Abstract

A flat reflector capable of scanning over wide angles is designed using a transformation optics approach. This reflector is derived from its virtual parabolic counterpart using a conformal coordinate transformation that determines the permittivity profile of the flat reflector. By changing the permittivity profile, the flat reflector is then capable of scanning up to 47° away from broadside while maintaining good beam characteristics across a wide frequency range. Moreover, its directivity is comparable to that of the virtual parabolic reflector, even at high scan angles. We use the Schwarz-Christoffel transformation as a versatile tool to produce perfect conformal mapping of coordinates between the virtual and flat reflectors, thereby avoiding the need to monitor the anisotropy of the material that results when employing quasi-conformal methods.

© 2013 Optical Society of America

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  4. D. Schurig, “An aberration-free lens with zero f-number,” New J. of Phys. 10, 115034 (2008).
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  5. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nature Materials 9, 129 – 32 (2010).
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  6. D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 16535–16542 (2009).
    [Crossref] [PubMed]
  7. D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. of Phys. 10, 115023 (2008).
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  8. N. Engheta, “Antenna-guided light,” Science 21, 317–318 (2011).
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  9. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
    [Crossref] [PubMed]
  10. F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 –253509–3 (2007).
    [Crossref]
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    [Crossref]
  12. H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89, 053509 (2006).
    [Crossref]
  13. Z. L. Mei and T. J. Cui, “Experimental realization of a broadband bend structure using gradient index metamaterials,” Opt. Express 17, 18354–18363 (2009).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  22. Y. Ji and M. Fujita, “Design and analysis of a folded Fresnel zone plate antenna,” Int. J. of Infrared and Millimeter Waves 15, 1385–1406 (1994).
    [Crossref]
  23. R. Yang, W. Tang, and Y. Hao, “Wideband beam-steerable flat reflectors via transformation optics,” IEEE Antennas Wireless Propag. Lett. 10, 1290 –1294 (2011).
    [Crossref]
  24. L. Tang, J. Yin, G. Yuan, J. Du, H. Gao, X. Dong, Y. Lu, and C. Du, “General conformal transformation method based on Schwarz-Christoffel approach,” Opt. Express 19, 15119–15126 (2011).
    [Crossref] [PubMed]
  25. U. Leonhardt, “Optical conformal mapping,” Science 23, 1777–1780 (2006).
    [Crossref]
  26. W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58, 3795 –3804 (2010).
    [Crossref]
  27. Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A 27, 968–972 (2010).
    [Crossref]
  28. T. A. Driscoll, A MATLAB toolbox for Schwartz-Christoffel mapping (ACM Trans. Math. Softw., 1996).
  29. D. Wunsch, Complex Variables with Applications (Addison Wesley, 1993).
  30. N. Kundtz, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proceedings of the IEEE 99, 1622 –1633 (2011).
    [Crossref]
  31. J. P. Turpin, Z. H. Jiang, P. L. Werner, and D. H. Werner, “Tunable metamaterials for conformally mapped transformation optics lenses,” IEEE Proc. AP–S Int. Symp. Antennas Propag. (2010).
  32. S. V. Hum, M. Okoniewski, and R. J. Davies, “Realizing an electronically tunable reflectarray using varactor diode-tuned elements,” IEEE Microw. Wireless Compon. Lett. (2005).
    [Crossref]

2012 (1)

M. Arrebola, J. A. Encinar, R. Cahill, and G. Toso, “Dual-reflector antenna with a reflectarray subreflector for wide beam scanning range at 120 GHz,” Int. Conf. Electromagn. in Advanced Applications, 848–851 (2012).

2011 (4)

R. Yang, W. Tang, and Y. Hao, “Wideband beam-steerable flat reflectors via transformation optics,” IEEE Antennas Wireless Propag. Lett. 10, 1290 –1294 (2011).
[Crossref]

N. Kundtz, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proceedings of the IEEE 99, 1622 –1633 (2011).
[Crossref]

N. Engheta, “Antenna-guided light,” Science 21, 317–318 (2011).
[Crossref]

L. Tang, J. Yin, G. Yuan, J. Du, H. Gao, X. Dong, Y. Lu, and C. Du, “General conformal transformation method based on Schwarz-Christoffel approach,” Opt. Express 19, 15119–15126 (2011).
[Crossref] [PubMed]

2010 (4)

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58, 3795 –3804 (2010).
[Crossref]

Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A 27, 968–972 (2010).
[Crossref]

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

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nature Materials 9, 129 – 32 (2010).
[Crossref]

2009 (4)

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

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912 –104912–6 (2009).
[Crossref]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 16535–16542 (2009).
[Crossref] [PubMed]

Z. L. Mei and T. J. Cui, “Experimental realization of a broadband bend structure using gradient index metamaterials,” Opt. Express 17, 18354–18363 (2009).
[Crossref] [PubMed]

2008 (4)

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).
[Crossref] [PubMed]

D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. of Phys. 10, 115023 (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, “An aberration-free lens with zero f-number,” New J. of Phys. 10, 115034 (2008).
[Crossref]

2007 (4)

K. Aydin and E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl. Phys. 101, 024911 (2007).
[Crossref]

M. Riel and J. J. Laurin, “Design of an electronically beam scanning reflectarray using aperture-coupled elements,” IEEE Trans. Antennas Propag. 55, 1260 –1266 (2007).
[Crossref]

S. V. Hum, M. Okoniewski, and R. J. Davies, “Modeling and design of electronically tunable reflectarrays,” IEEE Trans. Antennas Propag. 55, 2200 –2210 (2007).
[Crossref]

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 –253509–3 (2007).
[Crossref]

2006 (4)

J. Gutierrez-Rios and J. V. Sanz, “Simulated response of conic Fresnel zone plate reflectors (CFZPS),” in Europ. Conf. Antennas Propag. (2006).
[Crossref]

H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89, 053509 (2006).
[Crossref]

U. Leonhardt, “Optical conformal mapping,” Science 23, 1777–1780 (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]

1994 (1)

Y. Ji and M. Fujita, “Design and analysis of a folded Fresnel zone plate antenna,” Int. J. of Infrared and Millimeter Waves 15, 1385–1406 (1994).
[Crossref]

Argyropoulos, C.

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58, 3795 –3804 (2010).
[Crossref]

Arrebola, M.

M. Arrebola, J. A. Encinar, R. Cahill, and G. Toso, “Dual-reflector antenna with a reflectarray subreflector for wide beam scanning range at 120 GHz,” Int. Conf. Electromagn. in Advanced Applications, 848–851 (2012).

Aydin, K.

K. Aydin and E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl. Phys. 101, 024911 (2007).
[Crossref]

Burokur, S. N.

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912 –104912–6 (2009).
[Crossref]

Cabria, L.

L. Cabria, J. A. Garcia, J. Gutierrez-Rios, A. Tazon, and J. Vassal’lo, “Active reflectors: Possible solutions based on reflectarrays and Fresnel reflectors,” Int. J. Antennas Propag. (2009).
[Crossref]

Cahill, R.

M. Arrebola, J. A. Encinar, R. Cahill, and G. Toso, “Dual-reflector antenna with a reflectarray subreflector for wide beam scanning range at 120 GHz,” Int. Conf. Electromagn. in Advanced Applications, 848–851 (2012).

Chen, H.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 –253509–3 (2007).
[Crossref]

H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89, 053509 (2006).
[Crossref]

Cui, T. J.

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]

Davies, R. J.

S. V. Hum, M. Okoniewski, and R. J. Davies, “Modeling and design of electronically tunable reflectarrays,” IEEE Trans. Antennas Propag. 55, 2200 –2210 (2007).
[Crossref]

S. V. Hum, M. Okoniewski, and R. J. Davies, “Realizing an electronically tunable reflectarray using varactor diode-tuned elements,” IEEE Microw. Wireless Compon. Lett. (2005).
[Crossref]

de Lustrac, A.

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912 –104912–6 (2009).
[Crossref]

Deckelmann, M.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Dong, X.

Driscoll, T. A.

T. A. Driscoll, A MATLAB toolbox for Schwartz-Christoffel mapping (ACM Trans. Math. Softw., 1996).

Du, C.

Du, J.

Encinar, J. A.

M. Arrebola, J. A. Encinar, R. Cahill, and G. Toso, “Dual-reflector antenna with a reflectarray subreflector for wide beam scanning range at 120 GHz,” Int. Conf. Electromagn. in Advanced Applications, 848–851 (2012).

Engheta, N.

N. Engheta, “Antenna-guided light,” Science 21, 317–318 (2011).
[Crossref]

Follmann, R.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Fujita, M.

Y. Ji and M. Fujita, “Design and analysis of a folded Fresnel zone plate antenna,” Int. J. of Infrared and Millimeter Waves 15, 1385–1406 (1994).
[Crossref]

Gaebler, A.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Gao, H.

Garcia, J. A.

L. Cabria, J. A. Garcia, J. Gutierrez-Rios, A. Tazon, and J. Vassal’lo, “Active reflectors: Possible solutions based on reflectarrays and Fresnel reflectors,” Int. J. Antennas Propag. (2009).
[Crossref]

Goebel, M.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Goelden, F.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Grzegorczyk, T. M.

H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89, 053509 (2006).
[Crossref]

Gutierrez-Rios, J.

J. Gutierrez-Rios and J. V. Sanz, “Simulated response of conic Fresnel zone plate reflectors (CFZPS),” in Europ. Conf. Antennas Propag. (2006).
[Crossref]

L. Cabria, J. A. Garcia, J. Gutierrez-Rios, A. Tazon, and J. Vassal’lo, “Active reflectors: Possible solutions based on reflectarrays and Fresnel reflectors,” Int. J. Antennas Propag. (2009).
[Crossref]

Haase, W.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Halimeh, J. C.

Hao, Y.

R. Yang, W. Tang, and Y. Hao, “Wideband beam-steerable flat reflectors via transformation optics,” IEEE Antennas Wireless Propag. Lett. 10, 1290 –1294 (2011).
[Crossref]

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58, 3795 –3804 (2010).
[Crossref]

Huangfu, J.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 –253509–3 (2007).
[Crossref]

Hum, S. V.

S. V. Hum, M. Okoniewski, and R. J. Davies, “Modeling and design of electronically tunable reflectarrays,” IEEE Trans. Antennas Propag. 55, 2200 –2210 (2007).
[Crossref]

S. V. Hum, M. Okoniewski, and R. J. Davies, “Realizing an electronically tunable reflectarray using varactor diode-tuned elements,” IEEE Microw. Wireless Compon. Lett. (2005).
[Crossref]

Jakoby, R.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Ji, Y.

Y. Ji and M. Fujita, “Design and analysis of a folded Fresnel zone plate antenna,” Int. J. of Infrared and Millimeter Waves 15, 1385–1406 (1994).
[Crossref]

Jiang, Z. H.

J. P. Turpin, Z. H. Jiang, P. L. Werner, and D. H. Werner, “Tunable metamaterials for conformally mapped transformation optics lenses,” IEEE Proc. AP–S Int. Symp. Antennas Propag. (2010).

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]

Kallos, E.

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58, 3795 –3804 (2010).
[Crossref]

Kipka, A.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Koether, D.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Kong, F.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 –253509–3 (2007).
[Crossref]

Kong, J. A.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 –253509–3 (2007).
[Crossref]

H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89, 053509 (2006).
[Crossref]

Kuchenbecker, P.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Kundtz, N.

N. Kundtz, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proceedings of the IEEE 99, 1622 –1633 (2011).
[Crossref]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nature Materials 9, 129 – 32 (2010).
[Crossref]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 16535–16542 (2009).
[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. of Phys. 10, 115023 (2008).
[Crossref]

Lapanik, A.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Laurin, J. J.

M. Riel and J. J. Laurin, “Design of an electronically beam scanning reflectarray using aperture-coupled elements,” IEEE Trans. Antennas Propag. 55, 1260 –1266 (2007).
[Crossref]

Leonhardt, U.

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

U. Leonhardt, “Optical conformal mapping,” Science 23, 1777–1780 (2006).
[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]

Lu, Y.

Ma, Y. G.

Manabe, A.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Mei, Z. L.

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]

Modes, C.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Moessinger, A.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Mueller, S.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Okoniewski, M.

S. V. Hum, M. Okoniewski, and R. J. Davies, “Modeling and design of electronically tunable reflectarrays,” IEEE Trans. Antennas Propag. 55, 2200 –2210 (2007).
[Crossref]

S. V. Hum, M. Okoniewski, and R. J. Davies, “Realizing an electronically tunable reflectarray using varactor diode-tuned elements,” IEEE Microw. Wireless Compon. Lett. (2005).
[Crossref]

Ong, C. K.

Ozbay, E.

K. Aydin and E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl. Phys. 101, 024911 (2007).
[Crossref]

Pendry, J. B.

N. Kundtz, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proceedings of the IEEE 99, 1622 –1633 (2011).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (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]

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]

Rabe, T.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Rahm, M.

Ran, L.

H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89, 053509 (2006).
[Crossref]

Riel, M.

M. Riel and J. J. Laurin, “Design of an electronically beam scanning reflectarray using aperture-coupled elements,” IEEE Trans. Antennas Propag. 55, 1260 –1266 (2007).
[Crossref]

Roberts, D. A.

Sanz, J. V.

J. Gutierrez-Rios and J. V. Sanz, “Simulated response of conic Fresnel zone plate reflectors (CFZPS),” in Europ. Conf. Antennas Propag. (2006).
[Crossref]

Schmied, R.

Schulz, B.

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

Schurig, D.

D. Schurig, “An aberration-free lens with zero f-number,” New J. of Phys. 10, 115034 (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,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Smith, D. R.

N. Kundtz, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proceedings of the IEEE 99, 1622 –1633 (2011).
[Crossref]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nature Materials 9, 129 – 32 (2010).
[Crossref]

D. A. Roberts, N. Kundtz, and D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17, 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. Express 16, 11555–11567 (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]

Song, W.

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58, 3795 –3804 (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,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Tang, L.

Tang, W.

R. Yang, W. Tang, and Y. Hao, “Wideband beam-steerable flat reflectors via transformation optics,” IEEE Antennas Wireless Propag. Lett. 10, 1290 –1294 (2011).
[Crossref]

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58, 3795 –3804 (2010).
[Crossref]

Tazon, A.

L. Cabria, J. A. Garcia, J. Gutierrez-Rios, A. Tazon, and J. Vassal’lo, “Active reflectors: Possible solutions based on reflectarrays and Fresnel reflectors,” Int. J. Antennas Propag. (2009).
[Crossref]

Tichit, P. H.

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912 –104912–6 (2009).
[Crossref]

Toso, G.

M. Arrebola, J. A. Encinar, R. Cahill, and G. Toso, “Dual-reflector antenna with a reflectarray subreflector for wide beam scanning range at 120 GHz,” Int. Conf. Electromagn. in Advanced Applications, 848–851 (2012).

Turpin, J. P.

J. P. Turpin, Z. H. Jiang, P. L. Werner, and D. H. Werner, “Tunable metamaterials for conformally mapped transformation optics lenses,” IEEE Proc. AP–S Int. Symp. Antennas Propag. (2010).

Tyc, T.

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

Vassal’lo, J.

L. Cabria, J. A. Garcia, J. Gutierrez-Rios, A. Tazon, and J. Vassal’lo, “Active reflectors: Possible solutions based on reflectarrays and Fresnel reflectors,” Int. J. Antennas Propag. (2009).
[Crossref]

Wang, N.

Wegener, M.

Werner, D. H.

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

J. P. Turpin, Z. H. Jiang, P. L. Werner, and D. H. Werner, “Tunable metamaterials for conformally mapped transformation optics lenses,” IEEE Proc. AP–S Int. Symp. Antennas Propag. (2010).

Werner, P. L.

J. P. Turpin, Z. H. Jiang, P. L. Werner, and D. H. Werner, “Tunable metamaterials for conformally mapped transformation optics lenses,” IEEE Proc. AP–S Int. Symp. Antennas Propag. (2010).

Wu, B.-I.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 –253509–3 (2007).
[Crossref]

H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89, 053509 (2006).
[Crossref]

Wunsch, D.

D. Wunsch, Complex Variables with Applications (Addison Wesley, 1993).

Xi, S.

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 –253509–3 (2007).
[Crossref]

Yang, R.

R. Yang, W. Tang, and Y. Hao, “Wideband beam-steerable flat reflectors via transformation optics,” IEEE Antennas Wireless Propag. Lett. 10, 1290 –1294 (2011).
[Crossref]

Yin, J.

Yuan, G.

Appl. Phys. Lett. (2)

F. Kong, B.-I. Wu, J. A. Kong, J. Huangfu, S. Xi, and H. Chen, “Planar focusing antenna design by using coordinate transformation technology,” Appl. Phys. Lett. 91, 253509 –253509–3 (2007).
[Crossref]

H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89, 053509 (2006).
[Crossref]

Europ. Conf. Antennas Propag. (1)

J. Gutierrez-Rios and J. V. Sanz, “Simulated response of conic Fresnel zone plate reflectors (CFZPS),” in Europ. Conf. Antennas Propag. (2006).
[Crossref]

IEEE Antennas Wireless Propag. Lett. (1)

R. Yang, W. Tang, and Y. Hao, “Wideband beam-steerable flat reflectors via transformation optics,” IEEE Antennas Wireless Propag. Lett. 10, 1290 –1294 (2011).
[Crossref]

IEEE Trans. Antennas Propag. (3)

W. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58, 3795 –3804 (2010).
[Crossref]

M. Riel and J. J. Laurin, “Design of an electronically beam scanning reflectarray using aperture-coupled elements,” IEEE Trans. Antennas Propag. 55, 1260 –1266 (2007).
[Crossref]

S. V. Hum, M. Okoniewski, and R. J. Davies, “Modeling and design of electronically tunable reflectarrays,” IEEE Trans. Antennas Propag. 55, 2200 –2210 (2007).
[Crossref]

Int. Conf. Electromagn. in Advanced Applications (1)

M. Arrebola, J. A. Encinar, R. Cahill, and G. Toso, “Dual-reflector antenna with a reflectarray subreflector for wide beam scanning range at 120 GHz,” Int. Conf. Electromagn. in Advanced Applications, 848–851 (2012).

Int. J. of Infrared and Millimeter Waves (1)

Y. Ji and M. Fujita, “Design and analysis of a folded Fresnel zone plate antenna,” Int. J. of Infrared and Millimeter Waves 15, 1385–1406 (1994).
[Crossref]

J. Appl. Phys. (2)

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912 –104912–6 (2009).
[Crossref]

K. Aydin and E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl. Phys. 101, 024911 (2007).
[Crossref]

J. Opt. Soc. Am. A (1)

Nature Materials (1)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nature Materials 9, 129 – 32 (2010).
[Crossref]

New J. of Phys. (2)

D. Schurig, “An aberration-free lens with zero f-number,” New J. of Phys. 10, 115034 (2008).
[Crossref]

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

Opt. Express (5)

Phys. Rev. Lett. (1)

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

Proceedings of the IEEE (1)

N. Kundtz, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proceedings of the IEEE 99, 1622 –1633 (2011).
[Crossref]

Science (4)

U. Leonhardt, “Optical conformal mapping,” Science 23, 1777–1780 (2006).
[Crossref]

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

N. Engheta, “Antenna-guided light,” Science 21, 317–318 (2011).
[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]

Other (6)

A. Gaebler, A. Moessinger, F. Goelden, A. Manabe, M. Goebel, R. Follmann, D. Koether, C. Modes, A. Kipka, M. Deckelmann, T. Rabe, B. Schulz, P. Kuchenbecker, A. Lapanik, S. Mueller, W. Haase, and R. Jakoby, “Liquid crystal-reconfigurable antenna concepts for space applications at microwave and millimeter waves,” Int. J. of Antennas Propag. (2009).
[Crossref]

L. Cabria, J. A. Garcia, J. Gutierrez-Rios, A. Tazon, and J. Vassal’lo, “Active reflectors: Possible solutions based on reflectarrays and Fresnel reflectors,” Int. J. Antennas Propag. (2009).
[Crossref]

J. P. Turpin, Z. H. Jiang, P. L. Werner, and D. H. Werner, “Tunable metamaterials for conformally mapped transformation optics lenses,” IEEE Proc. AP–S Int. Symp. Antennas Propag. (2010).

S. V. Hum, M. Okoniewski, and R. J. Davies, “Realizing an electronically tunable reflectarray using varactor diode-tuned elements,” IEEE Microw. Wireless Compon. Lett. (2005).
[Crossref]

T. A. Driscoll, A MATLAB toolbox for Schwartz-Christoffel mapping (ACM Trans. Math. Softw., 1996).

D. Wunsch, Complex Variables with Applications (Addison Wesley, 1993).

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Figures (11)

Fig. 1
Fig. 1 An illustration of conformal mapping from z-plane, the physical space, to w-plane, the curved virtual space.

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Fig. 2
Fig. 2 Rotation of a parabolic reflector about its apex.

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Fig. 3
Fig. 3 Three SC transformations mapped from different canonical regions – (a) mapping of the upper half of complex plane to an open polygon, (b) a mapping from a rectangle to a closed polygon which contains a parabolic section and (c) mapping from a rectangle to a close polygon which contains a parabolic section rotated by 20°.

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Fig. 4
Fig. 4 SC transformation for a parabolic reflector with f/D = 1.5, D = 5 λ at 5 GHz. (a) virtual space, w-plane. (b) relative permittivity profile in physical space, z-plane.

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Fig. 5
Fig. 5 Permittivity profile for the flat reflector for αo = 30° for a reflected beam directed at ϕo = 60° from broadside.

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Fig. 6
Fig. 6 Directivity pattern at 5 GHz for the flat and the curved parabolic reflector for various scan angles ϕo ∈ {0, 20, 40, 50, 60}° shown as black radial lines. Solid curves are of the flat reflector and the dashed curves are of the curved parabolic reflector of the corresponding color.

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Fig. 7
Fig. 7 Relative permittivity profile for (a) ϕo = 0°, (b) ϕo = 20°, (c) ϕo = 40°, (d) ϕo = 50°. The permittivity profiles are truncated at a thickness of 2.5 λ. Note that color scale is limited to εr = 3 here to clearly show the relative permittivity distribution.

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Fig. 8
Fig. 8 Angle of the actual reflected beam and maximum directivity as a function desired reflected beam angle ϕo. Solid lines are of the flat reflector and the dashed lines are of the parabolic reflector.

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Fig. 9
Fig. 9 Directivity patterns for scan angle ϕo = 40° with different permittivity profiles at 5 GHz.

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Fig. 10
Fig. 10 Directivity pattern for ϕo = 40° for various frequencies. Solid curves are from the flat reflector and the dashed curves are from the curved parabolic reflector of the corresponding color.

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Fig. 11
Fig. 11 (a) Directivity as a function of frequency for various scan angles. (b) actual beam angle as a function of frequency. Solid curves and dashed curves are from the flat and curved parabolic reflector.

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Equations (3)

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

ε r ′ = | d w d z | 2 ε r ,
ε r taper = κ ε r + ( 1 − κ ) ,
κ = − 1 T t ( y − T ) + 1 ,

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