Skip to main content
SpringerLink
Log in

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

  • Chapter
  • First Online:
Transformation Electromagnetics and Metamaterials

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Barrow WL, Greene FM (1938) Rectangular hollow-pipe radiators. Proc IEEE 26:1498–1519

    Google Scholar 

  2. Barrow WL, Chu LJ (1939) Theory of the electromagnetic horn. Proc IEEE 27:51–64

    Google Scholar 

  3. Balanis CA (2005) Antenna theory: analysis and design, 3rd edn. Wiley, Hoboken

    Google Scholar 

  4. Burnside W, Chuang C (1982) An aperture-matched horn design. IEEE Trans Antennas Propag 30:790–796

    Article  Google Scholar 

  5. Lawrie RE, Peters L (1965) Modification of horn antennas for low sidelobe levels. In: Proceedings of International Symposium Antennas Propagation, pp 289–293

    Google Scholar 

  6. Love AW (1978) Reflector antennas. IEEE Press, New York

    Google Scholar 

  7. Dolph CL (1946) A current distribution for broadside arrays which optimizes the relationship between beam-width and side-lobe level. Proc IRE 34:335–348

    Article  Google Scholar 

  8. Foster RM (1926) Directive diagrams of antenna arrays. Bell Syst Tech J 5:292–307

    Google Scholar 

  9. Gregory MD, Petko JS, Spence TG, Werner DH (2010) Nature-inspired design techniques for ultra-wideband aperiodic antenna arrays. IEEE Antennas Propag Mag 52:28–45

    Article  Google Scholar 

  10. Hansen WW, Woodyard JR (1938) A new principle in directional antenna design. Proc IRE 26:333–345

    Article  Google Scholar 

  11. King RWP, Sandler SS (1964) The theory of endfire arrays. IEEE Trans Antennas Propag 12:276–280

    Article  Google Scholar 

  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 49–52

    Google Scholar 

  13. Kock WE (1946) Metal-lens antennas. Proc IRE 34:828–836

    Article  Google Scholar 

  14. Ruze J (1950) Wide-angle metal-plate optics. Proc IRE 38:53–59

    Article  Google Scholar 

  15. Martindale JPA (1953) Lens aerials at centimetric wavelengths: a critical survey of the present position. J British IRE 13:243–259

    Google Scholar 

  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 5:25–30

    Article  Google Scholar 

  17. Luneberg RK (1944) Mathematical theory of optics. Brown University Press, Providence

    MATH  Google Scholar 

  18. Rotman W, Turner R (1963) Wide-angle microwave lens for line source applications. IEEE Trans Antennas Propag 11:623–632

    Article  Google Scholar 

  19. Rinehart RF (1948) A solution of the problem of rapid scanning for radar antennae. J Appl Phys 19:860–862

    Article  Google Scholar 

  20. Alitalo P, Luukkonen O, Vehmas J, Tretyakov SA (2008) Impedance-matched microwave lens. IEEE Antennas Wireless Propag Lett 7:187–191

    Article  Google Scholar 

  21. Chang K (2005) Encyclopedia of RF and microwave engineering. Wiley, Hoboken

    Book  Google Scholar 

  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 12:48–50

    Article  Google Scholar 

  23. Guérin N, Enoch S, Tayeb G, Sabouroux P, Vincent P, Legay H (2006) A metallic Fabry-Pérot directive antenna. IEEE Trans Antennas Propag 54:220–224

    Article  Google Scholar 

  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 Propagation

    Google Scholar 

  25. Yablonovitch E (1993) Photonic band-gap structures. J Opt Soc Am 10:283–295

    Google Scholar 

  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 47:2059–2074

    Article  Google Scholar 

  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 51:2691–2703

    Article  Google Scholar 

  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 53:8–17

    Article  Google Scholar 

  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 51:2936–2946

    Article  Google Scholar 

  30. Thèvenot M, Cheype C, Reineix A, Jecko B (1999) Directive photonic-bandgap antennas. IEEE Trans Microw Theory Tech 47:2115–2122

    Article  Google Scholar 

  31. Cheype C, Serier C, Thèvenot M, Monédière T, Reineix A, Jecko B (2002) An electromagnetic bandgap resonator antenna. IEEE Trans Antennas Propag 50:1285–1290

    Article  Google Scholar 

  32. Shelby RA, Smith DR, Schultz S (2001) Experimental verification of a negative index of refraction. Science 292:77–79

    Article  Google Scholar 

  33. Smith DR, Pendry JB, Wiltshire MCK (2004) Metamaterials and negative refractive index. Science 305:788–792

    Article  Google Scholar 

  34. Soukoulis CM, Linden S, Wegener M (2007) Negative refractive index at optical wavelengths. Science 315:47–49

    Article  Google Scholar 

  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 455:376–379

    Article  Google Scholar 

  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 101:014101/1–3

    Google Scholar 

  37. Enoch S, Tayeb G, Sabouroux P, Guérin N, Vincent P (2002) A metamaterial for directive emission. Phys Rev Lett 89:213902/1–4

    Google Scholar 

  38. Ziolkowski RW (2004) Propagation in the scattering from a matched metamaterial having a zero index of refraction. Phys Rev E 70:046608/1–12

    Google Scholar 

  39. Kwon DH, Werner DH (2008) Low-index metamaterial designs in the visible spectrum. Opt Express 15:9267–9272

    Article  Google Scholar 

  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 5:499–505

    Article  Google Scholar 

  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 6:4475–4482

    Article  Google Scholar 

  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 109:013515/1–11

    Google Scholar 

  43. Kong JA (2000) Electromagnetic wave theory. EMW Cambridge, Boston

    Google Scholar 

  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 48:2581–2586

    Article  Google Scholar 

  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 58:79–87

    Article  Google Scholar 

  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 48:2542–2548

    Article  Google Scholar 

  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 54:1017–1030

    Article  Google Scholar 

  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 50:2902–2904

    Article  Google Scholar 

  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 29:493–498

    Article  Google Scholar 

  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 51:1973–1976

    Article  Google Scholar 

  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 24:1387–1396

    Google Scholar 

  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 52:1855–1858

    Article  Google Scholar 

  53. Xiao Z, Xu H (2008) Low refractive metamaterials for gain enhancement of horn antenna. J Infrared Mill Terahz Waves 30:225–232

    Article  Google Scholar 

  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 31:1289–1303

    Article  Google Scholar 

  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 23:953–962

    Google Scholar 

  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 51:2178–2180

    Article  Google Scholar 

  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 48:680–683

    Article  Google Scholar 

  58. Yuan Y, Shen L, Ran L, Jiang T, Huangfu J, Kong JA (2008) Directive emission based on anisotropic metamaterials. Phys Rev A 77:053821/1–4

    Google Scholar 

  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 94:044107/1–3

    Google Scholar 

  60. Zhou B, Cui TJ (2011) Directivity enhancement to Vivaldi antennas using compactly anisotropic zero-index metamaterials. IEEE Antennas Wirel Propag Lett 10:326–329

    Article  Google Scholar 

  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 120:235–247

    Google Scholar 

  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 51:295–328

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  64. Leonhardt U (2006) Optical conformal mapping. Science 312:1777–1780

    Article  MathSciNet  MATH  Google Scholar 

  65. Kwon DH, Werner DH (2010) Transformation electromagnetics: an overview of the theory and applications. IEEE Antennas Propag Mag 52:24–46

    Article  Google Scholar 

  66. Zhang JJ, Luo Y, Xi S, Chen HS, Ran LX, Wu BI, Kong JA (2008) Directive emission obtained by coordinate transformation. PIER 81:437–446

    Article  Google Scholar 

  67. Kwon DH, Werner DH (2008) Transformation optical designs for wave collimators flat lenses and right-angle bends. N J Phys 10:115023/1–13

    Google Scholar 

  68. Jiang WX, Cui TJ, Ma HF, Zhou XY, Cheng Q (2008) Cylindrical-to-plane-wave conversion via embedded transformation. Appl Phys Lett 92:261903/1–3

    Google Scholar 

  69. Jiang WX, Cui TJ, Ma HF, Yang XM, Cheng Q (2008) Layered high-gain lens antennas via discrete optical transformation. Appl Phys Lett 93:221906/1–3

    Google Scholar 

  70. Luo Y, Zhang J, Chen H, Huangfu J, Ran L (2009) High-directivity antenna with small antenna aperture. Appl Phys Lett 95:193506/1–3

    Google Scholar 

  71. Lu W, Lin Z, Chen H, Chan CT (2009) Transformation media based super focusing antenna. J Phys D: Appl Phys 42:212002/1–4

    Google Scholar 

  72. Cheng Q, Cui TJ (2010) Radiation of planar electromagnetic waves by a line source in anisotropic metamaterials. J Phys D: Appl Phys 43:335406/1–6

    Google Scholar 

  73. Kundtz N, Smith DR (2009) Extreme-angle broadband metamaterial lens. Nat Mater 9:129–132

    Article  Google Scholar 

  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 58:3795–3804

    Article  Google Scholar 

  75. Ma HF, Cui TJ (2010) Three-dimensional broadband and broad-angle transformation-optics lens. Nat Commun 1:124/1–7

    Google Scholar 

  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 18:244–252

    Article  Google Scholar 

  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 83:155108/1–7

    Google Scholar 

  78. Jiang ZH, Gregory MD, Werner DH (2011) Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission. Phys Rev B 84:165111/1–6

    Google Scholar 

  79. Garcia-Meca C, Martinez A, Leonhardt U (2011) Engineering antenna radiation patterns via quasi-conformal mappings. Opt Express 19:23743–23750

    Article  Google Scholar 

  80. Yao K, Jiang X, Chen H (2012) Collimating lenses from non-Euclidean transformation optics. N J Phys 14:023011/1–9

    Google Scholar 

  81. Li J, Pendry JB (2008) Hiding under the carpet: a new strategy for cloaking. Phys Rev Lett 101:203901/1–4

    Google Scholar 

  82. Landy NI, Padilla WJ (2009) Guiding light with conformal transformations. Opt Express 17:14872–14879

    Article  Google Scholar 

  83. Zeng Y, Liu J, Werner DH (2011) General properties of two-dimensional conformal transformations in electrostatics. Opt Express 19:20035–20047

    Article  Google Scholar 

  84. Zeng Y, Werner DH (2012) Two-dimensional inside-out Eaton lens: wave properties and design technique. Opt Express 20:2335–2345

    Article  Google Scholar 

  85. Driscoll TA (1996) A MATLAB toolbox for Schwarz-Christoffel mapping. ACM Trans Math Soft 22:168–186

    Article  MATH  Google Scholar 

  86. Schurig D, Mock JJ, Smith DR (2006) Electric-field-coupled resonators for negative permittivity metamaterials. Appl Phys Lett 88:041109/1–3

    Google Scholar 

  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 60:5717−5726

    Google Scholar 

  88. Turpin JP, Werner DH (2012) Cylindrical metamaterial lens for single-feed adaptive beamforming. In: Proceedings of IEEE International Symposium Antennas Propagation

    Google Scholar 

  89. Turpin JP, Werner DH (2012) Switchable near-zero-index magnetic metamaterial for dynamic beam-scanning lens. In: Proceedings of IEEE International Symposium Antennas Propagation

    Google Scholar 

  90. Ma HF, Cui TJ (2010) Three-dimensional broadband ground-plane cloak made of metamaterials. Nat Commun 1:21/1–6

    Google Scholar 

  91. Valentine J, Li J, Zentgraf T, Bartal G, Zhang X (2009) An optical cloak made of dielectrics. Nat Mater 8:568–571

    Article  Google Scholar 

  92. Semouchkina E, Werner DH, Semouchkin GB, Pantano C (2010) An infrared invisibility cloak composed of glass. Appl Phys Lett 96:233503/1–3

    Google Scholar 

  93. Ergin T, Stenger N, Brenner P, Pendry JB, Wegener M (2010) Three-dimensional invisibility cloak at optical wavelengths. Science 328:337–339

    Article  Google Scholar 

  94. Gabrielli LH, Cardenas J, Poitras CB, Lipson M (2009) Silicon nanostructure cloak operating at optical frequencies. Nat Photon 3:461–463

    Article  Google Scholar 

  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 17:12922–12928

    Article  Google Scholar 

  96. Thompson NP, Soni JF, Weatherill BK (1999) Handbook of grid generation. CRC Press, Boca Raton

    MATH  Google Scholar 

  97. Mastin CW, Thompson JF (1984) Quasiconformal mappings and grid generation. SIAM J Sci Stat Comput 5:305–310

    Article  MathSciNet  MATH  Google Scholar 

  98. Tichit PH, Burokur S, Lustrac A (2009) Ultradirective antenna via transformation optics. J Appl Phys 105:104912/1–3

    Google Scholar 

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

    Article  Google Scholar 

  100. Zhang B, Luo Y, Liu X, Barbastathis G (2011) Macroscopic invisibility cloak for visible light. Phys Rev Lett 106:033901/1–4

    Google Scholar 

  101. Chen X, Luo Y, Zhang J, Jiang K, Pendry JB, Zhang S (2011) Macroscopic invisibility cloaking of visible light. Nat Commun 2:176/1–6

    Google Scholar 

  102. David H (1999) New foundations for classical mechanics. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  103. http://www.comsol.com/

  104. Lier E, Werner DH, Scarborough CP, Wu Q, Bossard JA (2011) An octave-bandwidth negligible-loss radiofrequency metamaterial. Nat Mater 10:216–222

    Article  Google Scholar 

  105. Cho C, Choo H, Park I (2008) Printed symmetric inverted-F antenna with a quasi-isotropic radiation pattern. Microw Opt Technol Lett 50:927–930

    Article  Google Scholar 

  106. http://www.ansoft.com/products/hf/hfss/

  107. Caloz C, Itoh T (2005) Electromagnetic metamaterials: transmission line theory and microwave applications. Wiley, Hoboken

    Book  Google Scholar 

  108. Jiang ZH, Gregory MD, Werner DH (2012) Broadband high directivity multi-beam emission through transformation optics enabled metamaterial lenses. IEEE Trans Antennas Propag 60:5063−5074

    Google Scholar 

  109. Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF, Smith DR (2006) Metamaterial electromagnetic cloak at microwave frequencies. Science 314:977–980

    Article  Google Scholar 

  110. Novotny L, Hulst N (2007) Antennas for light. Nat Photon 5:83–90

    Article  Google Scholar 

  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 81:437–446

    Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, 16802, USA

    Douglas H. Werner, Zhi Hao Jiang, Jeremiah P. Turpin, Qi Wu & Micah D. Gregory

Authors
  1. Douglas H. Werner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi Hao Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jeremiah P. Turpin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qi Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Micah D. Gregory
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Douglas H. Werner .

Editor information

Editors and Affiliations

  1. The Pennsylvania State University, Electrical Engineering East 211A, University Park, 16802, USA

    Douglas H. Werner

  2. University of Massachusetts Amherst, Natural Resources Road Marcus 201 100, Amherst, 01003, USA

    Do-Hoon Kwon

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag London

About this chapter

Cite this chapter

Werner, D.H., Jiang, Z.H., Turpin, J.P., Wu, Q., Gregory, M.D. (2014). Transformation Electromagnetics Inspired Lens Designs and Associated Metamaterial Implementations for Highly Directive Radiation. In: Werner, D., Kwon, DH. (eds) Transformation Electromagnetics and Metamaterials. Springer, London. https://doi.org/10.1007/978-1-4471-4996-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-4996-5_8

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4995-8

  • Online ISBN: 978-1-4471-4996-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation