Abstract

Two-dimensional far-zone focusing lenses are designed using the coordinate transformation approach that feature minimized reflections from the lens boundaries. A flat lens of trapezoidal cross section completely converts incident waves with cylindrical wavefronts into transmitted waves with planar wavefronts. A rectangular lens with reduced non-magnetic material parameters that incorporates a nonlinear coordinate transformation features a significantly reduced amount of reflections compared with the non-magnetic lens based on a linear transformation. The improved reflection performance of each new lens design is verified using a full-wave finite-element analysis and compared with previously reported transformation optical lenses.

© 2009 Optical Society of America

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  1. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  3. 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]
  4. G.W. Milton, M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys. 8, 248 (2006).
    [CrossRef]
  5. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photon. 1, 224-227 (2007).
    [CrossRef]
  6. 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]
  7. 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]
  8. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
    [CrossRef]
  9. D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
    [CrossRef]
  10. D.-H. Kwon and D. H. Werner, "Restoration of antenna parameters in scattering environments using electromagnetic cloaking," Appl. Phys. Lett. 92, 113507 (2008).
    [CrossRef]
  11. D.-H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502 (2008).
    [CrossRef]
  12. 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, 063903 (2008).
    [CrossRef] [PubMed]
  13. J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Prog. Electromagn. Res. 81, 437-446 (2008).
    [CrossRef]
  14. W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded coordinate transformation," Appl. Phys. Lett. 92, 261903 (2008).
    [CrossRef]
  15. D.-H. Kwon and D. H. Werner, "Transformation optical designs for wave collimators, flat lenses, and right-angle bends," New J. Phys. 10, 115012 (2008).
    [CrossRef]
  16. 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, 11555-11567 (2008).
    [CrossRef] [PubMed]
  17. D.-H. Kwon and D. H. Werner, "Polarization splitter and polarization rotator designs based on transformation optics," Opt. Express 16, 18731-18738 (2008).
    [CrossRef]
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    [CrossRef]
  19. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Designs for optical cloaking with high-order transformations," Opt. Express 16, 5444-5452 (2008).
    [CrossRef] [PubMed]

2008 (11)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Restoration of antenna parameters in scattering environments using electromagnetic cloaking," Appl. Phys. Lett. 92, 113507 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502 (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, 063903 (2008).
[CrossRef] [PubMed]

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Prog. Electromagn. Res. 81, 437-446 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded coordinate transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Transformation optical designs for wave collimators, flat lenses, and right-angle bends," New J. Phys. 10, 115012 (2008).
[CrossRef]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Designs for optical cloaking with high-order transformations," Opt. Express 16, 5444-5452 (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, 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, 18731-18738 (2008).
[CrossRef]

2007 (4)

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

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, V. M. Shalaev, and G. W. Milton, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett. 91, 111105 (2007).
[CrossRef]

2006 (4)

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]

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]

G.W. Milton, M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys. 8, 248 (2006).
[CrossRef]

Briane, M.

G.W. Milton, M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys. 8, 248 (2006).
[CrossRef]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Designs for optical cloaking with high-order transformations," Opt. Express 16, 5444-5452 (2008).
[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]

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

Chen, H.

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. S.

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Prog. Electromagn. Res. 81, 437-446 (2008).
[CrossRef]

Cheng, Q.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded coordinate transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Designs for optical cloaking with high-order transformations," Opt. Express 16, 5444-5452 (2008).
[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]

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

Cui, T. J.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded coordinate transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 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, 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, 977-980 (2006).
[CrossRef] [PubMed]

Jiang, W. X.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded coordinate transformation," Appl. Phys. Lett. 92, 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, 977-980 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Designs for optical cloaking with high-order transformations," Opt. Express 16, 5444-5452 (2008).
[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]

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

Kong, J. A.

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Prog. Electromagn. Res. 81, 437-446 (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]

Kwon, D.-H.

D.-H. Kwon and D. H. Werner, "Restoration of antenna parameters in scattering environments using electromagnetic cloaking," Appl. Phys. Lett. 92, 113507 (2008).
[CrossRef]

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

D.-H. Kwon and D. H. Werner, "Transformation optical designs for wave collimators, flat lenses, and right-angle bends," New J. Phys. 10, 115012 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502 (2008).
[CrossRef]

Leonhardt, U.

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).
[CrossRef] [PubMed]

Luo, Y.

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Prog. Electromagn. Res. 81, 437-446 (2008).
[CrossRef]

Ma, H. F.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded coordinate transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

Milton, G. W.

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

Milton, G.W.

G.W. Milton, M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys. 8, 248 (2006).
[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]

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]

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, 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

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, 11555-11567 (2008).
[CrossRef] [PubMed]

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]

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]

Rahm, M.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 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, 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, 11555-11567 (2008).
[CrossRef] [PubMed]

Ran, L. X.

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Prog. Electromagn. Res. 81, 437-446 (2008).
[CrossRef]

Roberts, D. A.

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, 11555-11567 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[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]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 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, 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, 977-980 (2006).
[CrossRef] [PubMed]

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

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Designs for optical cloaking with high-order transformations," Opt. Express 16, 5444-5452 (2008).
[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]

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

Smith, D. R.

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, 063903 (2008).
[CrossRef] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

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, 11555-11567 (2008).
[CrossRef] [PubMed]

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]

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]

Werner, D. H.

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

D.-H. Kwon and D. H. Werner, "Restoration of antenna parameters in scattering environments using electromagnetic cloaking," Appl. Phys. Lett. 92, 113507 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Transformation optical designs for wave collimators, flat lenses, and right-angle bends," New J. Phys. 10, 115012 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

Willis, J. R.

G.W. Milton, M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys. 8, 248 (2006).
[CrossRef]

Wu, B.-I.

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Prog. Electromagn. Res. 81, 437-446 (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]

Xi, S.

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Prog. Electromagn. Res. 81, 437-446 (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]

Zhang, B.

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.

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Prog. Electromagn. Res. 81, 437-446 (2008).
[CrossRef]

Zhou, X. Y.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded coordinate transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

Appl. Phys. Lett. (5)

D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Restoration of antenna parameters in scattering environments using electromagnetic cloaking," Appl. Phys. Lett. 92, 113507 (2008).
[CrossRef]

D.-H. Kwon and D. H. Werner, "Two-dimensional electromagnetic cloak having a uniform thickness for elliptic cylindrical regions," Appl. Phys. Lett. 92, 113502 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded coordinate transformation," Appl. Phys. Lett. 92, 261903 (2008).
[CrossRef]

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

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. (2)

D.-H. Kwon and D. H. Werner, "Transformation optical designs for wave collimators, flat lenses, and right-angle bends," New J. Phys. 10, 115012 (2008).
[CrossRef]

G.W. Milton, M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys. 8, 248 (2006).
[CrossRef]

Opt. Express (3)

Photon. Nanostruct.: Fundam. Applic. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations," Photon. Nanostruct.: Fundam. Applic. 6, 87-95 (2008).
[CrossRef]

Phys. Rev. Lett. (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).
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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]

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, 063903 (2008).
[CrossRef] [PubMed]

Prog. Electromagn. Res. (1)

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Prog. Electromagn. Res. 81, 437-446 (2008).
[CrossRef]

Science (3)

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]

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]

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Figures (9)

Fig. 1.
Fig. 1.

(Color online) Simulation setup and incident field generation: (a) A COMSOL simulation model setup, (b) The angle-limited cylindrical wave generated by the electric surface current Js.

Fig. 2.
Fig. 2.

(Color online) The coordinate systems associated with the lens design: (a) The original system in free space, (b) The intermediate system obtained by stretching and compressing space only in the ±ŷ directions, and (c) The final transformed system.

Fig. 3.
Fig. 3.

(Color online) The material parameters of the trapezoidal lens design: (a) μxx , (b) μxy , (c) μyy , and (d) ϵzz . The geometry of the lens design is given by g = 0.4 m, w = 0.6 m, and l = 0.1 m.

Fig. 4.
Fig. 4.

(Color online) Comparison of the rectangular lens of [15] and the new trapezoidal lens: (a) A snapshot and (b) the magnitude distribution of the total electric field for the rectangular lens due to the cylindrical wave illumination from a line source at the coordinate origin. (c) A snapshot and (d) the magnitude of the electric field for the rectangular lens under an angle-limited Gaussian beam illumination. (e) A snapshot and (f) the magnitude distribution of the electric field for the trapezoidal lens under an angle-limited Gaussian beam illumination. The boundaries of the lenses are indicated by the black contours.

Fig. 5.
Fig. 5.

(Color online) Electric fields along the lens axis for the rectangular and the trapezoidal lenses: (a) The magnitudes of the total fields, (b) The ratio of the scattered field to the incident field.

Fig. 6.
Fig. 6.

(Color online) The coordinate transformation for the non-magnetic flat focusing lens design: (a) The original coordinate system, (b) the transformed system in the (x′, y′, z′) system.

Fig. 7.
Fig. 7.

(Color online) The material parameters for an example non-magnetic lens design for the TM mode: (a) ϵ x′,x, (b) ϵ x′,y, (c) ϵ yy′, and (d) μ zz′. The dimensions of the non-magnetic lens are given by w = 0.489 m and l = 0.13 m.

Fig. 8.
Fig. 8.

(Color online) Rectangular non-magnetic lens designs with linear and nonlinear coordinate transformations under a TM-mode beam illumination: (a) A snapshot and (b) the magnitude distribution of the total magnetic field for the design based on a linear transformation. (c) A snapshot and (d) the magnitude distribution of the magnetic field for the design based on a nonlinear coordinate transformation. The dimensions of these lenses are specified by w = 0.489 m, l = 0.13 m.

Fig. 9.
Fig. 9.

(Color online) Comparison of the magnetic field distributions along x′, = 0 between the lens designs obtained based on linear and non-linear transformations: (a) The magnitude of the total magnetic field, (b) The ratio of the scattered field to the incident field.

Equations (20)

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Js(ϕ)=ẑJ0exp[(ϕϕ0)22σϕ2],
x=x",y=la2x"2g(y"g)+g,z=z".
x=(1α)x+αasin1xa,y=y,z=z,
α=ygl.
A11=1+ x"(y"g)(a2x"2g)2a2x"2 (asin1x"zx")
+y"ga2x"2g(aa2x"21),
A12=1a2x"2g (asin1x"zx"),
A21= lx"(y"g)(a2x"2g)2a2x"2 ,
A22= la2x"2g ,
Es=EEi .
y=A(y"y"c)3+ B(y"y"c)+yc ,
A=ycyc2(gy"c)3,B=13(ycyc)2(gy"c).
Alin=0,Blin=gycgy"c=la2x"2g.
εxx=1[3A(y"y"c)2+B]2,
εxy=εyx= A21[3A(y"y"c)2+B]2,
εyy= 1+ A212[3A(y"y"c)2+B]2,
μzz=1,
A21=x"2a2x"2[3yc2y"cg2(gy"c)4(y"y"c)3+3A(y"y"c)2+3(ycg)2(gy"c)2(y"y"c)+B].
εxx,max=1B2,
A21=x"Blin2a2x"2(1y"y"cgy"c) =lx"(y"g)(a2x"2g)2a2x"2.

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