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Transformation Electromagnetics Inspired Lens Designs and Associated Metamaterial Implementations for Highly Directive Radiation

  • Douglas H. Werner
  • Zhi Hao Jiang
  • Jeremiah P. Turpin
  • Qi Wu
  • Micah D. Gregory
Chapter

Abstract

In this chapter, the transformation electromagnetics (TE) approach for achieving highly directive radiation is introduced and demonstrated by both numerical simulations and experimental results obtained from laboratory prototypes. In addition to conventional approaches for designing directive antennas, the recently developed metamaterial-related techniques, such as the electromagnetic bandgap (EBG) structures, zero-index metamaterials, and transformation optics (TO), are reviewed. In particular, several coordinate transformations which can provide simplified material parameters are proposed, including the conformal mapping, quasi-conformal (QC) mapping, geometry-similar transformation, and the uniaxial media simplification method. All of these techniques are capable of achieving a certain degree of simplification in the transformed material parameters without sacrificing the device performance. The design and demonstration of various beam collimating devices illustrate their unique properties and suitability for different applications such as in compact wireless systems. In all, these TE-enabled lenses with simple material parameters are expected to find widespread applications in the fields of microwave antennas as well as optical nanoantennas.

Keywords

Conformal Mapping Radiation Pattern Ground Plane Line Source Horn Antenna 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors wish to thank Erik Lier, Bonnie Martin, and Matt Bray of Lockheed Martin for their assistance with fabrication and measurements of the metalens designs. Portions of this work were supported by the Lockheed Martin University Research Initiative (LM URI) program. The QCTO and the geometrical similar coordinate transformation work were partially supported by the National Science Foundation’s Material Research Science and Engineering Center (MRSEC) Grant No. DMR-0820404.

References

  1. 1.
    Barrow WL, Greene FM (1938) Rectangular hollow-pipe radiators. Proc IEEE 26:1498–1519Google Scholar
  2. 2.
    Barrow WL, Chu LJ (1939) Theory of the electromagnetic horn. Proc IEEE 27:51–64Google Scholar
  3. 3.
    Balanis CA (2005) Antenna theory: analysis and design, 3rd edn. Wiley, HobokenGoogle Scholar
  4. 4.
    Burnside W, Chuang C (1982) An aperture-matched horn design. IEEE Trans Antennas Propag 30:790–796CrossRefGoogle Scholar
  5. 5.
    Lawrie RE, Peters L (1965) Modification of horn antennas for low sidelobe levels. In: Proceedings of International Symposium Antennas Propagation, pp 289–293Google Scholar
  6. 6.
    Love AW (1978) Reflector antennas. IEEE Press, New YorkGoogle Scholar
  7. 7.
    Dolph CL (1946) A current distribution for broadside arrays which optimizes the relationship between beam-width and side-lobe level. Proc IRE 34:335–348CrossRefGoogle Scholar
  8. 8.
    Foster RM (1926) Directive diagrams of antenna arrays. Bell Syst Tech J 5:292–307Google Scholar
  9. 9.
    Gregory MD, Petko JS, Spence TG, Werner DH (2010) Nature-inspired design techniques for ultra-wideband aperiodic antenna arrays. IEEE Antennas Propag Mag 52:28–45CrossRefGoogle Scholar
  10. 10.
    Hansen WW, Woodyard JR (1938) A new principle in directional antenna design. Proc IRE 26:333–345CrossRefGoogle Scholar
  11. 11.
    King RWP, Sandler SS (1964) The theory of endfire arrays. IEEE Trans Antennas Propag 12:276–280CrossRefGoogle Scholar
  12. 12.
    Yagi H, Uda S (1926) Projector of the sharpest beam of electric waves. In: Proceedings of the imperial academy of Japan, vol 2, pp 49–52Google Scholar
  13. 13.
    Kock WE (1946) Metal-lens antennas. Proc IRE 34:828–836CrossRefGoogle Scholar
  14. 14.
    Ruze J (1950) Wide-angle metal-plate optics. Proc IRE 38:53–59CrossRefGoogle Scholar
  15. 15.
    Martindale JPA (1953) Lens aerials at centimetric wavelengths: a critical survey of the present position. J British IRE 13:243–259Google Scholar
  16. 16.
    Holt FS, Mayer A (1957) A design procedure for dielectric microwave lenses of large aperture ratio and large scanning angle. IRE Trans Antennas Propag 5:25–30CrossRefGoogle Scholar
  17. 17.
    Luneberg RK (1944) Mathematical theory of optics. Brown University Press, ProvidenceMATHGoogle Scholar
  18. 18.
    Rotman W, Turner R (1963) Wide-angle microwave lens for line source applications. IEEE Trans Antennas Propag 11:623–632CrossRefGoogle Scholar
  19. 19.
    Rinehart RF (1948) A solution of the problem of rapid scanning for radar antennae. J Appl Phys 19:860–862CrossRefGoogle Scholar
  20. 20.
    Alitalo P, Luukkonen O, Vehmas J, Tretyakov SA (2008) Impedance-matched microwave lens. IEEE Antennas Wireless Propag Lett 7:187–191CrossRefGoogle Scholar
  21. 21.
    Chang K (2005) Encyclopedia of RF and microwave engineering. Wiley, HobokenCrossRefGoogle Scholar
  22. 22.
    Akalin T, Danglot J, Vanbésien O, Lippens D (2002) A highly directive dipole antenna embedded in a Fabry-Pérot cavity. IEEE Microwave Wirel Compon Lett 12:48–50CrossRefGoogle Scholar
  23. 23.
    Guérin N, Enoch S, Tayeb G, Sabouroux P, Vincent P, Legay H (2006) A metallic Fabry-Pérot directive antenna. IEEE Trans Antennas Propag 54:220–224CrossRefGoogle Scholar
  24. 24.
    Costa F, Carrubba E, Monorchio A, Manara G (2008) Multi-frequency highly directive Fabry-Pérot based antenna. In: Proceedings of IEEE International Symposium Antennas PropagationGoogle Scholar
  25. 25.
    Yablonovitch E (1993) Photonic band-gap structures. J Opt Soc Am 10:283–295Google Scholar
  26. 26.
    Sievenpiper D, Zhang L, Jimenez Broas RF, Alexópolous NG, Yablonovitch E (1999) High-impedance electromagnetic surfaces with a forbidden frequency band. IEEE Trans Microw Theory Tech 47:2059–2074CrossRefGoogle Scholar
  27. 27.
    Yang F, Rahmat-Samii Y (2003) Reflection phase characterizations of the EBG ground plane for low profile wire antenna applications. IEEE Trans Antennas Propag 51:2691–2703CrossRefGoogle Scholar
  28. 28.
    Kern DJ, Werner DH, Monorchio A, Lanuzza L, Wilhelm MJ (2005) The design synthesis of multi-band artificial magnetic conductors using high impedance frequency selective surfaces. IEEE Trans Antennas Propag 53:8–17CrossRefGoogle Scholar
  29. 29.
    Yang F, Rahmat-Samii Y (2003) Microstrip antennas integrated with electromagnetic band-gap (EBG) structures: a low mutual coupling design for array applications. IEEE Trans Antennas Propag 51:2936–2946CrossRefGoogle Scholar
  30. 30.
    Thèvenot M, Cheype C, Reineix A, Jecko B (1999) Directive photonic-bandgap antennas. IEEE Trans Microw Theory Tech 47:2115–2122CrossRefGoogle Scholar
  31. 31.
    Cheype C, Serier C, Thèvenot M, Monédière T, Reineix A, Jecko B (2002) An electromagnetic bandgap resonator antenna. IEEE Trans Antennas Propag 50:1285–1290CrossRefGoogle Scholar
  32. 32.
    Shelby RA, Smith DR, Schultz S (2001) Experimental verification of a negative index of refraction. Science 292:77–79CrossRefGoogle Scholar
  33. 33.
    Smith DR, Pendry JB, Wiltshire MCK (2004) Metamaterials and negative refractive index. Science 305:788–792CrossRefGoogle Scholar
  34. 34.
    Soukoulis CM, Linden S, Wegener M (2007) Negative refractive index at optical wavelengths. Science 315:47–49CrossRefGoogle Scholar
  35. 35.
    Valentine J, Zhang S, Zentgraf T, Ulin-Avila E, Genov DA, Bartal G, Zhang X (2008) Three-dimensional optical metamaterial with a negative refractive index. Nature 455:376–379CrossRefGoogle Scholar
  36. 36.
    Scarborough CP, Jiang ZH, Werner DH, Rivero-Baleine C, Drake C (2012) Experimental demonstration of an isotropic metamaterial super lens with negative unity permeability at 8.5 MHz. Appl Phys Lett 101:014101/1–3Google Scholar
  37. 37.
    Enoch S, Tayeb G, Sabouroux P, Guérin N, Vincent P (2002) A metamaterial for directive emission. Phys Rev Lett 89:213902/1–4Google Scholar
  38. 38.
    Ziolkowski RW (2004) Propagation in the scattering from a matched metamaterial having a zero index of refraction. Phys Rev E 70:046608/1–12Google Scholar
  39. 39.
    Kwon DH, Werner DH (2008) Low-index metamaterial designs in the visible spectrum. Opt Express 15:9267–9272CrossRefGoogle Scholar
  40. 40.
    Kocaman S, Aras MS, Hsieh P, McMillan JF, Biris CG, Panoiu NC, Yu MB, Kwong DL, Stein A, Wong CW (2011) Zero phase delay in negative-refractive-index photonic crystal superlattices. Nat Photon 5:499–505CrossRefGoogle Scholar
  41. 41.
    Yun S, Jiang ZH, Xu Q, Liu Z, Werner DH, Mayer TS (2012) Low-loss impedance-matched optical metamaterials with zero-phase delay. ACS Nano 6:4475–4482CrossRefGoogle Scholar
  42. 42.
    Jiang ZH, Bossard JA, Wang X, Werner DH (2011) Synthesizing metamaterials with angularly independent effective medium properties based on an anisotropic parameter retrieval technique coupled with a genetic algorithm. J Appl Phys 109:013515/1–11Google Scholar
  43. 43.
    Kong JA (2000) Electromagnetic wave theory. EMW Cambridge, BostonGoogle Scholar
  44. 44.
    Bonefačić D, Hrabar S, Kvakan D (2006) Experimental investigation of radiation properties of an antenna embedded in low permittivity thin-wire-based metamaterial. Microw Opt Technol Lett 48:2581–2586CrossRefGoogle Scholar
  45. 45.
    Zhou R, Zhang H, Xin H (2010) Metallic wire array as low-effective index of refraction medium for directive antenna application. IEEE Trans Antennas Propag 58:79–87CrossRefGoogle Scholar
  46. 46.
    Lovat G, Burghignoli P, Capolino F, Jackson DR (2006) High directivity in low-permittivity metamaterial slabs: ray-optic vs. leaky-wave models. Microw Opt Technol Lett 48:2542–2548CrossRefGoogle Scholar
  47. 47.
    Lovat G, Burghignoli G, Capolino F, Jackson DR, Wilton DR (2006) Analysis of directive radiation from a line source in a metamaterial slab with low permittivity. IEEE Trans Antennas Propag 54:1017–1030CrossRefGoogle Scholar
  48. 48.
    Weng Z, Song Y, Jiao Y, Zhang F (2008) A directive dual-band and dual-polarized antenna with zero index metamaterial. Microw Opt Technol Lett 50:2902–2904CrossRefGoogle Scholar
  49. 49.
    Xu H, Zhao Z, Lv Y, Du C, Luo X (2008) Metamaterial superstrate and electromagnetic band-gap substrate for high directive antenna. J Infrared Mill Terahz Waves 29:493–498CrossRefGoogle Scholar
  50. 50.
    Ju J, Kim D, Lee WJ, Choi JI (2009) Wideband high-gain antenna using metamaterial superstrate with the zero refractive index. Microw Opt Technol Lett 51:1973–1976CrossRefGoogle Scholar
  51. 51.
    Zhou H, Qu S, Pei Z, Yang Y, Zhang J, Wang J, Ma H, Gu C, Wang X, Xu Z, Peng W, Bai P (2010) A high-directive patch antenna based on all-dielectric near-zero-index metamaterial superstrates. JEMWA 24:1387–1396Google Scholar
  52. 52.
    Zhao G, Jiao YC, Zhang F, Zhang FS (2010) Design of high-gain low-profile resonant cavity antenna using metamaterial superstrate. Microw Opt Technol Lett 52:1855–1858CrossRefGoogle Scholar
  53. 53.
    Xiao Z, Xu H (2008) Low refractive metamaterials for gain enhancement of horn antenna. J Infrared Mill Terahz Waves 30:225–232CrossRefGoogle Scholar
  54. 54.
    Kim D, Choi J (2010) Analysis of antenna gain enhancement with a new planar metamaterial superstrate: an effective medium and a Fabry-Pérot resonance approach. J Infrared Mill Terahz Waves 31:1289–1303CrossRefGoogle Scholar
  55. 55.
    Zhou H, Pei Z, Qu S, Zhang S, Wang J, Li Q, Xu Z (2009) A planar zero-index metamaterial for directive emission. JEMWA 23:953–962Google Scholar
  56. 56.
    Zhu LX, Wang FM, Jiang ZY, Shen T, Ran LF (2009) Directive emission based on a new type of metamaterial. Microw Opt Technol Lett 51:2178–2180CrossRefGoogle Scholar
  57. 57.
    Wu BI, Wang W, Pacheco J, Chen X, Lu J, Grzegorczyk TM, Kong JA, Kao P, Theophelakes PA, Hogan MJ (2008) Anisotropic metamaterials as antenna substrate to enhance directivity. Microw Opt Technol Lett 48:680–683CrossRefGoogle Scholar
  58. 58.
    Yuan Y, Shen L, Ran L, Jiang T, Huangfu J, Kong JA (2008) Directive emission based on anisotropic metamaterials. Phys Rev A 77:053821/1–4Google Scholar
  59. 59.
    Ma YG, Wang P, Chen X, Ong CK (2009) Near-field plane-wave-like beam emitting antenna fabricated by anisotropic metamaterial. Appl Phys Lett 94:044107/1–3Google Scholar
  60. 60.
    Zhou B, Cui TJ (2011) Directivity enhancement to Vivaldi antennas using compactly anisotropic zero-index metamaterials. IEEE Antennas Wirel Propag Lett 10:326–329CrossRefGoogle Scholar
  61. 61.
    Zhou B, Li H, Zou XY, Cui TJ (2011) Broadband and high-gain planar Vivaldi antennas based on inhomogeneous anisotropic zero-index metamaterials. PIER 120:235–247Google Scholar
  62. 62.
    Wu BI, Wang W, Pacheco J, Chen X, Grzegorczyk TM, Kong JA (2005) A study of using metamaterials as antenna substrate to enhance gain. PIER 51:295–328CrossRefGoogle Scholar
  63. 63.
    Pendry JB, Schurig D, Smith DR (2006) Controlling electromagnetic fields. Science 312:1780–1782MathSciNetMATHCrossRefGoogle Scholar
  64. 64.
    Leonhardt U (2006) Optical conformal mapping. Science 312:1777–1780MathSciNetMATHCrossRefGoogle Scholar
  65. 65.
    Kwon DH, Werner DH (2010) Transformation electromagnetics: an overview of the theory and applications. IEEE Antennas Propag Mag 52:24–46CrossRefGoogle Scholar
  66. 66.
    Zhang JJ, Luo Y, Xi S, Chen HS, Ran LX, Wu BI, Kong JA (2008) Directive emission obtained by coordinate transformation. PIER 81:437–446CrossRefGoogle Scholar
  67. 67.
    Kwon DH, Werner DH (2008) Transformation optical designs for wave collimators flat lenses and right-angle bends. N J Phys 10:115023/1–13Google Scholar
  68. 68.
    Jiang WX, Cui TJ, Ma HF, Zhou XY, Cheng Q (2008) Cylindrical-to-plane-wave conversion via embedded transformation. Appl Phys Lett 92:261903/1–3Google Scholar
  69. 69.
    Jiang WX, Cui TJ, Ma HF, Yang XM, Cheng Q (2008) Layered high-gain lens antennas via discrete optical transformation. Appl Phys Lett 93:221906/1–3Google Scholar
  70. 70.
    Luo Y, Zhang J, Chen H, Huangfu J, Ran L (2009) High-directivity antenna with small antenna aperture. Appl Phys Lett 95:193506/1–3Google Scholar
  71. 71.
    Lu W, Lin Z, Chen H, Chan CT (2009) Transformation media based super focusing antenna. J Phys D: Appl Phys 42:212002/1–4Google Scholar
  72. 72.
    Cheng Q, Cui TJ (2010) Radiation of planar electromagnetic waves by a line source in anisotropic metamaterials. J Phys D: Appl Phys 43:335406/1–6Google Scholar
  73. 73.
    Kundtz N, Smith DR (2009) Extreme-angle broadband metamaterial lens. Nat Mater 9:129–132CrossRefGoogle Scholar
  74. 74.
    Tang W, Argyropoulos C, Kallos E, Song W, Hao Y (2010) Discrete coordinate transformation for designing all-dielectric flat antennas. IEEE Trans Antennas Propag 58:3795–3804CrossRefGoogle Scholar
  75. 75.
    Ma HF, Cui TJ (2010) Three-dimensional broadband and broad-angle transformation-optics lens. Nat Commun 1:124/1–7Google Scholar
  76. 76.
    Turpin JP, Massoud AT, Jiang ZH, Werner PL, Werner DH (2010) Conformal mappings to achieve simple material parameters for transformation optics devices. Opt Express 18:244–252CrossRefGoogle Scholar
  77. 77.
    Tichit PH, Burokur SN, Germain D, Lustrac A (2011) Design and experimental demonstration of a high-directive emission with transformation optics. Phys Rev B 83:155108/1–7Google Scholar
  78. 78.
    Jiang ZH, Gregory MD, Werner DH (2011) Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission. Phys Rev B 84:165111/1–6Google Scholar
  79. 79.
    Garcia-Meca C, Martinez A, Leonhardt U (2011) Engineering antenna radiation patterns via quasi-conformal mappings. Opt Express 19:23743–23750CrossRefGoogle Scholar
  80. 80.
    Yao K, Jiang X, Chen H (2012) Collimating lenses from non-Euclidean transformation optics. N J Phys 14:023011/1–9Google Scholar
  81. 81.
    Li J, Pendry JB (2008) Hiding under the carpet: a new strategy for cloaking. Phys Rev Lett 101:203901/1–4Google Scholar
  82. 82.
    Landy NI, Padilla WJ (2009) Guiding light with conformal transformations. Opt Express 17:14872–14879CrossRefGoogle Scholar
  83. 83.
    Zeng Y, Liu J, Werner DH (2011) General properties of two-dimensional conformal transformations in electrostatics. Opt Express 19:20035–20047CrossRefGoogle Scholar
  84. 84.
    Zeng Y, Werner DH (2012) Two-dimensional inside-out Eaton lens: wave properties and design technique. Opt Express 20:2335–2345CrossRefGoogle Scholar
  85. 85.
    Driscoll TA (1996) A MATLAB toolbox for Schwarz-Christoffel mapping. ACM Trans Math Soft 22:168–186MATHCrossRefGoogle Scholar
  86. 86.
    Schurig D, Mock JJ, Smith DR (2006) Electric-field-coupled resonators for negative permittivity metamaterials. Appl Phys Lett 88:041109/1–3Google Scholar
  87. 87.
    Turpin JP, Wu Q, Werner DH, Martin B, Bray M, Lier E (2012) Low cost and broadband dual-polarization metamaterial lens for directivity enhancement. IEEE Trans Antennas Propag 60:5717−5726Google Scholar
  88. 88.
    Turpin JP, Werner DH (2012) Cylindrical metamaterial lens for single-feed adaptive beamforming. In: Proceedings of IEEE International Symposium Antennas PropagationGoogle Scholar
  89. 89.
    Turpin JP, Werner DH (2012) Switchable near-zero-index magnetic metamaterial for dynamic beam-scanning lens. In: Proceedings of IEEE International Symposium Antennas PropagationGoogle Scholar
  90. 90.
    Ma HF, Cui TJ (2010) Three-dimensional broadband ground-plane cloak made of metamaterials. Nat Commun 1:21/1–6Google Scholar
  91. 91.
    Valentine J, Li J, Zentgraf T, Bartal G, Zhang X (2009) An optical cloak made of dielectrics. Nat Mater 8:568–571CrossRefGoogle Scholar
  92. 92.
    Semouchkina E, Werner DH, Semouchkin GB, Pantano C (2010) An infrared invisibility cloak composed of glass. Appl Phys Lett 96:233503/1–3Google Scholar
  93. 93.
    Ergin T, Stenger N, Brenner P, Pendry JB, Wegener M (2010) Three-dimensional invisibility cloak at optical wavelengths. Science 328:337–339CrossRefGoogle Scholar
  94. 94.
    Gabrielli LH, Cardenas J, Poitras CB, Lipson M (2009) Silicon nanostructure cloak operating at optical frequencies. Nat Photon 3:461–463CrossRefGoogle Scholar
  95. 95.
    Lee J, Blair J, Tamma V, Wu Q, Rhee S, Summers C, Park W (2009) Direct visualization of optical frequency invisibility cloak based on silicon nanorod array. Opt Express 17:12922–12928CrossRefGoogle Scholar
  96. 96.
    Thompson NP, Soni JF, Weatherill BK (1999) Handbook of grid generation. CRC Press, Boca RatonMATHGoogle Scholar
  97. 97.
    Mastin CW, Thompson JF (1984) Quasiconformal mappings and grid generation. SIAM J Sci Stat Comput 5:305–310MathSciNetMATHCrossRefGoogle Scholar
  98. 98.
    Tichit PH, Burokur S, Lustrac A (2009) Ultradirective antenna via transformation optics. J Appl Phys 105:104912/1–3Google Scholar
  99. 99.
    Kwon DH, Werner DH (2009) Flat focusing lens designs having minimized reflection based on coordinate transformation techniques. Opt Express 17:7807–7817CrossRefGoogle Scholar
  100. 100.
    Zhang B, Luo Y, Liu X, Barbastathis G (2011) Macroscopic invisibility cloak for visible light. Phys Rev Lett 106:033901/1–4Google Scholar
  101. 101.
    Chen X, Luo Y, Zhang J, Jiang K, Pendry JB, Zhang S (2011) Macroscopic invisibility cloaking of visible light. Nat Commun 2:176/1–6Google Scholar
  102. 102.
    David H (1999) New foundations for classical mechanics. Kluwer Academic Publishers, DordrechtGoogle Scholar
  103. 103.
  104. 104.
    Lier E, Werner DH, Scarborough CP, Wu Q, Bossard JA (2011) An octave-bandwidth negligible-loss radiofrequency metamaterial. Nat Mater 10:216–222CrossRefGoogle Scholar
  105. 105.
    Cho C, Choo H, Park I (2008) Printed symmetric inverted-F antenna with a quasi-isotropic radiation pattern. Microw Opt Technol Lett 50:927–930CrossRefGoogle Scholar
  106. 106.
  107. 107.
    Caloz C, Itoh T (2005) Electromagnetic metamaterials: transmission line theory and microwave applications. Wiley, HobokenCrossRefGoogle Scholar
  108. 108.
    Jiang ZH, Gregory MD, Werner DH (2012) Broadband high directivity multi-beam emission through transformation optics enabled metamaterial lenses. IEEE Trans Antennas Propag 60:5063−5074Google Scholar
  109. 109.
    Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF, Smith DR (2006) Metamaterial electromagnetic cloak at microwave frequencies. Science 314:977–980CrossRefGoogle Scholar
  110. 110.
    Novotny L, Hulst N (2007) Antennas for light. Nat Photon 5:83–90CrossRefGoogle Scholar
  111. 111.
    Zhang JJ, Luo Y, Xi S, Chen H, Ran L-X, Wu B-I, Kong JA (2008) Directive emission obtained by coordinate transformation. Prog Electromagnet Res 81:437–446CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Douglas H. Werner
    • 1
  • Zhi Hao Jiang
    • 1
  • Jeremiah P. Turpin
    • 1
  • Qi Wu
    • 1
  • Micah D. Gregory
    • 1
  1. 1.Department of Electrical EngineeringThe Pennsylvania State UniversityUniversity ParkUSA

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