Abstract

We describe the design of adaptive beam bends and beam splitters with arbitrary bend and split angles by use of finite embedded coordinate transformations. The devices do not exhibit reflection at the entrance or exit surfaces. It is shown that moderate and practically achievable values of the relative permittivity and permeability can be obtained for beam bends and splitters with both small and large bend radius. The devices are also discussed in the context of reconfigurable metamaterials, in which the bend and split angles can be dynamically tuned. The performance of adaptive beam bends and splitters is demonstrated in full wave simulations based on a finite-element method. Furthermore, the design of an adaptively adjustable transformation-optical beam expander/compressor is presented. It is observed that a pure transformation-optical design cannot result in a reflectionless beam expander/compressor.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]

2008 (9)

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

A. Alu and N. Engheta, "Multifrequency Optical Invisibility Cloak with Layered Plasmonic Shells," Phys. Rev. Lett. 100, 113901 (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 (2008).
[CrossRef]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. B. Pendry, M. Rahm, and A. Starr, "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell," Phys. Rev. Lett. 100, 024301 (2008).
[CrossRef] [PubMed]

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of Matter Waves,", Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

A. V. Kildishev and V. M. Shalaev, "Engineering space for light via transformation optics," Opt. Lett. 33, 43 (2008).
[CrossRef]

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035122 (2008).
[CrossRef]

N. A. Zharova, I. V. Shadrivov, and Y. S. Kivshar, "Inside-out electromagnetic cloaking," Opt. Express 16, 4615 (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. 100,063903 (2008).
[CrossRef] [PubMed]

2007 (14)

S. Cummer and D. Schurig, "One path to acoustic cloaking," New J. Phys. 9, 45 (2007).
[CrossRef]

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

U. Leonhardt and T. G. Philbin, "Quantum levitation by left-handed metamaterials," New J. Phys. 9, 254 (2007).
[CrossRef]

U. Leonhardt and T. G. Philbin, "Quantum optics of spatial transformation media," J. Opt. A: Pure Appl. Opt. 9, 289 (2007).
[CrossRef]

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

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772 (2007).
[CrossRef] [PubMed]

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

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photonics 1, 224 (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]

B. Wood and J. B. Pendry, "Metamaterials at zero frequency," J. Phys.: Condens. Matter 19, 076208 (2007).
[CrossRef]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Full-Wave Invisibility of Active Devices at All Frequencies," Commun. Math. Phys. 275, 749 (2007).
[CrossRef]

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

2006 (7)

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

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

U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (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 (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]

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

Alu, A.

A. Alu and N. Engheta, "Multifrequency Optical Invisibility Cloak with Layered Plasmonic Shells," Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef] [PubMed]

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, "Optical cloaking with metamaterials," Nature Photonics 1, 224 (2007).
[CrossRef]

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

Chan, C. T.

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

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

Chen, H.

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (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]

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

Chettiar, U. K.

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

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

Cummer, S.

S. Cummer and D. Schurig, "One path to acoustic cloaking," New J. Phys. 9, 45 (2007).
[CrossRef]

Cummer, S. A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. B. Pendry, M. Rahm, and A. Starr, "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell," Phys. Rev. Lett. 100, 024301 (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 (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 (2006).
[CrossRef] [PubMed]

Engheta, N.

A. Alu and N. Engheta, "Multifrequency Optical Invisibility Cloak with Layered Plasmonic Shells," Phys. Rev. Lett. 100, 113901 (2008).
[CrossRef] [PubMed]

Genov, D. A.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of Matter Waves,", Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Full-Wave Invisibility of Active Devices at All Frequencies," Commun. Math. Phys. 275, 749 (2007).
[CrossRef]

Guenneau, S.

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 (2006).
[CrossRef] [PubMed]

Kildishev, A. V.

A. V. Kildishev and V. M. Shalaev, "Engineering space for light via transformation optics," Opt. Lett. 33, 43 (2008).
[CrossRef]

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

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

Kivshar, Y. S.

Kong, J. A.

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[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]

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Full-Wave Invisibility of Active Devices at All Frequencies," Commun. Math. Phys. 275, 749 (2007).
[CrossRef]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Full-Wave Invisibility of Active Devices at All Frequencies," Commun. Math. Phys. 275, 749 (2007).
[CrossRef]

Leonhardt, U.

U. Leonhardt and T. G. Philbin, "Quantum levitation by left-handed metamaterials," New J. Phys. 9, 254 (2007).
[CrossRef]

U. Leonhardt and T. G. Philbin, "Quantum optics of spatial transformation media," J. Opt. A: Pure Appl. Opt. 9, 289 (2007).
[CrossRef]

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

U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777 (2006).
[CrossRef] [PubMed]

Milton, G. W.

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

Nicolet, A.

Nicorovici, N.-A.

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

Pendry, J. B.

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 (2008).
[CrossRef]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. B. Pendry, M. Rahm, and A. Starr, "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell," Phys. Rev. Lett. 100, 024301 (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. 100,063903 (2008).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772 (2007).
[CrossRef] [PubMed]

B. Wood and J. B. Pendry, "Metamaterials at zero frequency," J. Phys.: Condens. Matter 19, 076208 (2007).
[CrossRef]

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

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 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, 977 (2006).
[CrossRef] [PubMed]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, "Quantum optics of spatial transformation media," J. Opt. A: Pure Appl. Opt. 9, 289 (2007).
[CrossRef]

U. Leonhardt and T. G. Philbin, "Quantum levitation by left-handed metamaterials," New J. Phys. 9, 254 (2007).
[CrossRef]

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

Popa, B.-I.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. B. Pendry, M. Rahm, and A. Starr, "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell," Phys. Rev. Lett. 100, 024301 (2008).
[CrossRef] [PubMed]

Psaltis, D.

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035122 (2008).
[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]

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 (2008).
[CrossRef]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. B. Pendry, M. Rahm, and A. Starr, "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell," Phys. Rev. Lett. 100, 024301 (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. 100,063903 (2008).
[CrossRef] [PubMed]

Roberts, D. 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 (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 (2008).
[CrossRef]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. B. Pendry, M. Rahm, and A. Starr, "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell," Phys. Rev. Lett. 100, 024301 (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. 100,063903 (2008).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772 (2007).
[CrossRef] [PubMed]

S. Cummer and D. Schurig, "One path to acoustic cloaking," New J. Phys. 9, 45 (2007).
[CrossRef]

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

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (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 (2006).
[CrossRef] [PubMed]

Shadrivov, I. V.

Shalaev, V. M.

A. V. Kildishev and V. M. Shalaev, "Engineering space for light via transformation optics," Opt. Lett. 33, 43 (2008).
[CrossRef]

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

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

Smith, D. R.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. B. Pendry, M. Rahm, and A. Starr, "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell," Phys. Rev. Lett. 100, 024301 (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 (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. B. Pendry, and D. R. Smith, "Transformation-designed optical elements," Opt. Express 15, 14772 (2007).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312, 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, 977 (2006).
[CrossRef] [PubMed]

Starr, A.

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. B. Pendry, M. Rahm, and A. Starr, "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell," Phys. Rev. Lett. 100, 024301 (2008).
[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 (2006).
[CrossRef] [PubMed]

Sun, C.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of Matter Waves,", Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

Tsang, M.

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035122 (2008).
[CrossRef]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Full-Wave Invisibility of Active Devices at All Frequencies," Commun. Math. Phys. 275, 749 (2007).
[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]

Wood, B.

B. Wood and J. B. Pendry, "Metamaterials at zero frequency," J. Phys.: Condens. Matter 19, 076208 (2007).
[CrossRef]

Wu, B.-I.

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[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]

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.

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[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, S.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of Matter Waves,", Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

Zhang, X.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of Matter Waves,", Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

Zharova, N. A.

Zolla, F.

Appl. Phys. Lett. (3)

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

H. Chen and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett. 91, 183518 (2007).
[CrossRef]

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

Commun. Math. Phys. (1)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Full-Wave Invisibility of Active Devices at All Frequencies," Commun. Math. Phys. 275, 749 (2007).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

U. Leonhardt and T. G. Philbin, "Quantum optics of spatial transformation media," J. Opt. A: Pure Appl. Opt. 9, 289 (2007).
[CrossRef]

J. Phys.: Condens. Matter (1)

B. Wood and J. B. Pendry, "Metamaterials at zero frequency," J. Phys.: Condens. Matter 19, 076208 (2007).
[CrossRef]

Nature Photonics (1)

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

New J. Phys. (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]

S. Cummer and D. Schurig, "One path to acoustic cloaking," New J. Phys. 9, 45 (2007).
[CrossRef]

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

U. Leonhardt and T. G. Philbin, "Quantum levitation by left-handed metamaterials," New J. Phys. 9, 254 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

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 (2008).
[CrossRef]

Phys. Rev. B (1)

M. Tsang and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B 77, 035122 (2008).
[CrossRef]

Phys. Rev. Lett. (8)

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]

S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, J. B. Pendry, M. Rahm, and A. Starr, "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell," Phys. Rev. Lett. 100, 024301 (2008).
[CrossRef] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials," Phys. Rev. Lett. 99, 183901 (2007).
[CrossRef] [PubMed]

B. Zhang, H. Chen, B.-I. Wu, and J. A. Kong, "Extraordinary Surface Voltage Effect in the Invisibility Cloak with an Active Device Inside," Phys. Rev. Lett. 100, 063904 (2008).
[CrossRef] [PubMed]

A. Alu and N. Engheta, "Multifrequency Optical Invisibility Cloak with Layered Plasmonic Shells," Phys. Rev. Lett. 100, 113901 (2008).
[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]

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]

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, "Cloaking of Matter Waves,", Phys. Rev. Lett. 100, 123002 (2008).
[CrossRef] [PubMed]

Proc. R. Soc. A (1)

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

Science (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 (2006).
[CrossRef] [PubMed]

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

U. Leonhardt, "Optical Conformal Mapping," Science 312, 1777 (2006).
[CrossRef] [PubMed]

Other (7)

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Electromagnetic cloaking in the visible frequency range," http://arxiv.org/abs/0709.2862.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, "Perfect invisibility cloaks constructed by arbitrary coordinate transformations," http://arxiv.org/abs/0712.1694.

T. Ochiai, U. Leonhardt, and J.C. Nacher, "A Novel Design of Dielectric Perfect Invisibility Devices," http://arxiv.org/abs/0711.1122.

A. N. Norris, "Acoustic cloaking in 2D and 3D using finite mass," http://arxiv.org/abs/0802.0701v1.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, "Design and analytically full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," http://arxiv.org/abs/0712.2027.

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, "Controlling the Emission of Electromagnetic Sources by Coordinate transformation," http://arxiv.org/abs/0712.3776.

S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, "Molding the flow of light at deep sub-wavelength scale," http://arxiv.org/abs/0712.3813.

Supplementary Material (8)

» Media 1: MOV (371 KB)     
» Media 2: MOV (495 KB)     
» Media 3: MOV (632 KB)     
» Media 4: MOV (785 KB)     
» Media 5: MOV (3983 KB)     
» Media 6: MOV (3981 KB)     
» Media 7: MOV (367 KB)     
» Media 8: MOV (2656 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Illustration of the embedded coordinate transformation for a π/5-bend with (a) k=1 and (b) k=2.

Fig. 2.
Fig. 2.

(a) Relative permittivity and permeability η=ε=μ in the radial (ηr ), azimuthal (ηϕ ) and in the z-direction (ηz ) in dependence on the radial distance rnorm =r/R (R: arbitrary) from the origin of an α-bend for various values of γnorm . (b) Illustration of the contrivable physical dimensions of an α-bend with arbitrary α for various values of γnorm . The inner radius R 1 and the outer radius R 2 of the bends were chosen such that ε<10 and μ<10.

Fig. 3.
Fig. 3.

Distribution of the electric field component normal to the plane of propagation for a π/2-bend with (a) γ=0.02 (Media 1) and (b) γ=0.3 (Media 2). The dark grey lines represent the direction of power flow. The animation illustrates a phase advance of 2/9π per frame. Both realizations of a π/2-bend prove the reflectionless performance of the transformation-optical beam bend design independent on the choice of k.

Fig. 4.
Fig. 4.

(Movie) Distribution of the electric field component normal to the plane of propagation for a π/2-bend with γ=0.02 at oblique incidence at an angle (a) Θ=π/8 (Media 3) and (b) Θ=2/9π (Media 4). The dark grey lines represent the direction of power flow. The animation illustrates a phase advance of 2/9π per frame. The π/2-bend proves to operate reflectionless independently on the angle of incidence Θ.

Fig. 5.
Fig. 5.

Distribution of the electric field component normal to the plane of propagation for (a) a π/9-bend with γ=0.05 (Media 5) and (b) for a π/3 beam splitter with γ=0.05 (Media 6). The dark grey lines represent the direction of power flow. In the animations, the angular domain where the effective material parameters are set by Eq. (16) is increased from α=0…3π/2 in steps of π/18 for the tunable beam bend in (a). In case of the beam splitter in (b) the angular region is changed from α=0…±3π/2 with a step size of ±π/18, where the positive sign applies to the left half and the negative sign to the right half of the splitter. The angular step size was arbitrarily chosen and can adopt any value. The phase of the electric field is advanced by 2/3π per frame.

Fig. 6.
Fig. 6.

Two-dimensional intensity distribution (color map) for a (a) π/9-splitter, (b) 2/9π-splitter, (c) π/3-splitter, (d) 2/3π-splitter, (e) π/2-splitter and (f) π-splitter and the corresponding cross section plots of the intensity distribution along the white lines indicated in the color maps. The ratio between the intensity contained in the split beams and the intensity present in the scattered fields in the split gap increases with rising split angle 2α.

Fig. 7.
Fig. 7.

Ratio between the maximum intensity in the split gap Igap and the maximum intensity in either the left or right branch of the split beams Isplit in dependence on the split angle 2α between the beams. At split angles 2α>π/2, the ratio is smaller than 4%.

Fig. 8.
Fig. 8.

(Movie) Distribution of the electric field component normal to the plane of propagation for a left-handed π/2-bend with γ=0.02 (Media 7). In the animation, the phase of the electric field is advanced by 2/9π per frame. The phase fronts are propagating in the opposite direction of the power flow inside the transformation-optical medium.

Fig. 9.
Fig. 9.

Distribution of the electric field component normal to the plane of propagation for a beam expander with (a) a=6 and (b) a=-10. In the animation, the parameter a is changed from +6…-10 in steps of -2. The phase of the electric field is advanced by 2/9π per frame. For a≠0, reflections occur at the output facet of the lens which result in an amplitude modulation of the incoming wave. (Media 8)

Equations (27)

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

ε i′j′ = [ det ( A i i′ ) ] 1 A i i′ A j j′ ε ij
μ i′j′ = [ det ( A i i′ ) ] 1 A i i′ A j j′ μ ij
x′ ( x , y , z ) = sgn ( ) x cos ( y R 2 )
y′ ( x , y , z ) = sgn ( ) x sin ( y R 2 )
z′ ( x , y , z ) = z
r′ ( x , y , z ) = x 2 + y 2
ϕ′ ( x , y , z ) = arctan ( y x )
z′ ( x , y , z ) = z
x ( r′ , ϕ′ , z′ ) = r cos ( ϕ′ )
y ( r′ , ϕ′ , z′ ) = r′ sin ( ϕ′ )
z ( r′ , ϕ′ , z′ ) = z′
r″ ( x , y , z ) = x
ϕ″ ( x , y , z ) = ( k y R 2 ) α
z″ ( x , y , z ) = z
x [ R 1 , R 2 ] , y [ 0 , R 2 k ]
ε i′j′ = μ i′j′ = ( γ r 0 0 0 r γ 0 0 0 γ r )
x′ ( x , y , z ) = x
y′ ( x , y , z ) = u ( x ) y
z′ ( x , y , z ) = z
x ( x′ , y′ , z′ ) = x′
y ( x′ , y′ , z′ ) = y′ u ( x′ )
z ( x′ , y′ , z′ ) = z′
u ( ξ ) = 1 + a ( ξ + b 2 )
( ε r ) i′j′ = ( μ r ) i′j′ = ( 1 u ay u 2 0 ay u 2 ( ay ) 2 u 3 + u 0 0 0 1 u )
A i′ i = ( 1 0 0 ay′ u ( x′ ) 2 1 u ( x′ ) 0 0 0 1 u )
e 1′ ( x , y , z ) = e 1 ay u ( x ) e 2 , e 2′ ( x , y , z ) = e 2 u ( x ) , e 3′ ( x , y , z ) = e 3
e i = e i e i′ e i

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