CrossRef]
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  4. N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, "Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonancea," Opt. Express 15, 6314-6323 (2007).
    [CrossRef] [PubMed]
  5. J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  6. J. B. Pendry and S. A. Rmakrishna, "Focusing light using negative refraction," J. Phys.:Condens. Matter 15, 6345-6364 (2003).
    [CrossRef]
  7. S. A. Rmakrishna and J. B. Pendry, "Spherical perfect lens: solutions of Maxwell??s equations for spherical geometry," Phys. Rev. B 69, 115115 (2004).
    [CrossRef]
  8. S. Guenneau, A. C. Vutha, and S. A. Ramakrishna, "Negative Refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005).
    [CrossRef]
  9. D. O. S. Melville and R. J. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127-2134 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying Superlens in the Visible Frequency Range," Science 315, 1699-1701 (2007).
    [CrossRef] [PubMed]
  15. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  16. Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99, 113903 (2007).
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  17. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, "Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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2007 (6)

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]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying Superlens in the Visible Frequency Range," Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224 (2007).
[CrossRef]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, "Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).
[CrossRef] [PubMed]

N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, "Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonancea," Opt. Express 15, 6314-6323 (2007).
[CrossRef] [PubMed]

2006 (7)

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New. J. Phys. 8, 247 (2006).
[CrossRef]

A. Salandrino and N. Engheta, "Far-field sub-diffraction optical microscopy using metamaterial crystals: Theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Optical Hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-825 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

G. W. Milton and N. A. Nicorovici "On the cloaking effects associated with anomalous localized resonance," Proc. Roy. Lond. A 462, 3027-3059 (2006).
[CrossRef]

2005 (3)

S. Guenneau, A. C. Vutha, and S. A. Ramakrishna, "Negative Refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005).
[CrossRef]

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

2004 (1)

S. A. Rmakrishna and J. B. Pendry, "Spherical perfect lens: solutions of Maxwell??s equations for spherical geometry," Phys. Rev. B 69, 115115 (2004).
[CrossRef]

2003 (1)

J. B. Pendry and S. A. Rmakrishna, "Focusing light using negative refraction," J. Phys.:Condens. Matter 15, 6345-6364 (2003).
[CrossRef]

2000 (1)

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

1994 (1)

R. C. McPhedran, N. A. Nicorovici, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-38482 (1994).
[CrossRef]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys.-Usp. 10, 509-514 (1968).
[CrossRef]

Alekseyev, L. V.

Blaikie, R. J.

Botten, L. C.

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224 (2007).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224 (2007).
[CrossRef]

Cummer, S. A.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Davis, C. C.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying Superlens in the Visible Frequency Range," Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

Engheta, N.

A. Salandrino and N. Engheta, "Far-field sub-diffraction optical microscopy using metamaterial crystals: Theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

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]

Guenneau, S.

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, "Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).
[CrossRef] [PubMed]

S. Guenneau, A. C. Vutha, and S. A. Ramakrishna, "Negative Refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005).
[CrossRef]

Hung, Y.-J.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying Superlens in the Visible Frequency Range," Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

Jacob, Z.

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224 (2007).
[CrossRef]

Lee, H.

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]

Leonhardt, U.

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New. J. Phys. 8, 247 (2006).
[CrossRef]

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]

McPhedran, R. C.

N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, "Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonancea," Opt. Express 15, 6314-6323 (2007).
[CrossRef] [PubMed]

R. C. McPhedran, N. A. Nicorovici, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-38482 (1994).
[CrossRef]

Melville, D. O. S.

Milton, G. W.

N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, "Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonancea," Opt. Express 15, 6314-6323 (2007).
[CrossRef] [PubMed]

G. W. Milton and N. A. Nicorovici "On the cloaking effects associated with anomalous localized resonance," Proc. Roy. Lond. A 462, 3027-3059 (2006).
[CrossRef]

R. C. McPhedran, N. A. Nicorovici, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-38482 (1994).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Narimanov, E.

Neff, C. W.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Nicolet, A.

Nicorovici, N. A.

N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, "Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonancea," Opt. Express 15, 6314-6323 (2007).
[CrossRef] [PubMed]

G. W. Milton and N. A. Nicorovici "On the cloaking effects associated with anomalous localized resonance," Proc. Roy. Lond. A 462, 3027-3059 (2006).
[CrossRef]

R. C. McPhedran, N. A. Nicorovici, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-38482 (1994).
[CrossRef]

Pendry, J. B.

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, "Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect," Opt. Lett. 32, 1069-1071 (2007).
[CrossRef] [PubMed]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

S. A. Rmakrishna and J. B. Pendry, "Spherical perfect lens: solutions of Maxwell??s equations for spherical geometry," Phys. Rev. B 69, 115115 (2004).
[CrossRef]

J. B. Pendry and S. A. Rmakrishna, "Focusing light using negative refraction," J. Phys.:Condens. Matter 15, 6345-6364 (2003).
[CrossRef]

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

Philbin, T. G.

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New. J. Phys. 8, 247 (2006).
[CrossRef]

Popa, B. I.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Qiu, M.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Ramakrishna, S. A.

S. Guenneau, A. C. Vutha, and S. A. Ramakrishna, "Negative Refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005).
[CrossRef]

Rmakrishna, S. A.

S. A. Rmakrishna and J. B. Pendry, "Spherical perfect lens: solutions of Maxwell??s equations for spherical geometry," Phys. Rev. B 69, 115115 (2004).
[CrossRef]

J. B. Pendry and S. A. Rmakrishna, "Focusing light using negative refraction," J. Phys.:Condens. Matter 15, 6345-6364 (2003).
[CrossRef]

Ruan, Z.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Salandrino, A.

A. Salandrino and N. Engheta, "Far-field sub-diffraction optical microscopy using metamaterial crystals: Theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Schurig, D.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224 (2007).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

Smolyaninov, I. I.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, "Magnifying Superlens in the Visible Frequency Range," Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

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]

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]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys.-Usp. 10, 509-514 (1968).
[CrossRef]

Vutha, A. C.

S. Guenneau, A. C. Vutha, and S. A. Ramakrishna, "Negative Refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005).
[CrossRef]

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]

Yan, M.

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Zhang, X.

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]

Zolla, F.

J. Phys.:Condens. Matter (1)

J. B. Pendry and S. A. Rmakrishna, "Focusing light using negative refraction," J. Phys.:Condens. Matter 15, 6345-6364 (2003).
[CrossRef]

Nat. Photonics (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224 (2007).
[CrossRef]

New J. Phys. (1)

S. Guenneau, A. C. Vutha, and S. A. Ramakrishna, "Negative Refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses," New J. Phys. 7, 164 (2005).
[CrossRef]

New. J. Phys. (1)

U. Leonhardt and T. G. Philbin, "General relativity in electrical engineering," New. J. Phys. 8, 247 (2006).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (3)

A. Salandrino and N. Engheta, "Far-field sub-diffraction optical microscopy using metamaterial crystals: Theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

S. A. Rmakrishna and J. B. Pendry, "Spherical perfect lens: solutions of Maxwell??s equations for spherical geometry," Phys. Rev. B 69, 115115 (2004).
[CrossRef]

R. C. McPhedran, N. A. Nicorovici, and G. W. Milton, "Optical and dielectric properties of partially resonant composites," Phys. Rev. B 49, 8479-38482 (1994).
[CrossRef]

Phys. Rev. E (1)

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

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

Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, "Ideal Cylindrical cloak: perfect but sensitive to tiny perturbations," Phys. Rev. Lett. 99, 113903 (2007).
[CrossRef] [PubMed]

Proc. Roy. Lond. A (1)

G. W. Milton and N. A. Nicorovici "On the cloaking effects associated with anomalous localized resonance," Proc. Roy. Lond. A 462, 3027-3059 (2006).
[CrossRef]

Science (5)

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]

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Figures (9)

Fig. 1.
Fig. 1.

Diagram of the circular cylindrical perfect lens. Only the x and y axis are involved in the 2D case of the cylindrical stucture. With the coordinate transformation, the design can be processed in the following two steps: (1) the gray-colored space 0≤rb in (r, φ, z) system (left) is compressed into the 0≤r′<a region in the transformed space, and (2) the “emptied” ar′<b area is then filled by the single pink-colored constant r=b surface, resulting in the pink region (right) functioning as the desired circular perfect lens, any EM source on the inner circle can be magnified and perfect transmitted to the outer surface, as depicted by the red region in the perfect lens(right)

Fig. 2.
Fig. 2.

The sketch of the oblate cylindrical coordinate system. Three colored curves comprise the new orthogonal coordinate curves in x-y plane: the ellipse represents η curve (dark red), the confocal hyperbola for ξ curve (blue) and z axis for z curve (green) with unit vectors a⃑η , a⃑ξ and a⃑z respectively.

Fig. 3.
Fig. 3.

Diagram of Oblate cylindrical perfect lens. We demonstrate the design in x-y plane for simplicity. First, the general oblate cylindrical perfect lens with b≠0 (top right) is designed by coordinate transformation (top left to top right), and the one with flat object surface is then obtained by making the inner elliptical space degenerate to be a slice (top right to bottom right), corresponding to the limit case of ξ′=b=0. Half of the Oblate cylindrical perfect lens is convenient for practical use (bottom left).

Fig. 4.
Fig. 4.

The 2D (x-y plane) normalized electric field distribution in the planar perfect lens (right) and the normalized electric field distribution on the object and imaging plane. The width of the slab b=4µm. The TE plane wave propagates along x axis from the left side (the object plane) of the slab to the right (the imaging plane) with perfect fidelity.

Figure 5.
Figure 5.

The 2D (x-y plane) normalized electric field distribution in the circular cylindrical perfect lens. The inner circle with the radius of a=1µm represents the object surface and the outer circle with the radius of b=4µm is the imaging surface. The wavelength used here is much larger than the size of the whole structure.

Fig. 6.
Fig. 6.

The 2D (x-y plane) normalized electric field distribution in the general oblate cylindrical perfect lens. The inner ellipse with ξ′=ξ ex is the object surface and the outer ellipse with ξ′=ξ in is the imaging surface (a>b>0). For simplicity, we choose aex =8µm and bex = b ex = 48 μ m for the exterior ellipse, corresponding p=4µm. The inner ellipse has ain =5µm, bin =3µm and the same p. The wavelength of the TE wave is much larger than aex .

Fig. 7.
Fig. 7.

The angular magnification as a function of η′. aex =8µm, bex = b ex = 48 μ m ain =5µm and bin =3µm are used with the same p=4µm for the exterior and interior ellipse respectively.

Fig. 8.
Fig. 8.

The 2D (x-y plane) normalized electric field distribution in the oblate cylindrical perfect lens with flat object plane. The values of aex =8µm, bex = b ex = 48 μ m and p=4µm for the exterior ellipse in previous general case are preserved in this perfect lens structure. Seven pairs of line sources emitting TE plane wave are located on the flat plane with the same interval. The two plane wave sources of each pair are separated by a small distance, which is much smaller than the length of major axis.

Fig. 9.
Fig. 9.

The angular magnification as a function of η′ in the case of aex =8µm, bex = b ex = 48 μ m and bin =0, in which the object surface becomes to be flat.

Equations (16)

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r = { ( b a ) r 0 r < a b a r b , φ = φ , z = z r r > b
ε ̂ = μ ̂ = { [ 1 0 0 0 1 0 0 0 ( b a ) 2 ] 0 r a [ 0 0 0 0 0 0 0 0 ] a < r b
{ x = p cosh ξ cos η y = p sinh ξ sin η , 0 ξ < 0 η 2 π < z < z = z
ξ = { ξ + a 0 ξ < b a b ξ a , η = η , z = z ξ ξ > a
{ Q ξ = Q η = sinh 2 ( ξ + a ) + sin 2 η sinh 2 ξ + sin 2 η Q z = 1 , 0 ξ < b Q ξ = 0 Q η = Q z = 1 b ξ a
ε ̂ = μ ̂ = { [ 1 0 0 0 1 0 0 0 t z ] 0 ξ < b [ 0 0 0 0 0 0 0 0 ] b < ξ a
x = { x + b x < 0 δ x + b 0 x b , y = y , z = z x + δ b x > b
ε x = μ x = 1 δ , ε y = μ y = δ , ε z = μ z = δ
P = a 2 b 2
[ ε xx ε xy ε xz ε yx ε yy ε yz ε zx ε zy ε zz ] = T · ε ̂ · T 1
l ex = ds ex = p cosh 2 ξ ex cos 2 η d ξ
l in = d s in = p cosh 2 ξ in cos 2 η d ξ
M η = l ex l in = cosh 2 ξ ex cos 2 η cosh 2 ξ in cos 2 η = ( a ex p ) 2 cos 2 η ( a in p ) 2 cos 2 η
M η = l ex l in = cosh 2 ξ ex cos 2 η cosh 2 ξ in cos 2 η = ( a ex p ) 2 cos 2 η 1 cos 2 η
M η = [ ( a ex p ) 2 1 ] + ( 1 cos 2 η ) 1 cos 2 η = 1 + ( a ex p ) 2 1 1 cos 2 η
M ( π 2 ) = a ex p

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