Abstract

Inspired by the branch cut that can link two Riemann sheets in complex function theory, we utilize the branch cut to mimic an electromagnetic ‘wormhole’ linking two 2D ‘parallel spaces’ in a reference space. With the help of optical conformal mapping, we design a time-varying inhomogeneous medium that can effectively perform like an electromagnetic ‘wormhole’ in the real space. Based on this method, we can simulate the evolutionary process of an electromagnetic ‘wormhole’ and the wave propagation from one space to another in a laboratory environment. The proposed device may also be applied in light capture, light modulators, and absorption with directional dependence.

© 2017 Optical Society of America

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References

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2015 (2)

S. R. Boston, “Time travel in transformation optics: metamaterials with closed null geodesics,” Phys. Rev. D Part. Fields Gravit. Cosmol. 91(12), 124035 (2015).
[Crossref]

J. Prat-Camps, C. Navau, and A. Sanchez, “A magnetic wormhole,” Sci. Rep. 5(1), 12488 (2015).
[Crossref] [PubMed]

2014 (3)

M. Kadic, G. Dupont, S. Enoch, and S. Guenneau, “Invisible waveguides on metal plates for plasmonic analogs of electromagnetic wormholes,” Phys. Rev. A 90(4), 043812 (2014).
[Crossref]

L. Xu and H. Chen, “Conformal transformation optics,” Nat. Photonics 9(1), 15–23 (2014).
[Crossref]

L. Xu and H. Chen, “Logarithm conformal mapping brings the cloaking effect,” Sci. Rep. 4(1), 6862 (2014).
[Crossref] [PubMed]

2013 (3)

L. Xu and H. Chen, “Transformation optics with artificial Riemann sheets,” New J. Phys. 15(21), 3813–3818 (2013).

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3(1), 2182 (2013).
[Crossref] [PubMed]

H. Li, Y. Xu, and H. Chen, “Conformal cloaks at eigenfrequencies,” J. Phys. D Appl. Phys. 46(13), 135109 (2013).
[Crossref]

2012 (4)

T. Xu, Y. C. Liu, Y. Zhang, C. K. Ong, and Y. G. Ma, “Perfect invisibility cloaking by isotropic media,” Phys. Rev. A 86(4), 043827 (2012).
[Crossref]

Y. Urzhumov, N. Landy, and D. R. Smith, “Isotropic-medium three-dimensional cloaks for acoustic and electromagnetic waves,” J. Appl. Phys. 111(5), 053105 (2012).
[Crossref]

A. Q. Liu, W. M. Zhu, D. P. Tsai, and N. I. Zheludev, “Micromachined tunable metamaterials: a review,” J. Opt. 14(11), 114009 (2012).
[Crossref]

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481(7379), 62–65 (2012).
[Crossref] [PubMed]

2011 (3)

M. W. Mccall, A. Favaro, P. Kinsler, and A. A. Boardman, “spacetime cloak, or a history editor,” J. Opt. 13(2), 24003 (2011).
[Crossref]

H. Chen, U. Leonhardt, and T. Tyc, “Conformal cloak for waves,” Phys. Rev. A 83(5), 055801 (2011).
[Crossref]

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

2010 (2)

2009 (2)

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[Crossref]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
[Crossref]

2007 (2)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[Crossref] [PubMed]

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

2006 (2)

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]

2004 (1)

O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett. 84(7), 1198–1200 (2004).
[Crossref]

1988 (1)

M. S. Morris, K. S. Thorne, and U. Yurtsever, “Wormholes, time machines, and the weak energy condition,” Phys. Rev. Lett. 61(13), 1446–1449 (1988).
[Crossref] [PubMed]

Acher, O.

O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett. 84(7), 1198–1200 (2004).
[Crossref]

Boardman, A. A.

M. W. Mccall, A. Favaro, P. Kinsler, and A. A. Boardman, “spacetime cloak, or a history editor,” J. Opt. 13(2), 24003 (2011).
[Crossref]

Boardman, A. D.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

Boston, S. R.

S. R. Boston, “Time travel in transformation optics: metamaterials with closed null geodesics,” Phys. Rev. D Part. Fields Gravit. Cosmol. 91(12), 124035 (2015).
[Crossref]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Chen, H.

L. Xu and H. Chen, “Conformal transformation optics,” Nat. Photonics 9(1), 15–23 (2014).
[Crossref]

L. Xu and H. Chen, “Logarithm conformal mapping brings the cloaking effect,” Sci. Rep. 4(1), 6862 (2014).
[Crossref] [PubMed]

L. Xu and H. Chen, “Transformation optics with artificial Riemann sheets,” New J. Phys. 15(21), 3813–3818 (2013).

H. Li, Y. Xu, and H. Chen, “Conformal cloaks at eigenfrequencies,” J. Phys. D Appl. Phys. 46(13), 135109 (2013).
[Crossref]

H. Chen, U. Leonhardt, and T. Tyc, “Conformal cloak for waves,” Phys. Rev. A 83(5), 055801 (2011).
[Crossref]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

H. Chen, R. X. Miao, and M. Li, “Transformation optics that mimics the system outside a Schwarzschild black hole,” Opt. Express 18(14), 15183–15188 (2010).
[Crossref] [PubMed]

Du, B.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

Dupont, G.

M. Kadic, G. Dupont, S. Enoch, and S. Guenneau, “Invisible waveguides on metal plates for plasmonic analogs of electromagnetic wormholes,” Phys. Rev. A 90(4), 043812 (2014).
[Crossref]

Enoch, S.

M. Kadic, G. Dupont, S. Enoch, and S. Guenneau, “Invisible waveguides on metal plates for plasmonic analogs of electromagnetic wormholes,” Phys. Rev. A 90(4), 043812 (2014).
[Crossref]

Farsi, A.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481(7379), 62–65 (2012).
[Crossref] [PubMed]

Favaro, A.

M. W. Mccall, A. Favaro, P. Kinsler, and A. A. Boardman, “spacetime cloak, or a history editor,” J. Opt. 13(2), 24003 (2011).
[Crossref]

Fridman, M.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481(7379), 62–65 (2012).
[Crossref] [PubMed]

Gaeta, A. L.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481(7379), 62–65 (2012).
[Crossref] [PubMed]

Genov, D. A.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[Crossref]

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[Crossref] [PubMed]

Grimalsky, V. V.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

Guenneau, S.

M. Kadic, G. Dupont, S. Enoch, and S. Guenneau, “Invisible waveguides on metal plates for plasmonic analogs of electromagnetic wormholes,” Phys. Rev. A 90(4), 043812 (2014).
[Crossref]

He, S.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3(1), 2182 (2013).
[Crossref] [PubMed]

Jiang, W.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3(1), 2182 (2013).
[Crossref] [PubMed]

Kadic, M.

M. Kadic, G. Dupont, S. Enoch, and S. Guenneau, “Invisible waveguides on metal plates for plasmonic analogs of electromagnetic wormholes,” Phys. Rev. A 90(4), 043812 (2014).
[Crossref]

Kang, L.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

Kildishev, A. V.

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
[Crossref]

Kinsler, P.

M. W. Mccall, A. Favaro, P. Kinsler, and A. A. Boardman, “spacetime cloak, or a history editor,” J. Opt. 13(2), 24003 (2011).
[Crossref]

Kivshar, Y. S.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

Koshevaya, S. V.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[Crossref] [PubMed]

Lan, L.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3(1), 2182 (2013).
[Crossref] [PubMed]

Landy, N.

Y. Urzhumov, N. Landy, and D. R. Smith, “Isotropic-medium three-dimensional cloaks for acoustic and electromagnetic waves,” J. Appl. Phys. 111(5), 053105 (2012).
[Crossref]

Lapine, M.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[Crossref] [PubMed]

Leonhardt, U.

H. Chen, U. Leonhardt, and T. Tyc, “Conformal cloak for waves,” Phys. Rev. A 83(5), 055801 (2011).
[Crossref]

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

Li, B.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

Li, H.

H. Li, Y. Xu, and H. Chen, “Conformal cloaks at eigenfrequencies,” J. Phys. D Appl. Phys. 46(13), 135109 (2013).
[Crossref]

Li, M.

Liang, X.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

Litchinitser, N. M.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

Liu, A. Q.

A. Q. Liu, W. M. Zhu, D. P. Tsai, and N. I. Zheludev, “Micromachined tunable metamaterials: a review,” J. Opt. 14(11), 114009 (2012).
[Crossref]

Liu, Y.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3(1), 2182 (2013).
[Crossref] [PubMed]

Liu, Y. C.

T. Xu, Y. C. Liu, Y. Zhang, C. K. Ong, and Y. G. Ma, “Perfect invisibility cloaking by isotropic media,” Phys. Rev. A 86(4), 043827 (2012).
[Crossref]

Ma, Y.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3(1), 2182 (2013).
[Crossref] [PubMed]

Ma, Y. G.

T. Xu, Y. C. Liu, Y. Zhang, C. K. Ong, and Y. G. Ma, “Perfect invisibility cloaking by isotropic media,” Phys. Rev. A 86(4), 043827 (2012).
[Crossref]

Malnev, V. N.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

Mccall, M. W.

M. W. Mccall, A. Favaro, P. Kinsler, and A. A. Boardman, “spacetime cloak, or a history editor,” J. Opt. 13(2), 24003 (2011).
[Crossref]

Miao, R. X.

Morris, M. S.

M. S. Morris, K. S. Thorne, and U. Yurtsever, “Wormholes, time machines, and the weak energy condition,” Phys. Rev. Lett. 61(13), 1446–1449 (1988).
[Crossref] [PubMed]

Narimanov, E. E.

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
[Crossref]

Navau, C.

J. Prat-Camps, C. Navau, and A. Sanchez, “A magnetic wormhole,” Sci. Rep. 5(1), 12488 (2015).
[Crossref] [PubMed]

Noginov, M.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

Okawachi, Y.

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481(7379), 62–65 (2012).
[Crossref] [PubMed]

Ong, C. K.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3(1), 2182 (2013).
[Crossref] [PubMed]

T. Xu, Y. C. Liu, Y. Zhang, C. K. Ong, and Y. G. Ma, “Perfect invisibility cloaking by isotropic media,” Phys. Rev. A 86(4), 043827 (2012).
[Crossref]

Pendry, J. B.

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

Prat-Camps, J.

J. Prat-Camps, C. Navau, and A. Sanchez, “A magnetic wormhole,” Sci. Rep. 5(1), 12488 (2015).
[Crossref] [PubMed]

Rapoport, Y. G.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

Reynet, O.

O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett. 84(7), 1198–1200 (2004).
[Crossref]

Sanchez, A.

J. Prat-Camps, C. Navau, and A. Sanchez, “A magnetic wormhole,” Sci. Rep. 5(1), 12488 (2015).
[Crossref] [PubMed]

Schurig, D.

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

Shalaev, V. M.

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
[Crossref]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Smith, D. R.

Y. Urzhumov, N. Landy, and D. R. Smith, “Isotropic-medium three-dimensional cloaks for acoustic and electromagnetic waves,” J. Appl. Phys. 111(5), 053105 (2012).
[Crossref]

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

Tang, H.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

Thorne, K. S.

M. S. Morris, K. S. Thorne, and U. Yurtsever, “Wormholes, time machines, and the weak energy condition,” Phys. Rev. Lett. 61(13), 1446–1449 (1988).
[Crossref] [PubMed]

Tsai, D. P.

A. Q. Liu, W. M. Zhu, D. P. Tsai, and N. I. Zheludev, “Micromachined tunable metamaterials: a review,” J. Opt. 14(11), 114009 (2012).
[Crossref]

Tyc, T.

H. Chen, U. Leonhardt, and T. Tyc, “Conformal cloak for waves,” Phys. Rev. A 83(5), 055801 (2011).
[Crossref]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[Crossref] [PubMed]

Urzhumov, Y.

Y. Urzhumov, N. Landy, and D. R. Smith, “Isotropic-medium three-dimensional cloaks for acoustic and electromagnetic waves,” J. Appl. Phys. 111(5), 053105 (2012).
[Crossref]

Wu, T.

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3(1), 2182 (2013).
[Crossref] [PubMed]

Xu, L.

L. Xu and H. Chen, “Logarithm conformal mapping brings the cloaking effect,” Sci. Rep. 4(1), 6862 (2014).
[Crossref] [PubMed]

L. Xu and H. Chen, “Conformal transformation optics,” Nat. Photonics 9(1), 15–23 (2014).
[Crossref]

L. Xu and H. Chen, “Transformation optics with artificial Riemann sheets,” New J. Phys. 15(21), 3813–3818 (2013).

Xu, T.

T. Xu, Y. C. Liu, Y. Zhang, C. K. Ong, and Y. G. Ma, “Perfect invisibility cloaking by isotropic media,” Phys. Rev. A 86(4), 043827 (2012).
[Crossref]

Xu, Y.

H. Li, Y. Xu, and H. Chen, “Conformal cloaks at eigenfrequencies,” J. Phys. D Appl. Phys. 46(13), 135109 (2013).
[Crossref]

Yurtsever, U.

M. S. Morris, K. S. Thorne, and U. Yurtsever, “Wormholes, time machines, and the weak energy condition,” Phys. Rev. Lett. 61(13), 1446–1449 (1988).
[Crossref] [PubMed]

Zhang, B.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

Zhang, S.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[Crossref]

Zhang, X.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[Crossref]

Zhang, Y.

T. Xu, Y. C. Liu, Y. Zhang, C. K. Ong, and Y. G. Ma, “Perfect invisibility cloaking by isotropic media,” Phys. Rev. A 86(4), 043827 (2012).
[Crossref]

Zhao, Q.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

Zheludev, N. I.

A. Q. Liu, W. M. Zhu, D. P. Tsai, and N. I. Zheludev, “Micromachined tunable metamaterials: a review,” J. Opt. 14(11), 114009 (2012).
[Crossref]

Zhou, J.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
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Zhu, W. M.

A. Q. Liu, W. M. Zhu, D. P. Tsai, and N. I. Zheludev, “Micromachined tunable metamaterials: a review,” J. Opt. 14(11), 114009 (2012).
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Appl. Phys. Lett. (3)

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009).
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Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

J. Appl. Phys. (1)

Y. Urzhumov, N. Landy, and D. R. Smith, “Isotropic-medium three-dimensional cloaks for acoustic and electromagnetic waves,” J. Appl. Phys. 111(5), 053105 (2012).
[Crossref]

J. Opt. (2)

A. Q. Liu, W. M. Zhu, D. P. Tsai, and N. I. Zheludev, “Micromachined tunable metamaterials: a review,” J. Opt. 14(11), 114009 (2012).
[Crossref]

M. W. Mccall, A. Favaro, P. Kinsler, and A. A. Boardman, “spacetime cloak, or a history editor,” J. Opt. 13(2), 24003 (2011).
[Crossref]

J. Phys. D Appl. Phys. (1)

H. Li, Y. Xu, and H. Chen, “Conformal cloaks at eigenfrequencies,” J. Phys. D Appl. Phys. 46(13), 135109 (2013).
[Crossref]

Laser Photonics Rev. (1)

A. D. Boardman, V. V. Grimalsky, Y. S. Kivshar, S. V. Koshevaya, M. Lapine, N. M. Litchinitser, V. N. Malnev, M. Noginov, Y. G. Rapoport, and V. M. Shalaev, “Active and tunable metamaterials,” Laser Photonics Rev. 5(2), 287–307 (2011).
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Nat. Mater. (1)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
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Nat. Photonics (1)

L. Xu and H. Chen, “Conformal transformation optics,” Nat. Photonics 9(1), 15–23 (2014).
[Crossref]

Nat. Phys. (1)

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009).
[Crossref]

Nature (1)

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481(7379), 62–65 (2012).
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New J. Phys. (1)

L. Xu and H. Chen, “Transformation optics with artificial Riemann sheets,” New J. Phys. 15(21), 3813–3818 (2013).

Opt. Express (1)

Phys. Rev. A (3)

M. Kadic, G. Dupont, S. Enoch, and S. Guenneau, “Invisible waveguides on metal plates for plasmonic analogs of electromagnetic wormholes,” Phys. Rev. A 90(4), 043812 (2014).
[Crossref]

T. Xu, Y. C. Liu, Y. Zhang, C. K. Ong, and Y. G. Ma, “Perfect invisibility cloaking by isotropic media,” Phys. Rev. A 86(4), 043827 (2012).
[Crossref]

H. Chen, U. Leonhardt, and T. Tyc, “Conformal cloak for waves,” Phys. Rev. A 83(5), 055801 (2011).
[Crossref]

Phys. Rev. D Part. Fields Gravit. Cosmol. (1)

S. R. Boston, “Time travel in transformation optics: metamaterials with closed null geodesics,” Phys. Rev. D Part. Fields Gravit. Cosmol. 91(12), 124035 (2015).
[Crossref]

Phys. Rev. Lett. (2)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007).
[Crossref] [PubMed]

M. S. Morris, K. S. Thorne, and U. Yurtsever, “Wormholes, time machines, and the weak energy condition,” Phys. Rev. Lett. 61(13), 1446–1449 (1988).
[Crossref] [PubMed]

Sci. Rep. (3)

J. Prat-Camps, C. Navau, and A. Sanchez, “A magnetic wormhole,” Sci. Rep. 5(1), 12488 (2015).
[Crossref] [PubMed]

L. Xu and H. Chen, “Logarithm conformal mapping brings the cloaking effect,” Sci. Rep. 4(1), 6862 (2014).
[Crossref] [PubMed]

Y. Ma, Y. Liu, L. Lan, T. Wu, W. Jiang, C. K. Ong, and S. He, “First experimental demonstration of an isotropic electromagnetic cloak with strict conformal mapping,” Sci. Rep. 3(1), 2182 (2013).
[Crossref] [PubMed]

Science (2)

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

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

Other (4)

U. Leonhardt and T. Philbin, Geometry and Light: the Science of Invisibility (Dover, 2012).

D. H. Werner and D.-H. Kwon, Transformation Electromagnetics and Metamaterials-Fundamental Principles and Applications (Springer, 2014).

J. D. Jackson, Classical Electrodynamics (Wiley, 1962).

T. Needham, Visual Complex Analysis (Oxford, 2002).

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Figures (7)

Fig. 1
Fig. 1 The Zhukovski transformation. (a) the reference space. (b) the real space. The regions colored black and blue indicate two ‘parallel spaces’. The yellow line or circle indicates the branch cut that can be treated as the electromagnetic ‘wormhole’.
Fig. 2
Fig. 2 FEM simulation results by the ray tracing method (the wavelength of the incident light is chosen as λ0 = 680 nm). The light rays propagate from bottom to top in the real space. The size of the branch cut a is set as a varying parameter. From (a)-(f), a increases from 0 to 2.5 m. The small black circle corresponds to the yellow circle in Fig. 1(b) (i.e. the branch cut linking the two spaces).
Fig. 3
Fig. 3 The refractive index distribution when the size of the branch cut a changes. From (a)-(f), a increases from 0 to 2.5 m. The white region in the center means the value of the refractive index is beyond the value in the color bar. We should note that the refractive index in the whole space is larger than zero.
Fig. 4
Fig. 4 The time domain simulation results by the ray tracing method. The ‘wormhole’ is described by the reduced model in Eq. (12) with aM = 1m, b = 0.1m, t0 = 30ns, Δt = 50ns, and λ0 = 660nm (ω0 = 2.856e15s−1). The black circle indicates the boundary of the ‘wormhole’ (i.e. filled by the medium given in Eq. (12)). The region outside the black circle is free space. From t = 0~30ns, the ‘wormhole’ is not open (i.e. light rays propagate in free space). When t = t0 = 30ns, the ‘wormhole’ begins to open up, the light slows down and is attracted to the center in the ‘wormhole’ region. At t = 80ns, the ‘wormhole’ reaches its maximal size and begins to close (it still exists). Note that the traces of the attracted light rays during the closing process of the ‘wormhole’ are different from the frequency domain simulations in Fig. 2 due to the reduction on the medium. At t = 130ns, the ‘wormhole’ is totally closed. The directions of some light rays have been changed when the ‘wormhole’ closes and they keep propagating along these directions in the free space.
Fig. 5
Fig. 5 The time domain simulation results by the ray tracing method. The ‘wormhole’ is almost the same as the one used in Fig. 4 (only difference is that the regions where the refraction index is smaller than 1 is replaced by air).
Fig. 6
Fig. 6 The directional cloaking effect by the ray tracing method and full wave method in (a) and (b), respectively. The light rays/waves propagate from left to right in the real space. The rays/waves never touch the branch cut (i.e. the black circle), and just go around it.
Fig. 7
Fig. 7 The directional absorption effect by the full wave simulation. We plot the normalized absolute value of the z component of the electric field. The refractive index of the absorber is given by Eq. (14) with P = 0.03. A Gaussian beam propagates from -y to + y. The waist radius of the beam is chosen as w0 = 20λ0/7. The size of the absorber is chosen as a = 40λ0/7. The field in the center region is enlarged in the purple rectangle.

Equations (14)

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w = z + a 2 z or z = 1 2 ( w ± w 2 4 a 2 ) .
n = | d w d z | n ' ,
n ( z ) = | 1 a 2 z 2 | .
a ( t ) = { 2 a M Δ t ( t t 0 ) , t [ t 0 , t 0 + Δ t 2 ] 2 a M Δ t ( t t 0 Δ t ) , t [ t 0 + Δ t 2 , t 0 + Δ t ] 0 , e l s e ,
ε ( z , ω ) = ε 0 ( 1 A ( z ) ω 2 + i γ ω ) ,
ε ( z , ω 0 ) = ε 0 ( 1 A ( z ) ω 0 2 + i γ ω 0 ) = ε 0 | 1 a 2 z 2 | 2 .
A ( z ) = ( 1 | 1 a 2 z 2 | 2 ) ω 0 2 .
χ ( z , ω ) = ( 1 | 1 a 2 z 2 | 2 ) ω 0 2 ω 2 .
χ ( z , t ) = ( 1 | 1 a 2 z 2 | 2 ) ω 0 2 t H ( t ) .
D ( z , t ) = ε 0 E ( z , t ) + ε 0 ω 0 2 ( 1 | 1 a 2 z 2 | 2 ) t H ( t ) * E ( z , t ) ,
ε ( z , t ) = [ 1 + ω 0 2 a 2 ρ 2 ( 2 cos 2 θ a 2 ρ 2 ) t H ( t ) ] ε 0 .
n ( z ) = | 1 a ( t ) 2 f ( z ) 2 | ,
f ( z ) = { b 2 , | z | b z 2 , | z | > b ,
n ( z ) = | 1 a 2 z 2 | + i P ( a | z | 1 ) ,

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