Abstract

Integration of transformation optics with development of metamaterials offers great opportunities to create exotic material with electromagnetic functionality absent from nature. It has already led to several significant advancements in physical conceptions and technological applications such as invisible cloaking. Unfortunately practical application is often restricted by the complex requirements on material properties imposed by the general optical transformation theory. It is therefore necessary to relax the stringent requirements of materials properties in order to practicably use the power of transformation optics to design exotic optical devices. Development of new coordinate transformation mathematics to compromise between the stringent materials properties and the ultimate performance required by a useful novel device is required. In this work the authors employed strict conformal transformation to design physical materials that could guide light in a predetermined way. A simple and efficient numerical approach based on unusual inverse transformation is proposed here to quickly solve partial differential equations and construct the mapping relationship. The results showed that a transformed optical device could be made by purely using isotropic dielectric materials. Two application examples were numerically proposed to verify the versatility of conformal transformation and the robustness of the inverse approach. One was a 90° waveguide beam bend, and the other was a waveguide-type beam splitter or coupler.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780-1782 (2006).
    [CrossRef] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777-1780 (2006).
    [CrossRef] [PubMed]
  3. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
    [CrossRef]
  4. 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]
  5. D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15, 14772 (2007).
    [CrossRef] [PubMed]
  6. O. Ozgun and M. Kuzuoglu, “Utilization of anisotropic metamaterial layers in waveguide miniaturization and transitions,” IEEE Microw. Wirel. Compon. Lett. 17, 754-756 (2007).
    [CrossRef]
  7. 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]
  8. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
    [CrossRef] [PubMed]
  9. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nature Mater. 8, 642-645 (2009).
    [CrossRef]
  10. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  11. R. W. Ziolkowski, and A. D. Kipple, “Causality and double-negative metamaterial,” Phys. Rev. E 68, 026615 (2003).
    [CrossRef]
  12. W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1, 224-227 (2007).
    [CrossRef]
  13. Y. G. Ma, X. C. Wang, and C. K. Ong, “Negative refractive index of metallic cross-I-shaped pairs: Origin and evolution with pair gap width,” Phys. Rev. E 78, 016605 (2008).
    [CrossRef]
  14. U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323, 110 (2009).
    [CrossRef]
  15. J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101, 203901 (2008).
    [CrossRef] [PubMed]
  16. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366-369 (2009).
    [CrossRef] [PubMed]
  17. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Nanostructure cloaking at optical frequencies,” Nat. Photonics 3, 461-463 (2009).
    [CrossRef]
  18. U. Leonhardt, “Towards invisibility in the visible,” Nature Mater. 8, 537-538 (2009).
    [CrossRef]
  19. N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17, 14872-14879 (2009).
    [CrossRef] [PubMed]
  20. U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt. 53, 69-152 (2009).
    [CrossRef]
  21. J. F. Thompson, B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation (CRC Press, 1994).
  22. P. Henrici, Applied and Computational Complex Analysis, Vol. 3 (Wiley, 1986).
  23. S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
    [CrossRef]
  24. L. H. Shi, L. Gao, S. L. He, and B. W. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
    [CrossRef]

2009 (7)

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nature Mater. 8, 642-645 (2009).
[CrossRef]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366-369 (2009).
[CrossRef] [PubMed]

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Nanostructure cloaking at optical frequencies,” Nat. Photonics 3, 461-463 (2009).
[CrossRef]

U. Leonhardt, “Towards invisibility in the visible,” Nature Mater. 8, 537-538 (2009).
[CrossRef]

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

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 (2009).
[CrossRef]

2008 (4)

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

Y. G. Ma, X. C. Wang, and C. K. Ong, “Negative refractive index of metallic cross-I-shaped pairs: Origin and evolution with pair gap width,” Phys. Rev. E 78, 016605 (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, 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, 063903 (2008).
[CrossRef] [PubMed]

2007 (4)

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

O. Ozgun and M. Kuzuoglu, “Utilization of anisotropic metamaterial layers in waveguide miniaturization and transitions,” IEEE Microw. Wirel. Compon. Lett. 17, 754-756 (2007).
[CrossRef]

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1, 224-227 (2007).
[CrossRef]

L. H. Shi, L. Gao, S. L. He, and B. W. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

2006 (5)

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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

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

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[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,” Science 314, 977-980 (2006).
[CrossRef] [PubMed]

2003 (1)

R. W. Ziolkowski, and A. D. Kipple, “Causality and double-negative metamaterial,” Phys. Rev. E 68, 026615 (2003).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1994 (1)

J. F. Thompson, B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation (CRC Press, 1994).

1986 (1)

P. Henrici, Applied and Computational Complex Analysis, Vol. 3 (Wiley, 1986).

Cai, W. S.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1, 224-227 (2007).
[CrossRef]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Nanostructure cloaking at optical frequencies,” Nat. Photonics 3, 461-463 (2009).
[CrossRef]

Chettiar, U. K.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1, 224-227 (2007).
[CrossRef]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366-369 (2009).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366-369 (2009).
[CrossRef] [PubMed]

Cummer, S. A.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Nanostructure cloaking at optical frequencies,” Nat. Photonics 3, 461-463 (2009).
[CrossRef]

Gao, L.

L. H. Shi, L. Gao, S. L. He, and B. W. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

He, S. L.

L. H. Shi, L. Gao, S. L. He, and B. W. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

Henrici, P.

P. Henrici, Applied and Computational Complex Analysis, Vol. 3 (Wiley, 1986).

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366-369 (2009).
[CrossRef] [PubMed]

Justice, B. J.

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

Kildishev, A. V.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1, 224-227 (2007).
[CrossRef]

Kipple, A. D.

R. W. Ziolkowski, and A. D. Kipple, “Causality and double-negative metamaterial,” Phys. Rev. E 68, 026615 (2003).
[CrossRef]

Kuzuoglu, M.

O. Ozgun and M. Kuzuoglu, “Utilization of anisotropic metamaterial layers in waveguide miniaturization and transitions,” IEEE Microw. Wirel. Compon. Lett. 17, 754-756 (2007).
[CrossRef]

Landy, N. I.

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 (2009).
[CrossRef]

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nature Mater. 8, 642-645 (2009).
[CrossRef]

U. Leonhardt, “Towards invisibility in the visible,” Nature Mater. 8, 537-538 (2009).
[CrossRef]

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

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

Li, B. W.

L. H. Shi, L. Gao, S. L. He, and B. W. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[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]

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Nanostructure cloaking at optical frequencies,” Nat. Photonics 3, 461-463 (2009).
[CrossRef]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366-369 (2009).
[CrossRef] [PubMed]

Ma, Y. G.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nature Mater. 8, 642-645 (2009).
[CrossRef]

Y. G. Ma, X. C. Wang, and C. K. Ong, “Negative refractive index of metallic cross-I-shaped pairs: Origin and evolution with pair gap width,” Phys. Rev. E 78, 016605 (2008).
[CrossRef]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366-369 (2009).
[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]

Ong, C. K.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nature Mater. 8, 642-645 (2009).
[CrossRef]

Y. G. Ma, X. C. Wang, and C. K. Ong, “Negative refractive index of metallic cross-I-shaped pairs: Origin and evolution with pair gap width,” Phys. Rev. E 78, 016605 (2008).
[CrossRef]

Ozgun, O.

O. Ozgun and M. Kuzuoglu, “Utilization of anisotropic metamaterial layers in waveguide miniaturization and transitions,” IEEE Microw. Wirel. Compon. Lett. 17, 754-756 (2007).
[CrossRef]

Padilla, W. J.

Pendry, J. B.

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

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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

D. Schurig, J. 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]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[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, 247 (2006).
[CrossRef]

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Nanostructure cloaking at optical frequencies,” Nat. Photonics 3, 461-463 (2009).
[CrossRef]

Popa, B. I.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Rahm, M.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

D. 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]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[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]

Schurig, D.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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

D. Schurig, J. 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]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Shalaev, V. M.

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1, 224-227 (2007).
[CrossRef]

Shi, L. H.

L. H. Shi, L. Gao, S. L. He, and B. W. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

Smith, D. R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366-369 (2009).
[CrossRef] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

D. 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]

D. Schurig, J. B. Pendry, and D. R. Smith, “Transformation-designed optical elements,” Opt. Express 15, 14772 (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,” 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]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Soni, B. K.

J. F. Thompson, B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation (CRC Press, 1994).

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]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Thompson, J. F.

J. F. Thompson, B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation (CRC Press, 1994).

Tyc, T.

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

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nature Mater. 8, 642-645 (2009).
[CrossRef]

Wang, X. C.

Y. G. Ma, X. C. Wang, and C. K. Ong, “Negative refractive index of metallic cross-I-shaped pairs: Origin and evolution with pair gap width,” Phys. Rev. E 78, 016605 (2008).
[CrossRef]

Weatherill, N. P.

J. F. Thompson, B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation (CRC Press, 1994).

Ziolkowski, R. W.

R. W. Ziolkowski, and A. D. Kipple, “Causality and double-negative metamaterial,” Phys. Rev. E 68, 026615 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

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]

IEEE Microw. Wirel. Compon. Lett. (1)

O. Ozgun and M. Kuzuoglu, “Utilization of anisotropic metamaterial layers in waveguide miniaturization and transitions,” IEEE Microw. Wirel. Compon. Lett. 17, 754-756 (2007).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Nat. Photonics (2)

W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1, 224-227 (2007).
[CrossRef]

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Nanostructure cloaking at optical frequencies,” Nat. Photonics 3, 461-463 (2009).
[CrossRef]

Nature Mater. (2)

U. Leonhardt, “Towards invisibility in the visible,” Nature Mater. 8, 537-538 (2009).
[CrossRef]

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nature Mater. 8, 642-645 (2009).
[CrossRef]

New J. Phys. (1)

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

Opt. Express (2)

Phys. Rev. B (1)

L. H. Shi, L. Gao, S. L. He, and B. W. Li, “Superlens from metal-dielectric composites of nonspherical particles,” Phys. Rev. B 76, 045116 (2007).
[CrossRef]

Phys. Rev. E (3)

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Y. G. Ma, X. C. Wang, and C. K. Ong, “Negative refractive index of metallic cross-I-shaped pairs: Origin and evolution with pair gap width,” Phys. Rev. E 78, 016605 (2008).
[CrossRef]

R. W. Ziolkowski, and A. D. Kipple, “Causality and double-negative metamaterial,” Phys. Rev. E 68, 026615 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[CrossRef] [PubMed]

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

Prog. Opt. (1)

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

Science (5)

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

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

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366-369 (2009).
[CrossRef] [PubMed]

Other (2)

J. F. Thompson, B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation (CRC Press, 1994).

P. Henrici, Applied and Computational Complex Analysis, Vol. 3 (Wiley, 1986).

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 (3)

Fig. 1
Fig. 1

Schematic of conformal transformation process. The figure in (a) describes the pre-determined physical domain in the ( x , y ) plane and the rectangular virtual domain is shown in (b) in the ( ξ , η ) plane. Conformal mapping will in sequence transform the vertices A, B, C, and D in (a) onto the four corners A , B , C , and D in (b). ξ 1 and η 1 denote the unit coordinate vectors of the distorted virtual space in the physical domain.

Fig. 2
Fig. 2

Proposal for a 90° waveguide bend. Shown in (a) is the ε r -generalized permittivity map together with the curved virtual coordinates. One snapshot is given in (b) for the simulated transmitted electric field.

Fig. 3
Fig. 3

Proposal for a three-end optical waveguide. (a) shows the ε r -generalized permittivity map and the curved virtual domain coordinates. The electric field snapshots in (b), (c), and (d) are generated with the source fed through port 1, port 3, and ports 2 + 3 , respectively. In (d), the incident wave beams have an 180° out of phase difference at the inputting ports.

Equations (10)

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

x ξ = y η , x η = y ξ .
x ξ ξ + x η η = 0 , y ξ ξ + y η η = 0 .
x ξ x η + y ξ y η = 0 ,
ε = ε r det Λ , u = 1 ,
ξ x x + ξ y y = 0 , η x x + η y y = 0 .
ξ x ξ y + η x η y = 0 ,
| ξ | Γ 1 = 0 , | ξ | Γ 3 = a M , and n | ξ | Γ 2 , Γ 4 = 0
| η | Γ 2 = 0 , | η | Γ 4 = a , and n | η | Γ 1 , Γ 3 = 0
ε = ε r det Λ 1 = [ ( ξ x ) 2 + ( η x ) 2 ] ε r , u = 1 .
| ξ | port 1 = 0 , | ξ | ports 2 , 3 = a M , and n | ξ | other walls = 0 .

Metrics