Abstract

Transformation optics have developed rapidly in recent years as a novel method to control the propagation of electromagnetic waves or light rays, while conformal mapping is a powerful tool used for decades solving problems in fields. In this paper, following the similarity of both methods on manipulating coordinate meshes, we design transformation optical devices with the help of applications of conformal mapping, e.g., steady state heat transfer and electrostatics. We propose an isotropic optical lens, which transforms a radiating line source into a directional antenna, and both full-wave simulations and geometric interpretations are presented. We also give an alternative derivation of the isotropic waveguide bends, which shows a clear picture from the viewpoint of transformation. All the refractive indices we obtain are larger than one, implying feasibility and broadband property. Using the analog between different physical problems may provide a simple way to design feasible optical devices.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef] [PubMed]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
  3. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
    [CrossRef] [PubMed]
  4. 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]
  5. E. Cojocaru, “Exact analytical approaches for elliptic cylindrical invisibility cloaks,” J. Opt. Soc. Am. B 26, 1119–1128 (2009).
    [CrossRef]
  6. A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33, 1584–1586 (2008).
    [CrossRef] [PubMed]
  7. K. Yao, C. Li, and F. Li, “Two-dimensional dissimilar electromagnetic cloak for irregular regions,” Appl. Phys. B 96, 355–361 (2009).
    [CrossRef]
  8. Z. Liang, P. Yao, X. Sun, and X. Jiang, “Physical picture and the essential elements of the dynamical process for dispersive cloaking structures,” Appl. Phys. Lett. 92, 131118 (2008).
    [CrossRef]
  9. Y. Zhao, C. Argyropoulos, and Y. Hao, “Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures,” Opt. Express 16, 6717–6730 (2008).
    [CrossRef] [PubMed]
  10. 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, 253902 (2009).
    [CrossRef] [PubMed]
  11. U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323, 110–112 (2009).
    [CrossRef]
  12. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
    [CrossRef] [PubMed]
  13. R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express 18, 24361–24367 (2010).
    [CrossRef] [PubMed]
  14. N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105, 193902 (2010).
    [CrossRef]
  15. U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys. 11, 093040 (2009).
    [CrossRef]
  16. Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105, 104913(2009).
    [CrossRef]
  17. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912(2009).
    [CrossRef]
  18. M. Schimiele, V. S. Varma, C. Rockstuhl, and F. Lederer, “Designing optical elements from isotropic materials by using transformation optics,” Phys. Rev. A 81, 033837 (2010).
    [CrossRef]
  19. D. R. Smith, Y. Urzhumov, N. B. Kundtz, and N. I. Landy, “Enhancing imaging systems using transformation optics,” Opt. Express 18, 21238–21251 (2010).
    [CrossRef] [PubMed]
  20. R. Schinzinger and P. A. A. Laura, Conformal Mapping: Methods and Applications (Dover, 2003).
  21. U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009)
    [CrossRef]
  22. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  23. A. D. Yaghjian, S. Maci, and E. Martini, “Characteristic wave velocities in spherical electromagnetic cloaks,” New J. Phys. 11, 113011 (2009).
    [CrossRef]
  24. J. Zhang, Y. Luo, H. Chen, and B.-I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16, 10962–10967 (2008).
    [CrossRef] [PubMed]
  25. W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
    [CrossRef]
  26. M. J. Ablowitz and A. S. Fokas, Complex Variables (Cambridge University, 2003).
    [CrossRef]
  27. Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “Design of arbitrarily directional cloaks by solving the Laplace’s equation,” J. Appl. Phys. 107, 124502 (2010).
    [CrossRef]
  28. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10, 1991–1997 (2010).
    [CrossRef] [PubMed]
  29. T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nature Nanotechnol. 6, 151–155 (2011).
    [CrossRef]
  30. A. Climente, D. Torrent, and J. Sa´nchez-Dehesa, “Sound focusing by gradient index sonic lenses,” Appl. Phys. Lett. 97, 104103 (2010).
    [CrossRef]
  31. R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).
  32. 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, 251111 (2008).
    [CrossRef]
  33. N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17, 14872–14879(2009).
    [CrossRef] [PubMed]
  34. R. P. Feynman, R. B. Leighton, and M. Sands, “The electric field in various circumstances,” in The Feynman Lectures on Physics (Addison-Wesley, 1964), Vol.  2.

2011

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nature Nanotechnol. 6, 151–155 (2011).
[CrossRef]

2010

A. Climente, D. Torrent, and J. Sa´nchez-Dehesa, “Sound focusing by gradient index sonic lenses,” Appl. Phys. Lett. 97, 104103 (2010).
[CrossRef]

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “Design of arbitrarily directional cloaks by solving the Laplace’s equation,” J. Appl. Phys. 107, 124502 (2010).
[CrossRef]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10, 1991–1997 (2010).
[CrossRef] [PubMed]

R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express 18, 24361–24367 (2010).
[CrossRef] [PubMed]

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

M. Schimiele, V. S. Varma, C. Rockstuhl, and F. Lederer, “Designing optical elements from isotropic materials by using transformation optics,” Phys. Rev. A 81, 033837 (2010).
[CrossRef]

D. R. Smith, Y. Urzhumov, N. B. Kundtz, and N. I. Landy, “Enhancing imaging systems using transformation optics,” Opt. Express 18, 21238–21251 (2010).
[CrossRef] [PubMed]

2009

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

A. D. Yaghjian, S. Maci, and E. Martini, “Characteristic wave velocities in spherical electromagnetic cloaks,” New J. Phys. 11, 113011 (2009).
[CrossRef]

U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys. 11, 093040 (2009).
[CrossRef]

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105, 104913(2009).
[CrossRef]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912(2009).
[CrossRef]

E. Cojocaru, “Exact analytical approaches for elliptic cylindrical invisibility cloaks,” J. Opt. Soc. Am. B 26, 1119–1128 (2009).
[CrossRef]

K. Yao, C. Li, and F. Li, “Two-dimensional dissimilar electromagnetic cloak for irregular regions,” Appl. Phys. B 96, 355–361 (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, 253902 (2009).
[CrossRef] [PubMed]

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

N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17, 14872–14879(2009).
[CrossRef] [PubMed]

2008

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, 251111 (2008).
[CrossRef]

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

Z. Liang, P. Yao, X. Sun, and X. Jiang, “Physical picture and the essential elements of the dynamical process for dispersive cloaking structures,” Appl. Phys. Lett. 92, 131118 (2008).
[CrossRef]

Y. Zhao, C. Argyropoulos, and Y. Hao, “Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures,” Opt. Express 16, 6717–6730 (2008).
[CrossRef] [PubMed]

A. Nicolet, F. Zolla, and S. Guenneau, “Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section,” Opt. Lett. 33, 1584–1586 (2008).
[CrossRef] [PubMed]

J. Zhang, Y. Luo, H. Chen, and B.-I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16, 10962–10967 (2008).
[CrossRef] [PubMed]

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

2007

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]

2006

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

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Ablowitz, M. J.

M. J. Ablowitz and A. S. Fokas, Complex Variables (Cambridge University, 2003).
[CrossRef]

Argyropoulos, C.

Bai, J.

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “Design of arbitrarily directional cloaks by solving the Laplace’s equation,” J. Appl. Phys. 107, 124502 (2010).
[CrossRef]

Bartal, G.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10, 1991–1997 (2010).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Burokur, S. N.

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912(2009).
[CrossRef]

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, 253902 (2009).
[CrossRef] [PubMed]

Chen, H.

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, 253902 (2009).
[CrossRef] [PubMed]

J. Zhang, Y. Luo, H. Chen, and B.-I. Wu, “Manipulating the directivity of antennas with metamaterial,” Opt. Express 16, 10962–10967 (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]

Cheng, Q.

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

Climente, A.

A. Climente, D. Torrent, and J. Sa´nchez-Dehesa, “Sound focusing by gradient index sonic lenses,” Appl. Phys. Lett. 97, 104103 (2010).
[CrossRef]

Cojocaru, E.

Cui, T. J.

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “Design of arbitrarily directional cloaks by solving the Laplace’s equation,” J. Appl. Phys. 107, 124502 (2010).
[CrossRef]

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105, 104913(2009).
[CrossRef]

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

de Lustrac, A.

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912(2009).
[CrossRef]

Feynman, R. P.

R. P. Feynman, R. B. Leighton, and M. Sands, “The electric field in various circumstances,” in The Feynman Lectures on Physics (Addison-Wesley, 1964), Vol.  2.

Fokas, A. S.

M. J. Ablowitz and A. S. Fokas, Complex Variables (Cambridge University, 2003).
[CrossRef]

Guenneau, S.

Halimeh, J. C.

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, 253902 (2009).
[CrossRef] [PubMed]

Hao, Y.

Jiang, W. X.

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

Jiang, X.

Z. Liang, P. Yao, X. Sun, and X. Jiang, “Physical picture and the essential elements of the dynamical process for dispersive cloaking structures,” Appl. Phys. Lett. 92, 131118 (2008).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Kong, J. A.

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]

Kundtz, N.

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

Kundtz, N. B.

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, 253902 (2009).
[CrossRef] [PubMed]

Landy, N. I.

Laura, P. A. A.

R. Schinzinger and P. A. A. Laura, Conformal Mapping: Methods and Applications (Dover, 2003).

Lederer, F.

M. Schimiele, V. S. Varma, C. Rockstuhl, and F. Lederer, “Designing optical elements from isotropic materials by using transformation optics,” Phys. Rev. A 81, 033837 (2010).
[CrossRef]

Leighton, R. B.

R. P. Feynman, R. B. Leighton, and M. Sands, “The electric field in various circumstances,” in The Feynman Lectures on Physics (Addison-Wesley, 1964), Vol.  2.

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

U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys. 11, 093040 (2009).
[CrossRef]

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

Li, C.

K. Yao, C. Li, and F. Li, “Two-dimensional dissimilar electromagnetic cloak for irregular regions,” Appl. Phys. B 96, 355–361 (2009).
[CrossRef]

Li, F.

K. Yao, C. Li, and F. Li, “Two-dimensional dissimilar electromagnetic cloak for irregular regions,” Appl. Phys. B 96, 355–361 (2009).
[CrossRef]

Li, J.

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

Liang, Z.

Z. Liang, P. Yao, X. Sun, and X. Jiang, “Physical picture and the essential elements of the dynamical process for dispersive cloaking structures,” Appl. Phys. Lett. 92, 131118 (2008).
[CrossRef]

Liu, Y.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nature Nanotechnol. 6, 151–155 (2011).
[CrossRef]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10, 1991–1997 (2010).
[CrossRef] [PubMed]

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).

Luo, Y.

Ma, H. F.

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

Maci, S.

A. D. Yaghjian, S. Maci, and E. Martini, “Characteristic wave velocities in spherical electromagnetic cloaks,” New J. Phys. 11, 113011 (2009).
[CrossRef]

Martini, E.

A. D. Yaghjian, S. Maci, and E. Martini, “Characteristic wave velocities in spherical electromagnetic cloaks,” New J. Phys. 11, 113011 (2009).
[CrossRef]

Mei, Z. L.

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “Design of arbitrarily directional cloaks by solving the Laplace’s equation,” J. Appl. Phys. 107, 124502 (2010).
[CrossRef]

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105, 104913(2009).
[CrossRef]

Mikkelsen, M. H.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nature Nanotechnol. 6, 151–155 (2011).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

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, 253902 (2009).
[CrossRef] [PubMed]

Nicolet, A.

Niu, T. M.

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “Design of arbitrarily directional cloaks by solving the Laplace’s equation,” J. Appl. Phys. 107, 124502 (2010).
[CrossRef]

Padilla, W. J.

Pendry, J. B.

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, 251111 (2008).
[CrossRef]

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

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

Philbin, T. G.

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

Rahm, M.

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, 251111 (2008).
[CrossRef]

Roberts, D. A.

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, 251111 (2008).
[CrossRef]

Rockstuhl, C.

M. Schimiele, V. S. Varma, C. Rockstuhl, and F. Lederer, “Designing optical elements from isotropic materials by using transformation optics,” Phys. Rev. A 81, 033837 (2010).
[CrossRef]

Sa´nchez-Dehesa, J.

A. Climente, D. Torrent, and J. Sa´nchez-Dehesa, “Sound focusing by gradient index sonic lenses,” Appl. Phys. Lett. 97, 104103 (2010).
[CrossRef]

Sands, M.

R. P. Feynman, R. B. Leighton, and M. Sands, “The electric field in various circumstances,” in The Feynman Lectures on Physics (Addison-Wesley, 1964), Vol.  2.

Schimiele, M.

M. Schimiele, V. S. Varma, C. Rockstuhl, and F. Lederer, “Designing optical elements from isotropic materials by using transformation optics,” Phys. Rev. A 81, 033837 (2010).
[CrossRef]

Schinzinger, R.

R. Schinzinger and P. A. A. Laura, Conformal Mapping: Methods and Applications (Dover, 2003).

Schmied, R.

Schurig, D.

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Smith, D. R.

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105, 193902 (2010).
[CrossRef]

D. R. Smith, Y. Urzhumov, N. B. Kundtz, and N. I. Landy, “Enhancing imaging systems using transformation optics,” Opt. Express 18, 21238–21251 (2010).
[CrossRef] [PubMed]

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, 251111 (2008).
[CrossRef]

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Sun, X.

Z. Liang, P. Yao, X. Sun, and X. Jiang, “Physical picture and the essential elements of the dynamical process for dispersive cloaking structures,” Appl. Phys. Lett. 92, 131118 (2008).
[CrossRef]

Tichit, P.-H.

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912(2009).
[CrossRef]

Torrent, D.

A. Climente, D. Torrent, and J. Sa´nchez-Dehesa, “Sound focusing by gradient index sonic lenses,” Appl. Phys. Lett. 97, 104103 (2010).
[CrossRef]

Tyc, T.

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

Urzhumov, Y.

Valentine, J.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nature Nanotechnol. 6, 151–155 (2011).
[CrossRef]

Varma, V. S.

M. Schimiele, V. S. Varma, C. Rockstuhl, and F. Lederer, “Designing optical elements from isotropic materials by using transformation optics,” Phys. Rev. A 81, 033837 (2010).
[CrossRef]

Wegener, M.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Wu, B.-I.

Wu, B-I.

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]

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, 253902 (2009).
[CrossRef] [PubMed]

Yaghjian, A. D.

A. D. Yaghjian, S. Maci, and E. Martini, “Characteristic wave velocities in spherical electromagnetic cloaks,” New J. Phys. 11, 113011 (2009).
[CrossRef]

Yang, X. M.

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

Yao, K.

K. Yao, C. Li, and F. Li, “Two-dimensional dissimilar electromagnetic cloak for irregular regions,” Appl. Phys. B 96, 355–361 (2009).
[CrossRef]

Yao, P.

Z. Liang, P. Yao, X. Sun, and X. Jiang, “Physical picture and the essential elements of the dynamical process for dispersive cloaking structures,” Appl. Phys. Lett. 92, 131118 (2008).
[CrossRef]

Zentgraf, T.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nature Nanotechnol. 6, 151–155 (2011).
[CrossRef]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10, 1991–1997 (2010).
[CrossRef] [PubMed]

Zhang, B.

H. Chen, B-I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[CrossRef] [PubMed]

Zhang, J.

Zhang, X.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nature Nanotechnol. 6, 151–155 (2011).
[CrossRef]

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10, 1991–1997 (2010).
[CrossRef] [PubMed]

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, 253902 (2009).
[CrossRef] [PubMed]

Zhao, Y.

Zolla, F.

Appl. Phys. B

K. Yao, C. Li, and F. Li, “Two-dimensional dissimilar electromagnetic cloak for irregular regions,” Appl. Phys. B 96, 355–361 (2009).
[CrossRef]

Appl. Phys. Lett.

Z. Liang, P. Yao, X. Sun, and X. Jiang, “Physical picture and the essential elements of the dynamical process for dispersive cloaking structures,” Appl. Phys. Lett. 92, 131118 (2008).
[CrossRef]

W. X. Jiang, T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, “Layered high-gain lens antennas via discrete optical transformation,” Appl. Phys. Lett. 93, 221906 (2008).
[CrossRef]

A. Climente, D. Torrent, and J. Sa´nchez-Dehesa, “Sound focusing by gradient index sonic lenses,” Appl. Phys. Lett. 97, 104103 (2010).
[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, 251111 (2008).
[CrossRef]

J. Appl. Phys.

Z. L. Mei, J. Bai, T. M. Niu, and T. J. Cui, “Design of arbitrarily directional cloaks by solving the Laplace’s equation,” J. Appl. Phys. 107, 124502 (2010).
[CrossRef]

Z. L. Mei and T. J. Cui, “Arbitrary bending of electromagnetic waves using isotropic materials,” J. Appl. Phys. 105, 104913(2009).
[CrossRef]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912(2009).
[CrossRef]

J. Opt. Soc. Am. B

Nano Lett.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10, 1991–1997 (2010).
[CrossRef] [PubMed]

Nature Nanotechnol.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nature Nanotechnol. 6, 151–155 (2011).
[CrossRef]

New J. Phys.

A. D. Yaghjian, S. Maci, and E. Martini, “Characteristic wave velocities in spherical electromagnetic cloaks,” New J. Phys. 11, 113011 (2009).
[CrossRef]

U. Leonhardt, “Perfect imaging without negative refraction,” New J. Phys. 11, 093040 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

M. Schimiele, V. S. Varma, C. Rockstuhl, and F. Lederer, “Designing optical elements from isotropic materials by using transformation optics,” Phys. Rev. A 81, 033837 (2010).
[CrossRef]

Phys. Rev. Lett.

N. I. Landy, N. Kundtz, and D. R. Smith, “Designing three-dimensional transformation optical media using quasiconformal coordinate transformations,” Phys. Rev. Lett. 105, 193902 (2010).
[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]

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

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, 253902 (2009).
[CrossRef] [PubMed]

Prog. Opt.

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

Science

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

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

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Other

R. Schinzinger and P. A. A. Laura, Conformal Mapping: Methods and Applications (Dover, 2003).

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

M. J. Ablowitz and A. S. Fokas, Complex Variables (Cambridge University, 2003).
[CrossRef]

R. P. Feynman, R. B. Leighton, and M. Sands, “The electric field in various circumstances,” in The Feynman Lectures on Physics (Addison-Wesley, 1964), Vol.  2.

R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Mapping function in the form of Eq. (4) connects different configurations in (a) the virtual plane and (b) the physical plane, where the corresponding lines are depicted in the same color. These curved patterns can be interpreted to different physical problems, e.g., potential fields and radiations. (c) The index variation in the hemicylinder.

Fig. 2
Fig. 2

Resulting electric field distribution obtained at the frequency of (a)  1.0 GHz , and (b)  2.5 GHz . Power flow lines (correspond to light rays) colored in black show the expected performance in directivity.

Fig. 3
Fig. 3

Normalized radiation patterns of the hemicylindrical lens antenna at 1.0 GHz (in blue) and 2.5 GHz (in red). The direction of emission is defined as 0 ° .

Fig. 4
Fig. 4

(a) Stereographic projection shown in the cross section, which gives a one-to-one correspondence between the points on the Riemann sphere and on the extended complex plane. Curves, e.g., light rays on the sphere can be conformally mapped to the plane. (b) A point source at the south pole leads to the config uration of radial emission and circular wavefronts on the plane, corresponding to Fig. 1a. (c) Under Eq. (4), the surface of the sphere is vertically rotated by 90 ° , and the source is transformed onto the equator; hence light rays or geodesics on the former southern hemisphere (colored in blue) are now mapped to the configuration in Fig. 1b.

Fig. 5
Fig. 5

Configurations of (a) a planar capacitor and (b) a cylindrical capacitor can be used to describe the wave propagation in waveguides. The colored solid curves represent either equipotential or power flow lines, and the dashed lines indicate electric field lines or wavefronts. (c) Magnetic field distribution inside the waveguide bend of 90 ° at 2.4 GHz . Power flow lines are smoothly bent as expected.

Equations (8)

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

2 ψ + ω 2 n 0 2 c 2 | f ' ( w ) | 2 ψ = 0.
ε ¯ ¯ ε 0 = μ ¯ ¯ μ 0 = Λ Λ T det ( Λ ) = diag { 1 , 1 , | f ' ( w ) | 2 } ,
s ^ = S n = S | S | .
z = i i + w i w .
n ( x , y ) = 2 n 0 x 2 + ( 1 + y ) 2 ,
n = 2 n 0 x 2 + y 2 + ( 1 + z ) 2 .
z = e w / A ,
d u 2 + d v 2 = A 2 x 2 + y 2 ( d x 2 + d y 2 ) = A 2 ρ 2 ( d x 2 + d y 2 ) ,

Metrics