Vol. 13
Latest Volume
All Volumes
PIERM 137 [2026] PIERM 136 [2025] PIERM 135 [2025] PIERM 134 [2025] PIERM 133 [2025] PIERM 132 [2025] PIERM 131 [2025] PIERM 130 [2024] PIERM 129 [2024] PIERM 128 [2024] PIERM 127 [2024] PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2010-08-20
A Planar Focusing Antenna Design with the Quasi-Conformal Mapping
By
Progress In Electromagnetics Research M, Vol. 13, 261-273, 2010
Abstract
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.
Citation
Zhonglei 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.
doi:10.2528/PIERM10053102
References

1. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780-1782, 2006.
doi:10.1126/science.1125907        Google Scholar

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.
doi:10.1126/science.1133628        Google Scholar

3. Leonhardt, U., "Optical conformal mapping," Science, Vol. 312, 1777-1780, 2006.
doi:10.1126/science.1126493        Google Scholar

4. Cai, W., U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photon., Vol. 1, 224-227, 2007.
doi:10.1038/nphoton.2007.28        Google Scholar

5. Li, J. and J. B. Pendry, "Hiding under the carpet: A new strategy for cloaking," Phys. Rev. Lett., Vol. 101, 203901, 2008.
doi:10.1103/PhysRevLett.101.203901        Google Scholar

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.
doi:10.1126/science.1166949        Google Scholar

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.
doi:10.1038/nmat2461        Google Scholar

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.
doi:10.1038/nphoton.2009.117        Google Scholar

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.
doi:10.1103/PhysRevLett.102.213901        Google Scholar

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.
doi:10.2528/PIER09060705        Google Scholar

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.
doi:10.1103/PhysRevLett.102.093901        Google Scholar

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.
doi:10.1103/PhysRevLett.102.253902        Google Scholar

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.
doi:10.1364/OE.17.019947        Google Scholar

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.
doi:10.1364/OE.16.008094        Google Scholar

15. Tsang, M. and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B, Vol. 77, 035122, 2008.
doi:10.1103/PhysRevB.77.035122        Google Scholar

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.
doi:10.1088/1367-2630/10/11/115023        Google Scholar

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.
doi:10.1016/j.photonics.2007.07.013        Google Scholar

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.
doi:10.1063/1.2951485        Google Scholar

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.
doi:10.1364/OE.18.006089        Google Scholar

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.
doi:10.1364/JOSAA.27.000968        Google Scholar

21. Landy, N. I. and W. J. Padilla, "Guiding light with conformal transformations," Opt. Express, Vol. 17, 14872-14879, 2009.
doi:10.1364/OE.17.014872        Google Scholar

22. Enoch, S., G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. , Vol. 89, 213902, 2002.
doi:10.1103/PhysRevLett.89.213902        Google Scholar

23. Zhang, J., Y. Luo, H. Chen, and B. Wu, "Manipulating the directivity of antennas with metamaterial," Opt. Express, Vol. 16, 10962-10967, 2008.
doi:10.1364/OE.16.010962        Google Scholar

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.
doi:10.2528/PIER08062703        Google Scholar

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.
doi:10.1063/1.3040307        Google Scholar

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.
doi:10.1063/1.2826283        Google Scholar

27. Tichit, P. -H., S. N. Burokur, and A. de Lustrac, "Ultradirective antenna via transformation optics," J. Appl. Phys., Vol. 105, 104912, 2009.
doi:10.1063/1.3131843        Google Scholar

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.
doi:10.1063/1.3077128        Google Scholar

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.
doi:10.1063/1.3223608        Google Scholar

30. Leonhardt, U. and T. G. Philbin, "General relativity in electrical engineering," New J. Phys., Vol. 8, 247, 2006.
doi:10.1088/1367-2630/8/10/247        Google Scholar

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.
doi:10.1088/1367-2630/8/10/248        Google Scholar

32. Kundtz, N. and D. R. Smith, "Extreme-angle broadband metamaterial lens," Nat. Material, Vol. 9, 129-132, 2009.
doi:10.1038/nmat2610        Google Scholar

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.
doi:10.1088/0022-3727/43/5/055404        Google Scholar

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.
doi:10.1103/PhysRevLett.104.233903        Google Scholar