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Theory of Transformation Optics in Antenna Design

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Handbook of Antenna Technologies
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Abstract

Transformation optics provides a bridge between the electromagnetic functionality of the device and the material properties of the custom-engineered media. This chapter includes an overview of transformation optics theory and their application in antenna engineering. The basic theory of transformation optics is analyzed, including the general transformation and quasi-conformal mapping. Reviews are focused on the planar lens antenna, the multibeam antenna, the Luneburg lens antenna, and the metasurface Luneburg lens.

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References

  • Chang Z, Zhou X, Hu J, Hu G (2010) Design method for quasi-isotropic transformation materials based on inverse laplace’s equation with sliding boundaries. Opt Express 18(6):6089–6096

    Article  Google Scholar 

  • Chen X, Fu Y, Yuan N (2009) Invisible cloak design with controlled constitutive parameters and arbitrary shaped boundaries through helmholtz’s equation. Opt Express 17(5):3581–3586

    Article  Google Scholar 

  • Cheng Q, Cui TJ, Jiang WX, Cai BG (2010) An omnidirectional electromagnetic absorber made of metamaterials. New J Phys 12(6):063006

    Article  Google Scholar 

  • Crelinsten J (2006) Einstein’s jury: the race to test relativity. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Demetriadou A, Hao Y (2011) Slim Luneburg lens for antenna applications. Opt Express 19(21):19925–19934

    Article  Google Scholar 

  • Dolin L (1961) On a possibility of comparing three-dimensional electromagnetic systems with inhomogeneous filling. Izv Vyssh Uchebn Zaved Radiofiz 4:964–967

    Google Scholar 

  • Jiang WX, Cui TJ, Ma HF, Yang XM, Cheng Q (2008a) Layered high-gain lens antennas via discrete optical transformation. Appl Phys Lett 93(22):221906

    Article  Google Scholar 

  • Jiang WX, Cui TJ, Ma HF, Zhou XY, Cheng Q (2008b) Cylindrical-to-plane-wave conversion via embedded optical transformation. Appl Phys Lett 92(26):261903

    Article  Google Scholar 

  • Jiang ZH, Gregory MD, Werner DH (2011) Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission. Phys Rev B 84(16):165111

    Article  Google Scholar 

  • Jiang ZH, Gregory MD, Werner DH (2012) Broadband high directivity multibeam emission through transformation optics-enabled metamaterial lenses. IEEE Trans Antennas Propag 60(11):5063–5074

    Article  MathSciNet  MATH  Google Scholar 

  • Kong F, Wu B-I, Kong JA, Huangfu J, Xi S, Chen H (2007) Planar focusing antenna design by using coordinate transformation technology. Appl Phys Lett 91(25):253509

    Article  Google Scholar 

  • Kundtz N, Smith DR (2010) Extreme-angle broadband metamaterial lens. Nat Mater 9(2):129–132

    Article  Google Scholar 

  • Kwon D-H (2012) Quasi-conformal transformation optics lenses for conformal arrays. IEEE Antennas Wirel Propag Lett 11:1125–1128

    Article  Google Scholar 

  • Kwon D-H, Werner DH (2009) Flat focusing lens designs having minimized reflection based on coordinate transformation techniques. Opt Express 17(10):7807–7817

    Article  Google Scholar 

  • Leonhardt U (2006) Optical conformal mapping. Science 312:17771780

    Article  MathSciNet  MATH  Google Scholar 

  • Li J, Pendry J (2008) Hiding under the carpet: a new strategy for cloaking. Phys Rev Lett 101(20):203901

    Article  Google Scholar 

  • Liang L, Hum SV (2014) Realizing a flat UWB 2-D reflector designed using transformation optics. IEEE Trans Antennas Propag 62(5):2481–2487

    Article  Google Scholar 

  • Liberti JC, Rappaport TS (1999) Smart antennas for wireless communications: IS-95 and third generation CDMA applications. Prentice Hall PTR, Upper Saddle River

    Google Scholar 

  • Liu R, Ji C, Mock JJ, Chin JY, Cui TJ, Smith DR (2009) Broadband ground-plane cloak. Science 323(5912):366–369

    Article  Google Scholar 

  • Lu W, Lin Z, Chen H, Chan CT (2009) Transformation media based super focusing antenna. J Phys D Appl Phys 42(21):212002

    Google Scholar 

  • Luo Y, Zhang J, Chen H, Huangfu J, Ran L (2009) High-directivity antenna with small antenna aperture. Appl Phys Lett 95(19):193506

    Article  Google Scholar 

  • Ma HF, Cui TJ (2010) Three-dimensional broadband and broad-angle transformation-optics lens. Nat Commun 1:124

    Article  Google Scholar 

  • Ma H, Jiang W, Yang X, Zhou X, Cui T (2009) Compact-sized and broadband carpet cloak and free-space cloak. Opt Express 17(22):19947–19959

    Article  Google Scholar 

  • Mateo-Segura C, Dyke A, Dyke H, Haq S, Hao Y (2014) Flat luneburg lens via transformation optics for directive antenna applications. IEEE Trans Antennas Propag 62(4, 2):1945–1953

    Article  Google Scholar 

  • Mei ZL, Cui TJ (2012) Transformation electromagnetics and its applications. Int J RF Microwave Comput Aided Eng 22(4, SI):496–511

    Article  MathSciNet  Google Scholar 

  • Mei Z-L, Bai J, Niu TM, Cui T-J (2010) A planar focusing antenna design with the quasi-conformal mapping. Prog Electromagn Res M 13:261–273

    Article  Google Scholar 

  • Mei ZL, Bai J, Cui TJ (2011) Experimental verification of a broadband planar focusing antenna based on transformation optics. New J Phys 13:063028

    Article  Google Scholar 

  • Narimanov E, Kildishev A (2009) Optical black hole: broadband omnidirectional light absorber. Appl Phys Lett 95:041106

    Article  Google Scholar 

  • Oliveri G, Bekele ET, Werner DH, Turpin JP, Massa A (2014) Generalized QCTO for metamaterial-lens-coated conformal arrays. IEEE Trans Antennas Propag 62(8):4089–4095

    Article  MATH  Google Scholar 

  • Pendry J, Holden A, Robbins D, Stewart W (1999) Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans Microwave Theory Tech 47(11):2075–2084

    Article  Google Scholar 

  • Pendry JB, Schurig D, Smith DR (2006) Controlling electromagnetic fields. Science 312:1780–1782

    Article  MathSciNet  MATH  Google Scholar 

  • Quevedo-Teruel O, Hao Y (2013) Directive radiation from a diffuse Luneburg lens. Opt Lett 38(4):392–394

    Article  Google Scholar 

  • Quevedo-Teruel O, Tang W, Hao Y (2012) Isotropic and nondispersive planar fed Luneburg lens from Hamiltonian transformation optics. Opt Lett 37(23):4850–4852

    Article  Google Scholar 

  • Rahm M, Schurig D, Roberts DA, Cummer SA, Smith DR, Pendry JB (2008) Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of maxwell’s equations. Photonics Nanostruct Fundam Appl 6(1):87–95

    Article  Google Scholar 

  • Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF, Smith DR (2006) Metamaterial electromagnetic cloak at microwave frequencies. Science 314:977980

    Article  Google Scholar 

  • Shelby RA, Smith DR, Schultz S (2001) Experimental verification of a negative index of refraction. Science 292:7779

    Article  Google Scholar 

  • Smith D, Schultz S, MarkoÅ¡ P, Soukoulis C (2002) Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Phys Rev B 65(19):195104

    Article  Google Scholar 

  • Tang W, Argyropoulos C, Kallos E, Song W, Hao Y (2010) Discrete coordinate transformation for designing all-dielectric flat antennas. IEEE Trans Antennas Propag 58(12):3795–3804

    Article  Google Scholar 

  • Tichit PH, Burokur SN, de Lustrac A (2009) Ultradirective antenna via transformation optics. J Appl Phys 105(10):104912

    Article  Google Scholar 

  • Tichit PH, Burokur SN, Germain D, de Lustrac A (2011) Design and experimental demonstration of a high-directive emission with transformation optics. Phys Rev B 83(15):155108

    Google Scholar 

  • Wald R (1984) General relativity. University of Chicago Press, Chicago

    Book  MATH  Google Scholar 

  • Wan X, Jiang WX, Ma HF, Cui TJ (2014) A broadband transformation-optics metasurface lens. Appl Phys Lett 104(15):151601

    Article  Google Scholar 

  • Ward A, Pendry J (1996) Refraction and geometry in maxwell’s equations. J Mod Opt 43(4):773–793

    Article  MathSciNet  MATH  Google Scholar 

  • Ward A, Pendry J (1998) Calculating photonic greens functions using a nonorthogonal finite-difference time-domain method. Phys Rev B 58(11):7252

    Article  Google Scholar 

  • Werner DH, Kwon D-H (2014) Transformation electromagnetics and metamaterials. Springer, London

    Book  Google Scholar 

  • Wu Q, Jiang ZH, Quevedo-Teruel O, Turpin JP, Tang W, Hao Y, Werner DH (2013) Transformation optics inspired multibeam lens antennas for broadband directive radiation. IEEE Trans Antennas Propag 61(12):5910–5922

    Article  Google Scholar 

  • Yaghjian AD, Maci S (2009) Alternative derivation of electromagnetic cloaks and concentrators. New J Phys 10(11):115022

    Google Scholar 

  • Yang R, Tang W, Hao Y (2011a) Wideband beam-steerable flat reflectors via transformation optics. IEEE Antennas Wirel Propag Lett 10:1290–1294

    Article  Google Scholar 

  • Yang R, Tang W, Hao Y, Youngs I (2011b) A coordinate transformation-based broadband flat lens via microstrip array. IEEE Antennas Wirel Propag Lett 10:99–102

    Article  Google Scholar 

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Correspondence to Tie Jun Cui .

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Bao, D., Cui, T.J. (2016). Theory of Transformation Optics in Antenna Design. In: Chen, Z., Liu, D., Nakano, H., Qing, X., Zwick, T. (eds) Handbook of Antenna Technologies. Springer, Singapore. https://doi.org/10.1007/978-981-4560-44-3_22

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