Abstract

The design rules of transformation optics generally lead to spatially inhomogeneous and anisotropic impedance-matched magneto-dielectric material distributions for, e.g., free-space invisibility cloaks. Recently, simplified anisotropic non-magnetic free-space cloaks made of a locally uniaxial dielectric material (calcite) have been realized experimentally. In a two-dimensional setting and for in-plane polarized light propagating in this plane, the cloaking performance can still be perfect for light rays. However, for general views in three dimensions, various imperfections are expected. In this paper, we study two different purely dielectric uniaxial cylindrical free-space cloaks. For one, the optic axis is along the radial direction, for the other one it is along the azimuthal direction. The azimuthal uniaxial cloak has not been suggested previously to the best of our knowledge. We visualize the cloaking performance of both by calculating photorealistic images rendered by ray tracing. Following and complementing our previous ray-tracing work, we use an equation of motion directly derived from Fermat’s principle. The rendered images generally exhibit significant imperfections. This includes the obvious fact that cloaking does not work at all for horizontal or for ordinary linear polarization of light. Moreover, more subtle effects occur such as viewing-angle-dependent aberrations. However, we still find amazingly good cloaking performance for the purely dielectric azimuthal uniaxial cloak.

© 2012 OSA

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  4. C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).
  5. H. Hashemi, B. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-Bandwidth and Delay-Loss Limitations for Cloaking of Large Objects,” Phys. Rev. Lett.104(25), 253903 (2010).
    [CrossRef] [PubMed]
  6. H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep.2, 255 (2012).
    [CrossRef] [PubMed]
  7. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
    [CrossRef] [PubMed]
  8. A. Akbarzadeh and A. J. Danner, “Generalization of ray tracing in a linear inhomogeneous anisotropic medium: a coordinate-free approach,” J. Opt. Soc. Am. A27(12), 2558–2562 (2010).
    [CrossRef] [PubMed]
  9. 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,” Science314(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  10. J. C. Halimeh and M. Wegener, “Time-of-flight imaging of invisibility cloaks,” Opt. Express20(1), 63–74 (2012).
    [CrossRef] [PubMed]
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  12. R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express18(23), 24361–24367 (2010).
    [CrossRef] [PubMed]
  13. J. C. Halimeh, R. Schmied, and M. Wegener, “Newtonian photorealistic ray tracing of grating cloaks and correlation-function-based cloaking-quality assessment,” Opt. Express19(7), 6078–6092 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. A. Weidlich and A. Wilkie, “Realistic rendering of birefringency in uniaxial crystals,” ACM Trans. Graph.27(10), 1–12 (2008).
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    [CrossRef]
  19. T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
    [CrossRef] [PubMed]
  20. S. Hrabar, I. Krois, and A. Kiricenko, “Towards active dispersionless ENZ metamaterial for cloaking applications,” Metamaterials (Amst.)4(2-3), 89–97 (2010).
    [CrossRef]
  21. S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett.99(25), 254103 (2011).
    [CrossRef]

2012

H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep.2, 255 (2012).
[CrossRef] [PubMed]

J. C. Halimeh and M. Wegener, “Time-of-flight imaging of invisibility cloaks,” Opt. Express20(1), 63–74 (2012).
[CrossRef] [PubMed]

2011

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
[CrossRef] [PubMed]

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett.99(25), 254103 (2011).
[CrossRef]

J. C. Halimeh, R. Schmied, and M. Wegener, “Newtonian photorealistic ray tracing of grating cloaks and correlation-function-based cloaking-quality assessment,” Opt. Express19(7), 6078–6092 (2011).
[CrossRef] [PubMed]

2010

A. Akbarzadeh and A. J. Danner, “Generalization of ray tracing in a linear inhomogeneous anisotropic medium: a coordinate-free approach,” J. Opt. Soc. Am. A27(12), 2558–2562 (2010).
[CrossRef] [PubMed]

R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express18(23), 24361–24367 (2010).
[CrossRef] [PubMed]

S. Hrabar, I. Krois, and A. Kiricenko, “Towards active dispersionless ENZ metamaterial for cloaking applications,” Metamaterials (Amst.)4(2-3), 89–97 (2010).
[CrossRef]

H. Hashemi, B. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-Bandwidth and Delay-Loss Limitations for Cloaking of Large Objects,” Phys. Rev. Lett.104(25), 253903 (2010).
[CrossRef] [PubMed]

2008

2007

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

2006

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

Akbarzadeh, A.

Bonic, I.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett.99(25), 254103 (2011).
[CrossRef]

Braat, J. J. M.

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

Chen, H.

H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep.2, 255 (2012).
[CrossRef] [PubMed]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

Cummer, S. A.

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Danner, A. J.

de Boer, D. K. G.

Ergin, T.

T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
[CrossRef] [PubMed]

Fischer, J.

T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
[CrossRef] [PubMed]

Halimeh, J. C.

Hashemi, H.

H. Hashemi, B. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-Bandwidth and Delay-Loss Limitations for Cloaking of Large Objects,” Phys. Rev. Lett.104(25), 253903 (2010).
[CrossRef] [PubMed]

Hrabar, S.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett.99(25), 254103 (2011).
[CrossRef]

S. Hrabar, I. Krois, and A. Kiricenko, “Towards active dispersionless ENZ metamaterial for cloaking applications,” Metamaterials (Amst.)4(2-3), 89–97 (2010).
[CrossRef]

Joannopoulos, J. D.

H. Hashemi, B. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-Bandwidth and Delay-Loss Limitations for Cloaking of Large Objects,” Phys. Rev. Lett.104(25), 253903 (2010).
[CrossRef] [PubMed]

Johnson, S. G.

H. Hashemi, B. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-Bandwidth and Delay-Loss Limitations for Cloaking of Large Objects,” Phys. Rev. Lett.104(25), 253903 (2010).
[CrossRef] [PubMed]

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,” Science314(5801), 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. Photonics1(4), 224–227 (2007).
[CrossRef]

Kiricenko, A.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett.99(25), 254103 (2011).
[CrossRef]

S. Hrabar, I. Krois, and A. Kiricenko, “Towards active dispersionless ENZ metamaterial for cloaking applications,” Metamaterials (Amst.)4(2-3), 89–97 (2010).
[CrossRef]

Krois, I.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett.99(25), 254103 (2011).
[CrossRef]

S. Hrabar, I. Krois, and A. Kiricenko, “Towards active dispersionless ENZ metamaterial for cloaking applications,” Metamaterials (Amst.)4(2-3), 89–97 (2010).
[CrossRef]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Pendry, J. B.

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

Schmied, R.

Schurig, D.

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

Sluijter, M.

Smith, D. R.

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Wegener, M.

J. C. Halimeh and M. Wegener, “Time-of-flight imaging of invisibility cloaks,” Opt. Express20(1), 63–74 (2012).
[CrossRef] [PubMed]

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
[CrossRef] [PubMed]

J. C. Halimeh, R. Schmied, and M. Wegener, “Newtonian photorealistic ray tracing of grating cloaks and correlation-function-based cloaking-quality assessment,” Opt. Express19(7), 6078–6092 (2011).
[CrossRef] [PubMed]

R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express18(23), 24361–24367 (2010).
[CrossRef] [PubMed]

Weidlich, A.

A. Weidlich and A. Wilkie, “Realistic rendering of birefringency in uniaxial crystals,” ACM Trans. Graph.27(10), 1–12 (2008).

Wilkie, A.

A. Weidlich and A. Wilkie, “Realistic rendering of birefringency in uniaxial crystals,” ACM Trans. Graph.27(10), 1–12 (2008).

Zhang, B.

H. Hashemi, B. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-Bandwidth and Delay-Loss Limitations for Cloaking of Large Objects,” Phys. Rev. Lett.104(25), 253903 (2010).
[CrossRef] [PubMed]

Zheng, B.

H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep.2, 255 (2012).
[CrossRef] [PubMed]

ACM Trans. Graph.

A. Weidlich and A. Wilkie, “Realistic rendering of birefringency in uniaxial crystals,” ACM Trans. Graph.27(10), 1–12 (2008).

Appl. Phys. Lett.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Negative capacitor paves the way to ultra-broadband metamaterials,” Appl. Phys. Lett.99(25), 254103 (2011).
[CrossRef]

J. Opt. Soc. Am. A

Metamaterials (Amst.)

S. Hrabar, I. Krois, and A. Kiricenko, “Towards active dispersionless ENZ metamaterial for cloaking applications,” Metamaterials (Amst.)4(2-3), 89–97 (2010).
[CrossRef]

Nat. Photonics

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1(4), 224–227 (2007).
[CrossRef]

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

Opt. Express

Phys. Rev. Lett.

H. Hashemi, B. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-Bandwidth and Delay-Loss Limitations for Cloaking of Large Objects,” Phys. Rev. Lett.104(25), 253903 (2010).
[CrossRef] [PubMed]

T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
[CrossRef] [PubMed]

Sci. Rep.

H. Chen and B. Zheng, “Broadband polygonal invisibility cloak for visible light,” Sci. Rep.2, 255 (2012).
[CrossRef] [PubMed]

Science

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Other

U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover, Mineola, 2010).

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, Vol. 8 (Butterworth-Heinemann, Oxford, 1984).

M. Born and E. Wolf, Principles of Optics, 7. Ed. (University Press, Cambridge, 1999).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., 1999).

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