Abstract

We propose to use the concept of transformation optics for the design of novel radiating devices. By applying transformations that compress space, and then that match it to the surrounding environment, we show how the electromagnetic appearance of radiating elements can be tailored at will. Our efficient approach allows one to realize a large aperture emission from a small aperture one. We describe transformation of the metric space and the calculation of the material parameters. Full wave simulations are performed to validate the proposed approach on different space compression shapes, factors and impedance matching. The idea paves the way to interesting applications in various domains in microwave and optical regimes, but also in acoustics.

© 2013 OSA

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    [CrossRef] [PubMed]
  5. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
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  6. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
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  7. R. A. Crudo and J. G. O’Brien, “Metric approach to transformation optics,” Phys. Rev. A80(3), 033824 (2009).
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  8. U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt.53, 69–152 (2009).
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  9. 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,” Science314(5801), 977–980 (2006).
    [CrossRef] [PubMed]
  10. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett.32(9), 1069–1071 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett.102(18), 183903 (2009).
    [CrossRef] [PubMed]
  13. D.-H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys.10(11), 115023 (2008).
    [CrossRef]
  14. M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B77(3), 035122 (2008).
    [CrossRef]
  15. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
    [CrossRef] [PubMed]
  16. D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express17(19), 16535–16542 (2009).
    [CrossRef] [PubMed]
  17. 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]
  18. A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. J. Phys. Appl. Phys.28(2), 153–157 (2004).
    [CrossRef]
  19. 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]
  20. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express16(15), 11555–11567 (2008).
    [CrossRef] [PubMed]
  21. J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
    [CrossRef]
  22. D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett.93(25), 251111 (2008).
    [CrossRef]
  23. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express18(2), 767–772 (2010).
    [CrossRef] [PubMed]
  24. V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B82(11), 113102 (2010).
    [CrossRef]
  25. V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys.14(3), 033007 (2012).
    [CrossRef]
  26. Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009).
    [CrossRef] [PubMed]
  27. W. H. Wee and J. B. Pendry, “Shrinking optical devices,” New J. Phys.11(7), 073033 (2009).
    [CrossRef]
  28. W. Lu, Z. Lin, H. Chen, and C. T. Chan, “Transformation media based super focusing antenna,” J. Phys. D Appl. Phys.42(21), 212002 (2009).
    [CrossRef]
  29. Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online4(7), 795–800 (2008).
    [CrossRef]
  30. J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett.94(19), 194101 (2009).
    [CrossRef]
  31. B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett.94(24), 244102 (2009).
    [CrossRef]
  32. P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B83(15), 155108 (2011).
    [CrossRef]
  33. P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Coordinate transformation based ultra-directive emission,” Electron. Lett.47(10), 580–582 (2011).
    [CrossRef]
  34. Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B84(16), 165111 (2011).
    [CrossRef]
  35. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express19(21), 20551–20556 (2011).
    [CrossRef] [PubMed]

2012 (1)

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys.14(3), 033007 (2012).
[CrossRef]

2011 (4)

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B83(15), 155108 (2011).
[CrossRef]

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Coordinate transformation based ultra-directive emission,” Electron. Lett.47(10), 580–582 (2011).
[CrossRef]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B84(16), 165111 (2011).
[CrossRef]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express19(21), 20551–20556 (2011).
[CrossRef] [PubMed]

2010 (3)

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express18(2), 767–772 (2010).
[CrossRef] [PubMed]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B82(11), 113102 (2010).
[CrossRef]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
[CrossRef] [PubMed]

2009 (9)

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express17(19), 16535–16542 (2009).
[CrossRef] [PubMed]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett.102(18), 183903 (2009).
[CrossRef] [PubMed]

R. A. Crudo and J. G. O’Brien, “Metric approach to transformation optics,” Phys. Rev. A80(3), 033824 (2009).
[CrossRef]

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt.53, 69–152 (2009).
[CrossRef]

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett.94(19), 194101 (2009).
[CrossRef]

B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett.94(24), 244102 (2009).
[CrossRef]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

W. H. Wee and J. B. Pendry, “Shrinking optical devices,” New J. Phys.11(7), 073033 (2009).
[CrossRef]

W. Lu, Z. Lin, H. Chen, and C. T. Chan, “Transformation media based super focusing antenna,” J. Phys. D Appl. Phys.42(21), 212002 (2009).
[CrossRef]

2008 (8)

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online4(7), 795–800 (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]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express16(15), 11555–11567 (2008).
[CrossRef] [PubMed]

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett.93(25), 251111 (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(11), 115023 (2008).
[CrossRef]

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B77(3), 035122 (2008).
[CrossRef]

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. Appl.6(1), 87–95 (2008).
[CrossRef]

2007 (2)

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett.32(9), 1069–1071 (2007).
[CrossRef] [PubMed]

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]

2006 (5)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

2005 (1)

2004 (1)

A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. J. Phys. Appl. Phys.28(2), 153–157 (2004).
[CrossRef]

2003 (1)

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter15(37), 6345–6364 (2003).
[CrossRef]

Allen, J.

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett.94(19), 194101 (2009).
[CrossRef]

B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett.94(24), 244102 (2009).
[CrossRef]

Ao, X.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett.102(18), 183903 (2009).
[CrossRef] [PubMed]

Burokur, S. N.

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B83(15), 155108 (2011).
[CrossRef]

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Coordinate transformation based ultra-directive emission,” Electron. Lett.47(10), 580–582 (2011).
[CrossRef]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express19(21), 20551–20556 (2011).
[CrossRef] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express18(2), 767–772 (2010).
[CrossRef] [PubMed]

Chan, C. T.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

W. Lu, Z. Lin, H. Chen, and C. T. Chan, “Transformation media based super focusing antenna,” J. Phys. D Appl. Phys.42(21), 212002 (2009).
[CrossRef]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett.102(18), 183903 (2009).
[CrossRef] [PubMed]

Chen, H.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett.102(18), 183903 (2009).
[CrossRef] [PubMed]

W. Lu, Z. Lin, H. Chen, and C. T. Chan, “Transformation media based super focusing antenna,” J. Phys. D Appl. Phys.42(21), 212002 (2009).
[CrossRef]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online4(7), 795–800 (2008).
[CrossRef]

Chen, S.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett.102(18), 183903 (2009).
[CrossRef] [PubMed]

Crudo, R. A.

R. A. Crudo and J. G. O’Brien, “Metric approach to transformation optics,” Phys. Rev. A80(3), 033824 (2009).
[CrossRef]

Cummer, S. A.

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett.94(19), 194101 (2009).
[CrossRef]

B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett.94(24), 244102 (2009).
[CrossRef]

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. 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]

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Danckaert, J.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys.14(3), 033007 (2012).
[CrossRef]

de Lustrac, A.

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B83(15), 155108 (2011).
[CrossRef]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express19(21), 20551–20556 (2011).
[CrossRef] [PubMed]

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Coordinate transformation based ultra-directive emission,” Electron. Lett.47(10), 580–582 (2011).
[CrossRef]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express18(2), 767–772 (2010).
[CrossRef] [PubMed]

Germain, D.

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Coordinate transformation based ultra-directive emission,” Electron. Lett.47(10), 580–582 (2011).
[CrossRef]

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B83(15), 155108 (2011).
[CrossRef]

Ginis, V.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys.14(3), 033007 (2012).
[CrossRef]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B82(11), 113102 (2010).
[CrossRef]

Gralak, B.

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]

Gregory, M. D.

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B84(16), 165111 (2011).
[CrossRef]

Guenneau, S.

Han, D.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Hou, B.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett.102(18), 183903 (2009).
[CrossRef] [PubMed]

Huangfu, J.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

Jiang, Z. H.

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B84(16), 165111 (2011).
[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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kong, F.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

Kong, J. A.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online4(7), 795–800 (2008).
[CrossRef]

Kundtz, N.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
[CrossRef] [PubMed]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express17(19), 16535–16542 (2009).
[CrossRef] [PubMed]

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett.94(19), 194101 (2009).
[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]

Kwon, D.-H.

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

Lai, Y.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009).
[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(18), 183901 (2007).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt.53, 69–152 (2009).
[CrossRef]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Lin, Z.

W. Lu, Z. Lin, H. Chen, and C. T. Chan, “Transformation media based super focusing antenna,” J. Phys. D Appl. Phys.42(21), 212002 (2009).
[CrossRef]

Lu, W.

W. Lu, Z. Lin, H. Chen, and C. T. Chan, “Transformation media based super focusing antenna,” J. Phys. D Appl. Phys.42(21), 212002 (2009).
[CrossRef]

Luo, Y.

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online4(7), 795–800 (2008).
[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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Ng, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Nicolet, A.

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett.32(9), 1069–1071 (2007).
[CrossRef] [PubMed]

A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. J. Phys. Appl. Phys.28(2), 153–157 (2004).
[CrossRef]

O’Brien, J. G.

R. A. Crudo and J. G. O’Brien, “Metric approach to transformation optics,” Phys. Rev. A80(3), 033824 (2009).
[CrossRef]

Pendry, J. B.

W. H. Wee and J. B. Pendry, “Shrinking optical devices,” New J. Phys.11(7), 073033 (2009).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett.93(25), 251111 (2008).
[CrossRef]

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. Appl.6(1), 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. Express16(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]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett.32(9), 1069–1071 (2007).
[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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

S. Guenneau, B. Gralak, and J. B. Pendry, “Perfect corner reflector,” Opt. Lett.30(10), 1204–1206 (2005).
[CrossRef] [PubMed]

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter15(37), 6345–6364 (2003).
[CrossRef]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt.53, 69–152 (2009).
[CrossRef]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

Popa, B. I.

B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett.94(24), 244102 (2009).
[CrossRef]

Psaltis, D.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B77(3), 035122 (2008).
[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. Express16(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. 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. Appl.6(1), 87–95 (2008).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett.93(25), 251111 (2008).
[CrossRef]

Ramakrishna, S. A.

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter15(37), 6345–6364 (2003).
[CrossRef]

Ran, L.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online4(7), 795–800 (2008).
[CrossRef]

Roberts, D. A.

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett.94(19), 194101 (2009).
[CrossRef]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express17(19), 16535–16542 (2009).
[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. Express16(15), 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. Appl.6(1), 87–95 (2008).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett.93(25), 251111 (2008).
[CrossRef]

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. 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]

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
[CrossRef] [PubMed]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express17(19), 16535–16542 (2009).
[CrossRef] [PubMed]

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett.94(19), 194101 (2009).
[CrossRef]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett.93(25), 251111 (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]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express16(15), 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. Appl.6(1), 87–95 (2008).
[CrossRef]

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Soukoulis, C. M.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys.14(3), 033007 (2012).
[CrossRef]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B82(11), 113102 (2010).
[CrossRef]

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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Tassin, P.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys.14(3), 033007 (2012).
[CrossRef]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B82(11), 113102 (2010).
[CrossRef]

Tichit, P.-H.

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B83(15), 155108 (2011).
[CrossRef]

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Coordinate transformation based ultra-directive emission,” Electron. Lett.47(10), 580–582 (2011).
[CrossRef]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express19(21), 20551–20556 (2011).
[CrossRef] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express18(2), 767–772 (2010).
[CrossRef] [PubMed]

Tsang, M.

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B77(3), 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(18), 183901 (2007).
[CrossRef] [PubMed]

Veretennicoff, I.

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys.14(3), 033007 (2012).
[CrossRef]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B82(11), 113102 (2010).
[CrossRef]

Wang, D.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

Wee, W. H.

W. H. Wee and J. B. Pendry, “Shrinking optical devices,” New J. Phys.11(7), 073033 (2009).
[CrossRef]

Wen, W.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett.102(18), 183903 (2009).
[CrossRef] [PubMed]

Werner, D. H.

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B84(16), 165111 (2011).
[CrossRef]

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

Wu, B.-I.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

Xi, S.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

Xiao, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Zhang, J.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online4(7), 795–800 (2008).
[CrossRef]

Zhang, Z.-Q.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

Zolla, F.

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett.32(9), 1069–1071 (2007).
[CrossRef] [PubMed]

A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. J. Phys. Appl. Phys.28(2), 153–157 (2004).
[CrossRef]

Appl. Phys. Lett. (3)

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett.93(25), 251111 (2008).
[CrossRef]

J. Allen, N. Kundtz, D. A. Roberts, S. A. Cummer, and D. R. Smith, “Electromagnetic source transformations using superellipse equations,” Appl. Phys. Lett.94(19), 194101 (2009).
[CrossRef]

B. I. Popa, J. Allen, and S. A. Cummer, “Conformal array design with transformation electromagnetics,” Appl. Phys. Lett.94(24), 244102 (2009).
[CrossRef]

Electron. Lett. (1)

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Coordinate transformation based ultra-directive emission,” Electron. Lett.47(10), 580–582 (2011).
[CrossRef]

Eur. J. Phys. Appl. Phys. (1)

A. Nicolet, F. Zolla, and S. Guenneau, “A finite element modelling for twisted electromagnetic waveguides,” Eur. J. Phys. Appl. Phys.28(2), 153–157 (2004).
[CrossRef]

J. Appl. Phys. (1)

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguide,” J. Appl. Phys.104(1), 014502 (2008).
[CrossRef]

J. Phys. Condens. Matter (1)

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter15(37), 6345–6364 (2003).
[CrossRef]

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

W. Lu, Z. Lin, H. Chen, and C. T. Chan, “Transformation media based super focusing antenna,” J. Phys. D Appl. Phys.42(21), 212002 (2009).
[CrossRef]

Nat. Mater. (1)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010).
[CrossRef] [PubMed]

New J. Phys. (4)

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

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

W. H. Wee and J. B. Pendry, “Shrinking optical devices,” New J. Phys.11(7), 073033 (2009).
[CrossRef]

V. Ginis, P. Tassin, J. Danckaert, C. M. Soukoulis, and I. Veretennicoff, “Creating electromagnetic cavities using transformation optics,” New J. Phys.14(3), 033007 (2012).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Photon. Nanostruct.: Fundam. Appl. (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. Appl.6(1), 87–95 (2008).
[CrossRef]

Phys. Rev. A (1)

R. A. Crudo and J. G. O’Brien, “Metric approach to transformation optics,” Phys. Rev. A80(3), 033824 (2009).
[CrossRef]

Phys. Rev. B (4)

M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B77(3), 035122 (2008).
[CrossRef]

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B84(16), 165111 (2011).
[CrossRef]

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B83(15), 155108 (2011).
[CrossRef]

V. Ginis, P. Tassin, C. M. Soukoulis, and I. Veretennicoff, “Confining light in deep subwavelength electromagnetic cavities,” Phys. Rev. B82(11), 113102 (2010).
[CrossRef]

Phys. Rev. Lett. (4)

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009).
[CrossRef] [PubMed]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett.102(18), 183903 (2009).
[CrossRef] [PubMed]

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. 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]

PIERS Online (1)

Y. Luo, J. Zhang, L. Ran, H. Chen, and J. A. Kong, “Controlling the emission of electromagnetic source,” PIERS Online4(7), 795–800 (2008).
[CrossRef]

Prog. Opt. (1)

U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt.53, 69–152 (2009).
[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,” Science314(5801), 977–980 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Representation of the proposed coordinate transformation: (a) initial and (b) virtual space. (c) The region 1 of the material enlarges the aperture of the source whereas region 2 allows matching the impedance with that of the surrounding environment. (d) Operating principle of the transformation, which consists in firstly a compression of the central space (0 < r’ < R1) and secondly, an expansion to match the space metric (R1 < r’ < R2). Continuity of the transformations is assured at the boundary of the compressed region (point A) and at the outer boundary of the device (point B).

Fig. 2
Fig. 2

(a) Representation of the transformations in regions 1 and 2. The blue and red traces correspond respectively to q1 = 1/40 and q1 = 1/16 and the continuous and dashed traces correspond respectively to a linear and exponential transformations. (b)–(c) Variation of the components in Cartesian coordinates of the matching region 2. The permittivity and permeability are respectively plotted for the linear transformation with q1 = 1/40, R1 = 2 mm (continuous blue traces case) and for the exponential transformation with q1 = 1/16, q2 = 15 and R1 = 5 mm (continuous and dashed red traces case).

Fig. 3
Fig. 3

Electric field distribution at 10 GHz of a linear source: (a) with dimension d = 80 mm radiating in free space, (b) with dimension d = 2 mm embedded in a metamaterial shell, and (c) with dimension d = 2 mm radiating in free space. Electric field distribution at 10 GHz of a crossed-type source: (d) with dimension d = 80 mm radiating in free space, (e) with dimension d = 2 mm embedded in a metamaterial shell, and (f) with dimension d = 2 mm radiating in free space. The metamaterial shell is defined by a double linear transformation where R1 = 2 mm, R2 = 45 mm and q1 = 1/40.

Fig. 4
Fig. 4

(a)-(c) Norm of the electric field of a line source with dimension d = 2 mm. The metamaterial shell is defined by a linear transformation with q1 = 1/40 followed by an exponential one with q2 = 15 where R1 = 2 mm and R2 = 45 mm. (d)-(f) Norm of the electric field of a crossed-type source with dimension d = 2 mm. The metamaterial shell is defined by a linear transformation with q1 = 1/16 followed by an exponential one with q2 = 15 where R1 = 5 mm and R2 = 45 mm.

Fig. 5
Fig. 5

Norm of the electric field of a line source with dimension d = 2 mm. The metamaterial shell is defined by only a compression region presenting a linear transformation with q1 = 1/40. No matching region is used in this case.

Fig. 6
Fig. 6

3 sources with length L = 12.5 mm spaced by a distance a = 5 mm and with a 30° phase shift between each element radiate in free space (a, d) at 10 GHz (z-components of the electric field). When all the dimensions are reduced by a factor of 25 (L = 0.5 mm and a = 0.2 mm) the electric field distribution (z-component) in free space is represented in (b). Embedding the miniaturized sources in the metamaterial shell defined by a double linear transformation leads to a similar radiation pattern as the original sized sources as shown in (c) with perfect matching to free space (e).

Equations (6)

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

{ r'= f i ( r,θ ) θ'=θ z'=z
J cyl ¯ ¯ =( r' r r' θ r' z θ' r θ' θ θ' z z' r z' θ z' z )=( f i,r f i,θ 0 0 1 0 0 0 1 )
J i ¯ ¯ =( f i,r f i,θ r 0 0 r' r 0 0 0 1 )
{ ( ψ rr ) i = r f i,r r' + f i,θ 2 rr' f i,r ( ψ rθ ) i = f i,θ r f i,r ( ψ θθ ) i = r' f i,r r ( ψ zz ) i = r r' f i,r
ε ¯ ¯ =( ψ xx ψ xy 0 ψ yx ψ yy 0 0 0 ψ zz ) ε 0 μ ¯ ¯ =( ψ xx ψ xy 0 ψ yx ψ yy 0 0 0 ψ zz ) μ 0 with { ψ xx = ψ rr cos 2 ( θ )+ ψ θθ sin 2 ( θ ) ψ rθ sin( 2θ ) ψ xy = ψ yx =( ψ rr ψ θθ )sin( θ )cos( θ )+ ψ rθ cos( 2θ ) ψ yy = ψ rr sin 2 ( θ )+ ψ θθ cos 2 ( θ )+ ψ rθ sin( 2θ )
α= R 2 R 1 q 1 R 2 R 1 and γ=1+ R 2 ( 1α ) R 1 α

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