Abstract

A universal 2D transformation formula for embedded transformation optics is suggested. Linear and nonlinear transformation results using the suggested formula under different conditions reveal several interesting phenomena and potential applications, and designs for various polarization controllers can be achieved based on this idea. For example, an incident Gaussian beam can be transformed into a typical spherical wave, and a “cloak” based on a polarization splitter is proposed for the first time.

© 2009 OSA

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [CrossRef] [PubMed]
  3. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
    [CrossRef] [PubMed]
  4. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
    [CrossRef] [PubMed]
  5. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
    [CrossRef] [PubMed]
  6. L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
    [CrossRef]
  7. J. Lee, J. Blair, V. Tamma, Q. Wu, S. Rhee, C. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express 17(15), 12922–12928 (2009).
    [CrossRef] [PubMed]
  8. T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” N. J. Phys. 10(11), 115038 (2008).
    [CrossRef]
  9. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
    [CrossRef] [PubMed]
  10. U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
    [CrossRef]
  11. U. Leonhardt and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 70 (2009).
  12. 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(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  13. W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
    [CrossRef]
  14. H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
    [CrossRef]
  15. M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
    [CrossRef]
  16. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
    [CrossRef] [PubMed]
  17. W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92(26), 261903 (2008).
    [CrossRef]
  18. D. Kwon and D. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” N. J. Phys. 10(11), 115023 (2008).
    [CrossRef]
  19. J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B. Wu, and J. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. PIER 81, 437–446 (2008).
    [CrossRef]
  20. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
    [CrossRef] [PubMed]
  21. D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008).
    [CrossRef]

2009 (7)

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

U. Leonhardt and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 70 (2009).

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 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(7), 568–571 (2009).
[CrossRef] [PubMed]

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

J. Lee, J. Blair, V. Tamma, Q. Wu, S. Rhee, C. Summers, and W. Park, “Direct visualization of optical frequency invisibility cloak based on silicon nanorod array,” Opt. Express 17(15), 12922–12928 (2009).
[CrossRef] [PubMed]

2008 (9)

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[CrossRef] [PubMed]

D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008).
[CrossRef]

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” N. J. Phys. 10(11), 115038 (2008).
[CrossRef]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92(26), 261903 (2008).
[CrossRef]

D. Kwon and D. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” N. J. Phys. 10(11), 115023 (2008).
[CrossRef]

J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B. Wu, and J. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. PIER 81, 437–446 (2008).
[CrossRef]

2007 (2)

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

2006 (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Blair, J.

Cai, W.

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

Cardenas, J.

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Chan, C.

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

Chen, H.

J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B. Wu, and J. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. PIER 81, 437–446 (2008).
[CrossRef]

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

Cheng, Q.

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92(26), 261903 (2008).
[CrossRef]

Chettiar, U.

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (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(5912), 366–369 (2009).
[CrossRef] [PubMed]

Cui, T.

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92(26), 261903 (2008).
[CrossRef]

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(5912), 366–369 (2009).
[CrossRef] [PubMed]

Cummer, S.

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Cummer, S. A.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Gabrielli, L.

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

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(5912), 366–369 (2009).
[CrossRef] [PubMed]

Jiang, W.

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92(26), 261903 (2008).
[CrossRef]

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

Kildishev, A.

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

Kong, J.

J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B. Wu, and J. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. PIER 81, 437–446 (2008).
[CrossRef]

Kwon, D.

D. Kwon and D. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” N. J. Phys. 10(11), 115023 (2008).
[CrossRef]

Kwon, D. H.

Lee, J.

Leonhardt, U.

U. Leonhardt and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 70 (2009).

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” N. J. Phys. 10(11), 115038 (2008).
[CrossRef]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 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(7), 568–571 (2009).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

Lipson, M.

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 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(5912), 366–369 (2009).
[CrossRef] [PubMed]

Luo, Y.

J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B. Wu, and J. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. PIER 81, 437–446 (2008).
[CrossRef]

Ma, H.

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92(26), 261903 (2008).
[CrossRef]

Ma, Y. G.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

Milton, G.

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[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(5912), 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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Ong, C. K.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

Park, W.

Pendry, J.

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Pendry, J. B.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(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,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 70 (2009).

Poitras, C.

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Rahm, M.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[CrossRef] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Ran, L.

J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B. Wu, and J. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. PIER 81, 437–446 (2008).
[CrossRef]

Rhee, S.

Roberts, D.

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Roberts, D. A.

Schurig, D.

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(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,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Shalaev, V.

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

Smith, D.

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

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(5912), 366–369 (2009).
[CrossRef] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(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,” Science 314(5801), 977–980 (2006).
[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(5801), 977–980 (2006).
[CrossRef] [PubMed]

Summers, C.

Tamma, V.

Tyc, T.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
[CrossRef] [PubMed]

U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
[CrossRef]

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” N. J. Phys. 10(11), 115038 (2008).
[CrossRef]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Werner, D.

D. Kwon and D. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” N. J. Phys. 10(11), 115023 (2008).
[CrossRef]

Werner, D. H.

Wu, B.

J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B. Wu, and J. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. PIER 81, 437–446 (2008).
[CrossRef]

Wu, Q.

Xi, S.

J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B. Wu, and J. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. PIER 81, 437–446 (2008).
[CrossRef]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B. Wu, and J. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. PIER 81, 437–446 (2008).
[CrossRef]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhou, X.

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92(26), 261903 (2008).
[CrossRef]

Appl. Phys. Lett. (3)

W. Cai, U. Chettiar, A. Kildishev, V. Shalaev, and G. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007).
[CrossRef]

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[CrossRef]

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92(26), 261903 (2008).
[CrossRef]

N. J. Phys. (2)

D. Kwon and D. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” N. J. Phys. 10(11), 115023 (2008).
[CrossRef]

T. Tyc and U. Leonhardt, “Transmutation of singularities in optical instruments,” N. J. Phys. 10(11), 115038 (2008).
[CrossRef]

Nat. Mater. (2)

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009).
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J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Nat. Photonics (1)

L. Gabrielli, J. Cardenas, C. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[CrossRef]

Opt. Express (3)

Photonics Nanostruct. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
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J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
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Prog. Electromagn. Res. (1)

J. Zhang, Y. Luo, S. Xi, H. Chen, L. Ran, B. Wu, and J. Kong, “Directive emission obtained by coordinate transformation,” Prog. Electromagn. Res. PIER 81, 437–446 (2008).
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Prog. Opt. (1)

U. Leonhardt and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 70 (2009).

Science (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(5801), 977–980 (2006).
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U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009).
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R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009).
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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of the embedded coordinate transformation for a polarization controller.

Fig. 2.
Fig. 2.

Field distribution of linear transformation.(a) k1=1.8   ,         k2=1 (b) k1=1.2   ,         k2=1 .

Fig. 3.
Fig. 3.

Energy distribution of linear transformation. (a) k1=1.2   ,         k2=1 . (b) k1=1.2   ,         k2=0.5 .

Fig. 4.
Fig. 4.

Field distribution of nonlinear transformation without cross product term. ( m1 , n = 1)(a) m=2   ,     k1=1.8,     k2=1 .(b) m=5   ,     k1=1.8,     k2=1 . (c) m=2   ,     k1=0.3,     k2=1 . (d) m=2   ,     k1=3,     k2=1 .

Fig. 5.
Fig. 5.

Field distribution without cross product term for various values of n when . k1=0 ..(a) n=2   ,     k1=0,     k2=1 . (b) n=3   ,     k1=0,     k2=1 . (c) n=0.5   ,     k1=0,     k2=1 .

Fig. 6.
Fig. 6.

Nonlinear transformation containing only cross product term. ( s=1,     t=1 ) (a) and (b): k3 = 1. (c) and (d): k3 = 80. (a) and (c): Field distribution. (b) and (d): Energy distribution.

Fig. 7.
Fig. 7.

Nonlinear transformation containing only cross product term. ( s1   ,     t=1 ). (a) and (b): s=2,     t=1,     k3=2 . (c) and (d): s=2,     t=1,     k3=0.3 . (a) and (c): Field distribution. (b) and (d): Energy distribution.

Fig. 8.
Fig. 8.

Field distribution of nonlinear transformation containing only cross product term. ( s=1   ,     t1 ) (a) s = 1, t = 0.2,k3 = 1. (b) s = 1, t = 2, k3 = −2.5. (c) s = 1, t = 2, k3 = −1. (d) s = 1, t = 2, k3 = 1.5.

Fig. 9.
Fig. 9.

Linear polarization beam splitter with adjustable angle and transmission. (a) and (b): Field transformation results for angle controlled linear polarization beam splitter. (a): k1=1 , k1=1.8 , k2=k2=1 . (b): k1=0.5 , k1=1.8 , k2=k2=1 . (c) and (d): Energy transformation results for transmission controlled linear polarization beam splitter. (c): k1=k1=1.8 , k2=1 , k2=0.5 . (d): k1=k1=1.8 , k2=1 , k2=3 .

Fig. 10.
Fig. 10.

Field distribution and energy distribution of mixed linear and nonlinear transformation polarization beam splitters. (a): k1=1.8   ,     k2=1   ,     m=n=1 , k3=0 , k1=5 , k2=1 , m=5 , n=1 , k3=0 . (b): k1=1.8   ,     k2=1   ,     m=n=1 , k3=0 , k1'=k2'=0 , k3'=5 , s'=t'=1 . (c): k1=1.8   ,     k2=1   ,     m=n=1 , k3=0 , k1'=k2'=0 , k3'=0.55 , s'=0.5 , t'=1 .

Fig. 11.
Fig. 11.

Nonlinear transformation polarization beam splitter. (a) and (b) : k1=3,     k2=1,     m=4,     n=1,     k3=0 , k1'=3,     k2'=1,     m'=4,     n'=1,     k3'=0 . (c) and (d) : k1=0 , k2=1 , k3=0 , n=3 , k1'=k2'=0 , k3'=3 , s'=t'=1 . (a) and (c): Field distribution. (b) and (d): Energy distribution.

Fig. 12.
Fig. 12.

A linear and nonlinear mixed transformation TM wave polarizer. (a) and (b): k1=1.8,     k2=1,     k3=0,     m=n=1 , k1'=3,     k2'=1,     k3'=0,     m'=2,     n'=1 . (a) Field distribution. (b): Energy distribution.

Fig. 13.
Fig. 13.

Typical examples of cloak based on polarization splitting. (a) Combination of two linear transformations regions ( d1=d2 ). For the first transformation region k1=k1=1.8 , k2=k2=1 , m=m=1 , n=n=1 , k3=k3=0 . For the second transformation region k1=k1=1.8 , k2=k2=1 , m=m=1 , n=n=1 , k3=k3=0 . (b) Combination of two nonlinear transformation regions ( d1=d2 ). For the first transformation region k1=k1=0.9 , k2=k2=1 , m=m=0.5 , n=n=1 , k3=k3=0 . For the second transformation region k1=k1=1.7 , k2=k2=1 , m=m=0.5 , n=n=1 , k3=k3=0 . (c) Oblique incidence (incident angle is 6°, d1=d2 ). For the first transformation region k1=k1=1.5 , k2=k2=1 , m=m=1 , n=n=1 , k3=k3=0 . For the second transformation region k1=k1=1.5 , k2=k2=1 , m=m=1 , n=n=1 , k3=k3=0 . (d) Combination of two regions with different thickness ( 1.5d1=d2 ). For the first transformation region k1=k1=0.25 , k2=k2=1 , m=m=1 , n=n=1 , k3=k3=0 . For the second transformation region k1=k1=2.5 , k2=k2=1 , m=m=9 , n=n=1 , k3=k3=0 .

Equations (8)

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x=x ,  y=f(x,y) ,  x,yB ,  z=z
Ψ=1a22[1a210a21a212+a2220001]
a21=f(x,y)/x
a22=f(x,y)/y
f(x,y)=k1xm+k2yn+k3xsyt
s = 1, t = 1, i.e.f(x,y)=k3xy
s1 , t = 1, i.e.  f(x,y)=k3xsy .
s=1   ,     t1 , i.e.   f(x,y)=k3xyt .

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