Abstract

Currently, the most popular method for technically obtaining the geometric and electromagnetic parameters of invisibility cloaks is mainly based upon transformation optics. In this paper, by introducing transfer functions to elucidate the roles of the invisibility cloaks played on angular spectrum of the objects, we present an optical imaging theory to unify both Pendry cloaks and complementary media-based invisibility cloaks. The theory can not only give an analytical insight into the physical mechanism behind the invisibility cloaks and perfect lenses in hiding objects, creating illusions, and performing perfect imaging, but also provide a way for getting the electromagnetic parameters of the systems. The results are strictly of consistence with that obtained from transformation optics, confirming the validity of our Fourier optics theory.

© 2011 Optical Society of America

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  1. A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
    [CrossRef]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef] [PubMed]
  3. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
  4. A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901(2008).
    [CrossRef] [PubMed]
  5. Z. Jacob, L. A. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
    [CrossRef] [PubMed]
  6. 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]
  7. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227(2007).
    [CrossRef]
  8. 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]
  9. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
    [CrossRef] [PubMed]
  10. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369(2009).
    [CrossRef] [PubMed]
  11. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
    [CrossRef] [PubMed]
  12. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
    [CrossRef]
  13. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
    [CrossRef] [PubMed]
  14. J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57, 37–43 (2004).
    [CrossRef]
  15. A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  16. Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
    [CrossRef] [PubMed]
  17. Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
    [CrossRef] [PubMed]
  18. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  19. Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
    [CrossRef]
  20. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three dimensional optical metamaterial exhibiting negative refractive index,” Nature 455, 376–379 (2008).
    [CrossRef] [PubMed]
  21. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79(2001).
    [CrossRef] [PubMed]
  22. B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104, 233903 (2010).
    [CrossRef] [PubMed]
  23. H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
    [CrossRef] [PubMed]
  24. A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10, 115022(2008).
    [CrossRef]
  25. K. Wu and G. P. Wang, “General insight into the complementary medium-based camouflage devices from Fourier optics,” Opt. Lett. 35, 2242–2244 (2010).
    [CrossRef] [PubMed]
  26. K. Wu and G. P. Wang, “Hiding objects and creating illusions above a carpet filter using a Fourier optics approach,” Opt. Express 18, 19894–19901 (2010).
    [CrossRef] [PubMed]
  27. J. Zhang, Y. Luo, H. Chen, J. Huangfu, B.-I. Wu, L. Ran, and J. A. Kong, “Guiding waves through an invisible tunnel,” Opt. Express 17, 6203–6208 (2009).
    [CrossRef] [PubMed]
  28. Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).
    [CrossRef]
  29. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).
  30. M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).
  31. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 2004).
  32. J. B. Pendry, “Taking the wraps off cloaking,” Physics 2, 95–100 (2009).
    [CrossRef]
  33. Y. Luo, J.-J. Zhang, H.-S. Chen, B.-I. Wu, and L.-X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178(2009).
    [CrossRef]
  34. 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, 253903 (2010).
    [CrossRef] [PubMed]
  35. 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]

2010 (5)

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef] [PubMed]

B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104, 233903 (2010).
[CrossRef] [PubMed]

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, 253903 (2010).
[CrossRef] [PubMed]

K. Wu and G. P. Wang, “General insight into the complementary medium-based camouflage devices from Fourier optics,” Opt. Lett. 35, 2242–2244 (2010).
[CrossRef] [PubMed]

K. Wu and G. P. Wang, “Hiding objects and creating illusions above a carpet filter using a Fourier optics approach,” Opt. Express 18, 19894–19901 (2010).
[CrossRef] [PubMed]

2009 (9)

J. Zhang, Y. Luo, H. Chen, J. Huangfu, B.-I. Wu, L. Ran, and J. A. Kong, “Guiding waves through an invisible tunnel,” Opt. Express 17, 6203–6208 (2009).
[CrossRef] [PubMed]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).
[CrossRef]

J. B. Pendry, “Taking the wraps off cloaking,” Physics 2, 95–100 (2009).
[CrossRef]

Y. Luo, J.-J. Zhang, H.-S. Chen, B.-I. Wu, and L.-X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178(2009).
[CrossRef]

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369(2009).
[CrossRef] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[CrossRef]

2008 (5)

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef] [PubMed]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three dimensional optical metamaterial exhibiting negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef] [PubMed]

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10, 115022(2008).
[CrossRef]

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901(2008).
[CrossRef] [PubMed]

2007 (3)

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (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,” Nature Photon. 1, 224–227(2007).
[CrossRef]

2006 (5)

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]

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]

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

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

2005 (1)

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

2004 (1)

J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57, 37–43 (2004).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79(2001).
[CrossRef] [PubMed]

2000 (1)

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

1996 (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[CrossRef]

Alekseyev, L. A.

Alu, A.

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901(2008).
[CrossRef] [PubMed]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three dimensional optical metamaterial exhibiting negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef] [PubMed]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227(2007).
[CrossRef]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[CrossRef]

Chan, C. T.

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Chan, T.

B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104, 233903 (2010).
[CrossRef] [PubMed]

Chen, H.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).
[CrossRef]

J. Zhang, Y. Luo, H. Chen, J. Huangfu, B.-I. Wu, L. Ran, and J. A. Kong, “Guiding waves through an invisible tunnel,” Opt. Express 17, 6203–6208 (2009).
[CrossRef] [PubMed]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[CrossRef]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Chen, H. Y.

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Chen, H.-S.

Y. Luo, J.-J. Zhang, H.-S. Chen, B.-I. Wu, and L.-X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178(2009).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227(2007).
[CrossRef]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369(2009).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369(2009).
[CrossRef] [PubMed]

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,” Science 314, 977–980 (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]

Engheta, N.

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901(2008).
[CrossRef] [PubMed]

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Ergin, T.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef] [PubMed]

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[CrossRef]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three dimensional optical metamaterial exhibiting negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).

Han, D. Z.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

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, 253903 (2010).
[CrossRef] [PubMed]

Huangfu, J.

J. Zhang, Y. Luo, H. Chen, J. Huangfu, B.-I. Wu, L. Ran, and J. A. Kong, “Guiding waves through an invisible tunnel,” Opt. Express 17, 6203–6208 (2009).
[CrossRef] [PubMed]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 2004).

Jacob, Z.

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369(2009).
[CrossRef] [PubMed]

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, 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, 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,” 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,” Nature Photon. 1, 224–227(2007).
[CrossRef]

Kong, J. A.

J. Zhang, Y. Luo, H. Chen, J. Huangfu, B.-I. Wu, L. Ran, and J. A. Kong, “Guiding waves through an invisible tunnel,” Opt. Express 17, 6203–6208 (2009).
[CrossRef] [PubMed]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[CrossRef]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Lai, Y.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef] [PubMed]

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[CrossRef]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369(2009).
[CrossRef] [PubMed]

Luo, Y.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).
[CrossRef]

J. Zhang, Y. Luo, H. Chen, J. Huangfu, B.-I. Wu, L. Ran, and J. A. Kong, “Guiding waves through an invisible tunnel,” Opt. Express 17, 6203–6208 (2009).
[CrossRef] [PubMed]

Y. Luo, J.-J. Zhang, H.-S. Chen, B.-I. Wu, and L.-X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178(2009).
[CrossRef]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Maci, S.

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10, 115022(2008).
[CrossRef]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369(2009).
[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,” 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]

Ng, J.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Pendry, J. B.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef] [PubMed]

J. B. Pendry, “Taking the wraps off cloaking,” Physics 2, 95–100 (2009).
[CrossRef]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[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,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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]

J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57, 37–43 (2004).
[CrossRef]

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

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[CrossRef]

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[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]

Ran, L.

J. Zhang, Y. Luo, H. Chen, J. Huangfu, B.-I. Wu, L. Ran, and J. A. Kong, “Guiding waves through an invisible tunnel,” Opt. Express 17, 6203–6208 (2009).
[CrossRef] [PubMed]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).
[CrossRef]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Ran, L.-X.

Y. Luo, J.-J. Zhang, H.-S. Chen, B.-I. Wu, and L.-X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178(2009).
[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]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79(2001).
[CrossRef] [PubMed]

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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 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,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227(2007).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79(2001).
[CrossRef] [PubMed]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369(2009).
[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,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (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]

J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57, 37–43 (2004).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79(2001).
[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]

Stenger, N.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef] [PubMed]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three dimensional optical metamaterial exhibiting negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef] [PubMed]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three dimensional optical metamaterial exhibiting negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef] [PubMed]

Wang, G. P.

Ward, A. J.

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[CrossRef]

Wegener, M.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).

Wu, B.-I.

B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104, 233903 (2010).
[CrossRef] [PubMed]

J. Zhang, Y. Luo, H. Chen, J. Huangfu, B.-I. Wu, L. Ran, and J. A. Kong, “Guiding waves through an invisible tunnel,” Opt. Express 17, 6203–6208 (2009).
[CrossRef] [PubMed]

Y. Luo, J.-J. Zhang, H.-S. Chen, B.-I. Wu, and L.-X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178(2009).
[CrossRef]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Wu, K.

Xiao, J. J.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Yaghjian, A. D.

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10, 115022(2008).
[CrossRef]

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]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three dimensional optical metamaterial exhibiting negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef] [PubMed]

Zhang, B.

B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104, 233903 (2010).
[CrossRef] [PubMed]

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, 253903 (2010).
[CrossRef] [PubMed]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang, Y. Luo, H. Chen, J. Huangfu, B.-I. Wu, L. Ran, and J. A. Kong, “Guiding waves through an invisible tunnel,” Opt. Express 17, 6203–6208 (2009).
[CrossRef] [PubMed]

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).
[CrossRef]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Zhang, J.-J.

Y. Luo, J.-J. Zhang, H.-S. Chen, B.-I. Wu, and L.-X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178(2009).
[CrossRef]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three dimensional optical metamaterial exhibiting negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three dimensional optical metamaterial exhibiting negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef] [PubMed]

Zhang, Z.-Q.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).
[CrossRef]

J. Mod. Opt. (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[CrossRef]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

Nat. Photon. (1)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photon. 3, 461–463 (2009).
[CrossRef]

Nature (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three dimensional optical metamaterial exhibiting negative refractive index,” Nature 455, 376–379 (2008).
[CrossRef] [PubMed]

Nature Photon. (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nature Photon. 1, 224–227(2007).
[CrossRef]

New J. Phys. (1)

A. D. Yaghjian and S. Maci, “Alternative derivation of electromagnetic cloaks and concentrators,” New J. Phys. 10, 115022(2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Phys. Rev. E (2)

A. Alu and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[CrossRef]

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. (9)

Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 093901 (2009).
[CrossRef] [PubMed]

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[CrossRef] [PubMed]

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

A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. 100, 113901(2008).
[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]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
[CrossRef] [PubMed]

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, 253903 (2010).
[CrossRef] [PubMed]

B. Zhang, T. Chan, and B.-I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104, 233903 (2010).
[CrossRef] [PubMed]

H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Phys. Today (1)

J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today 57, 37–43 (2004).
[CrossRef]

Physics (1)

J. B. Pendry, “Taking the wraps off cloaking,” Physics 2, 95–100 (2009).
[CrossRef]

Prog. Electromagn. Res. (1)

Y. Luo, J.-J. Zhang, H.-S. Chen, B.-I. Wu, and L.-X. Ran, “Wave and ray analysis of a type of cloak exhibiting magnified and shifted scattering effect,” Prog. Electromagn. Res. 95, 167–178(2009).
[CrossRef]

Science (6)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79(2001).
[CrossRef] [PubMed]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328, 337–339 (2010).
[CrossRef] [PubMed]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369(2009).
[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,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

Other (3)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 2004).

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Figures (4)

Fig. 1
Fig. 1

Schematics of the 3D (2D) complementary media-based cloak. Red, yellow, and blue regions are the impedance matching layer, the complementary media layer, and the air layer, respectively. a, b, and c are the radii of the interfaces of these three regions.

Fig. 2
Fig. 2

Schematics of the Pendry invisibility cloaks. Orange and green regions are the expanded space for placing objects to be hidden and the cloak, respectively. a and b are the inner and outer radii of the cloaks.

Fig. 3
Fig. 3

Calculated field distributions as a TE-polarized plane light passes through a 2D (a) lossy and (b) gain media-assisted complementary media-based cloak, respectively.

Fig. 4
Fig. 4

Calculated field distributions as a TE-polarized plane light passes through a 2D (a) lossy and (b) gain media-assisted Pendry invisibility cloak, respectively.

Equations (40)

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

A ( 0 , f θ , f φ ) = 0 π 0 2 π U ( 0 , θ , φ ) exp [ j 2 π ( f θ θ + f φ φ ) ] r 2 sin φ d θ d φ ,
A ( r , f θ , f φ ) = A ( 0 , f θ , f φ ) H ( r , f θ , f φ ) ,
H ( r , f θ , f φ ) = exp { j ( 2 π / λ ) n r r [ 1 ( λ f θ n θ r ) 2 ( λ f φ n φ r sin φ ) 2 ] 1 / 2 } ,
H c ( b a ) = exp { j ( 2 π / λ ) a b [ 1 ( λ f θ r n c θ ) 2 ( λ f φ r sin φ n c φ ) 2 ] 1 / 2 n c r d r } ,
H air ( c b ) = exp { j ( 2 π / λ ) b c [ 1 ( λ f θ R ) 2 ( λ f φ R sin φ ) 2 ] 1 / 2 n air d R } .
n c r = c b a b n c θ = R r n c φ = R r ,
ε c r = μ c r = R 2 r 2 a b c b ε c θ = μ c θ = c b a b ε c φ = μ c φ = c b a b .
A ( c ) = A ( a ) = A ( 0 ) H p ( a 0 ) ,
H p ( a 0 ) = exp { j ( 2 π / λ ) 0 a [ 1 ( λ f θ r n p θ ) 2 ( λ f φ r sin φ n p φ ) 2 ] 1 / 2 n p r d r }
A ( c ) = A ( 0 ) H air ( c 0 ) ,
H air ( c 0 ) = exp { j ( 2 π / λ ) 0 c [ 1 ( λ f θ R ) 2 ( λ f φ R sin φ ) 2 ] 1 / 2 n air d R } ,
n p r = c a , n p θ = c a , n p φ = c a ,
ε p r = μ p r = c a , ε p θ = μ p θ = c a , ε p φ = μ p φ = c a ,
n c ρ = c b a b , n c θ = R r , n c z = 1 ,
n p ρ = c a , n p θ = c a , n p z = 1 ,
ε c ρ = μ c ρ = R r a b c b , ε c θ = μ c θ = r R c b a b , ε c z = μ c z = R r c b a b ,
ε p ρ = μ p ρ = 1 , ε p θ = μ p θ = 1 , ε p z = μ p z = c 2 a 2 ,
A ( c ) = A ( 0 ) H p ( a 0 ) H c ( b a ) H air ( c b ) .
A ( c ) = A ( 0 ) H air ( c b ) H c ( b a ) H p ( a 0 ) ,
A ( b ) = A ( a ) H c ( b a ) ,
H c ( b a ) = exp { j ( 2 π / λ ) a b [ 1 ( λ f θ R n θ ) 2 ( λ f φ R sin φ n φ ) 2 ] 1 / 2 n r d R }
A ( b ) = A ( 0 ) H air ( b ) ,
H air ( b ) = exp { j ( 2 π / λ ) 0 b [ 1 ( λ f θ r ) 2 ( λ f φ r sin φ ) 2 ] 1 / 2 n air d r }
a b [ 1 ( λ f θ r n θ ) 2 ( λ f φ r sin φ n φ ) 2 ] 1 / 2 n r d r = 0 b [ 1 ( λ f θ R ) 2 ( λ f φ R sin φ ) 2 ] 1 / 2 n air d R .
n r = b b a , n θ = R r = b ( r a ) ( b a ) r , n φ = R r = b ( r a ) ( b a ) r .
ε r = μ r = b b a ( r a r ) 2 , ε θ = μ θ = b b a , ε φ = μ φ = b b a ,
A ( b ) = A ( 0 ) exp { j ( 2 π / λ ) a b [ 1 ( λ f θ ) 2 / ( r n θ ) 2 ( λ f z / n z ) 2 ] 1 / 2 n ρ d r } ,
A ( b ) = A ( 0 ) exp { j ( 2 π / λ ) 0 b [ 1 ( λ f θ / R ) 2 ( λ f z ) 2 ] 1 / 2 n air d R } .
n ρ = b b a , n θ = R r = b ( r a ) ( b a ) r , n z = 1 .
ε ρ = μ ρ = r a r , ε θ = μ θ = r r a , ε z = μ z = b 2 ( b a ) 2 r a r ,
A ( l + d ) = l l + d A ( d ) exp { j ( 2 π / λ ) [ 1 ( λ f x ) 2 ( λ f y ) 2 ] 1 / 2 n z d z } = l l + d A ( 0 ) exp { j ( 2 π / λ ) [ 1 ( λ f x ) 2 ( λ f y ) 2 ] 1 / 2 n z d z } .
A ( l + d ) = 0 l + d A ( 0 ) exp { j ( 2 π / λ ) [ 1 ( λ f x ) 2 ( λ f y ) 2 ] 1 / 2 n air d z } .
n z = ( l + d ) / d .
H c ( b a ) = exp { j ( 2 π / λ ) a b [ 1 ( λ f θ r n c θ ) 2 ( λ f z n c z ) 2 ] 1 / 2 n c ρ d ρ } ,
H c ( b a ) = H c ( b a ) exp { ( 2 π / λ ) a b [ 1 ( λ f θ r n c θ ) 2 ( λ f z n c z ) 2 ] 1 / 2 ( n c ρ δ ) d ρ } ,
H gain ( c b ) = exp { j ( 2 π / λ ) b c [ 1 ( λ f θ R ) 2 ( λ f z ) 2 ] 1 / 2 ( 1 δ j ) d ρ } = H air ( c b ) exp { ( 2 π / λ ) b c [ 1 ( λ f θ R ) 2 ( λ f z ) 2 ] 1 / 2 δ d ρ } .
ε gain ρ = μ gain ρ = 1 / ( 1 δ j ) , ε gain θ = μ gain θ = ( 1 δ j ) , ε gain z = μ gain z = ( 1 δ j ) .
H c ( b a ) = H c ( b a ) exp { ( 2 π / λ ) a b [ 1 ( λ f θ r n θ ) 2 ( λ f z n z ) 2 ] 1 / 2 ( n ρ δ ) d ρ } ,
H gain ( 2 b b ) = exp { j ( 2 π / λ ) b 2 b [ 1 ( λ f θ R ) 2 ( λ f z ) 2 ] 1 / 2 ( 1 δ j ) d ρ } = H air ( 2 b b ) exp { ( 2 π / λ ) b 2 b [ 1 ( λ f θ R ) 2 ( λ f z ) 2 ] 1 / 2 δ d ρ } .
ε gain ρ = μ gain ρ = 1 / ( 1 δ j ) , ε gain θ = μ gain θ = ( 1 δ j ) , ε gain z = μ gain z = ( 1 δ j ) .

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