Vol. 13

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

A Planar Focusing Antenna Design with the Quasi-Conformal Mapping

By Zhong-Lei Mei, Jing Bai, Tiao Ming Niu, and Tie-Jun Cui
Progress In Electromagnetics Research M, Vol. 13, 261-273, 2010


We propose a planar focusing antenna design, which has the same performance as its parabolic counterparts and can be realized using PEC-backed gradient index dielectrics. In this design, quasi-conformal transformation optics is first utilized to transform a parabolic surface into a planar one, then the anisotropy factor of the resultant material is minimized, and the material is approximately treated as isotropic. Examples with realizable material parameters are given, and the simulation results validate the design. The proposed method could be used to design planar focusing antennas with high directivity and similar devices. The idea can also be applied to new device designs in optics engineering.


Zhong-Lei Mei, Jing Bai, Tiao Ming Niu, and Tie-Jun Cui, "A Planar Focusing Antenna Design with the Quasi-Conformal Mapping," Progress In Electromagnetics Research M, Vol. 13, 261-273, 2010.


    1. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780-1782, 2006.

    2. Schurig, D., 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, Vol. 314, 977-980, 2006.

    3. Leonhardt, U., "Optical conformal mapping," Science, Vol. 312, 1777-1780, 2006.

    4. Cai, W., U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photon., Vol. 1, 224-227, 2007.

    5. Li, J. and J. B. Pendry, "Hiding under the carpet: A new strategy for cloaking," Phys. Rev. Lett., Vol. 101, 203901, 2008.

    6. Liu, R., C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, "Broadband ground-plane cloak," Science, Vol. 323, 366-369, 2009.

    7. Valentine, J., J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics ," Nat. Materials, Vol. 8, 568-571, 2009.

    8. Gabrielli, L. H., J. Cardenas, C. B. Poitras, and M. Lipson, "Silicon nanostructure cloak operating at optical frequencies," Nat. Phonotics, Vol. 3, 461-463, 2009.

    9. Smolyaninov, I. I., V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, "Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking ," Phys. Rev. Lett., Vol. 102, 213901, 2009.

    10. Cheng, Q., W. X. Jiang, and T. J. Cui, "Investigations of the electromagnetic properties of three-dimensional arbitrarily-shaped cloaks ," Progress In Electromagnetics Research, Vol. 94, 105-117, 2009.

    11. Lai, Y., H. Chen, Z. Q. Zhang, and C. T. Chan, "Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell," Phys. Rev. Lett., Vol. 102, 093901, 2009.

    12. Lai, Y., J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, "Illusion optics: The optical transformation of an object into another object," Phys. Rev. Lett., Vol. 102, 253902, 2009.

    13. Ma, H. F., W. X. Jiang, X. M. Yang, X. Y. Zhou, and T. J. Cui, "Compact-sized and broadband carpet cloak and free-space cloak," Opt. Express, Vol. 17, 19947-19959, 2009.

    14. Wang, W., L. Lin, X. Yang, J. Cui, C. Du, and X. Luo, "Design of oblate cylindrical perfect lens using coordinate transformation," Opt. Express, Vol. 16, 8094-8105, 2008.

    15. Tsang, M. and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B, Vol. 77, 035122, 2008.

    16. Kwon, D. and D. H. Werner, "Transformation optical designs for wave collimators, flat lenses and right-angle bends," New J. Phys., Vol. 10, 115023, 2008.

    17. Rahm, M., D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of concentrators using form-invariant coordinate transformations of Maxwell's equations," Photonics Nanostruct. Fund. Appl., Vol. 6, 87-95, 2008.

    18. Jiang, W. X., T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, "Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces ," Appl. Phys. Lett., Vol. 92, 264101, 2008.

    19. Chang, Z., X. Zhou, J. Hu, and G. Hu, "Design method for quasiisotropic transformation materials based on inverse Laplace's equation with sliding boundaries," Opt. Express, Vol. 18, 6089-6096, 2010.

    20. Ma, Y. G., N. Wang, and C. K. Ong, "Application of inverse, strict conformal transformation to design waveguide devices," J. Opt. Soc. Am. A, Vol. 27, 968-972, 2010.

    21. Landy, N. I. and W. J. Padilla, "Guiding light with conformal transformations," Opt. Express, Vol. 17, 14872-14879, 2009.

    22. Enoch, S., G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. , Vol. 89, 213902, 2002.

    23. Zhang, J., Y. Luo, H. Chen, and B. Wu, "Manipulating the directivity of antennas with metamaterial," Opt. Express, Vol. 16, 10962-10967, 2008.

    24. Duan, Z. Y., B.-I. Wu, J. A. Kong, F. M. Kong, and S. Xi, "Enhancement of radiation properties of a compact planar antenna using transformation media as substrates," Progress In Electromagnetics Research, Vol. 83, 375-384, 2008.

    25. Jiang, W. X., T. J. Cui, H. F. Ma, X. M. Yang, and Q. Cheng, "Layered high-gain lens antennas via discrete optical transformation," Appl. Phys. Lett., Vol. 93, 221906, 2008.

    26. Kong, F., 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., Vol. 91, 253509-2007.

    27. Tichit, P. -H., S. N. Burokur, and A. de Lustrac, "Ultradirective antenna via transformation optics," J. Appl. Phys., Vol. 105, 104912, 2009.

    28. Ma, Y. G., P. Wang, X. Chen, and C. K. Ong, "Near-field plane-wave-like beam emitting antenna fabricated by anisotropic metamaterial ," Appl. Phys. Lett., Vol. 94, 044107, 2009.

    29. Ma, H. F., X. Chen, H. S. Xu, X. M. Yang, W. X. Jiang, and T. J. Cui, "Experiments on high-performance beam-scanning antennas made of gradient-index metamaterials ," Appl. Phys. Lett., Vol. 95, 094107, 2009.

    30. Leonhardt, U. and T. G. Philbin, "General relativity in electrical engineering," New J. Phys., Vol. 8, 247, 2006.

    31. Milton, G. W., M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form ," New J. Phys., Vol. 8, 248, 2006.

    32. Kundtz, N. and D. R. Smith, "Extreme-angle broadband metamaterial lens," Nat. Material, Vol. 9, 129-132, 2009.

    33. Mei, Z. L., J. Bai, and T. J. Cui, "Gradient index metamaterials realized by drilling hole arrays," J. Phys. D: Appl. Phys., Vol. 43, 055404, 2010.

    34. Knupp, P. and S. Steinberg, Fundamentals of Grid Generation, CRC Press, Boca Raton, 1994.

    35. Thompson, J. F., B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation, CRC Press, Boca Raton, 1999.

    36. Zhang, B., T. Chan, and B.-I. Wu, "Lateral shift makes ground-plane cloak detectable," Phys. Rev. Lett., Vol. 104, 233903, 2010.