• Arnold McKinleyEmail author
Part of the Signals and Communication Technology book series (SCT)


This chapter establishes the mathematical foundations used throughout the volume. We focus first on the geometry and coordinate systems of the loop and Maxwell’s fundamental equations including material characteristics. Since energy propagates through space and through materials as waves, propagation parameters, frequency dependence of material parameters, and characteristics of materials from RF through the optical region are covered. A description of Scalar and Vector potentials paves the way for establishing the governing equations of thin-wire and thick-wire loops and rings in later chapters. Methods of coupling energy into the ring end the chapter. No technical distinction has been made in the literature between “loops” and “rings”; the literature seems to make a distinction based on size. Small loops, smaller than say 30 mm in circumference seem to be called “rings” more often than not, while those larger are called “loops”. All meta-atoms that appear in the literature are in the GHz and higher frequency regions and fit that description. Historically, small loops approaching this same region were used as sensors and generally called “loops”, rather than “rings”.


  1. 1.
    R. King, J. Harrison, C., D. Tingley, IEEE Trans. Antennas Propag. 12(4), 434 (1964).
  2. 2.
    J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1999)zbMATHGoogle Scholar
  3. 3.
    G. Harbeke, Optical Properties of Semi-Conductors (North-Holland Publishing Company, Amsterdam, 1972), pp. 21–94Google Scholar
  4. 4.
    F. Abeles, Optical Properties of Metals (North-Holland Publishing Company, Amsterdam, 1972), p. 1026Google Scholar
  5. 5.
    C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH Verlag GmbH and Co, KGaA, 2004)Google Scholar
  6. 6.
    F. Sagnard, IEEE Trans. Instrum. Meas. 54(3), 1266 (2005)CrossRefGoogle Scholar
  7. 7.
    E. Hecht, Optics, 3rd edn. (Addison-Wesley, Boston, 1998)Google Scholar
  8. 8.
    Agilent, Basics of Measuring the Dielectric Properites of Materials, Application Note, 5989th edn. (Agilent Technologies, Inc, Santa Clara, 2104)Google Scholar
  9. 9.
    J. Leng, J. Opsal, H. Chu, M. Senko, D.E. Aspnes, Thin Film Solids-Elsevier Sci. SA 313–314, 132 (1998)CrossRefGoogle Scholar
  10. 10.
    P.G. Techegoin, E.C. Le Ru, M. Meyer, J. Chem. Phys. 125(October), 164705 (2006)Google Scholar
  11. 11.
    P.G. Etchegoin, E.C. Le Ru, M. M, J. Chem. Phys. 127, 189901 (2007)Google Scholar
  12. 12.
    A. Vial, T. Laroche, J. Phys. D: Appl. Phys. 40, 7152 (2007)CrossRefGoogle Scholar
  13. 13.
    A. Vial, J. Opt. A: Pure Appl. Opt. 9, 745 (2007)CrossRefGoogle Scholar
  14. 14.
    V. A, L. T, Appl. Phys. B 93, 139 (2008)Google Scholar
  15. 15.
    P.B. Johnson, R.W. Christy, Phys. Rev. B 6(12), 4370 (1972)CrossRefGoogle Scholar
  16. 16.
    D.E. Aspnes, A.A. Studna, Phys. Rev. B 27, 985 (1983).
  17. 17.
    A.F. McKinley, T.P. White, K.R. Catchpole, J. Appl. Phys. 114(4), 044317 (2013).
  18. 18.
    J.D. Jackson, Am. J. Phys. 70(9), 917 (2002).
  19. 19.
    S.A. Schelkunoff, Electromagnetic Waves (D) (Van Nostrand, 1966)Google Scholar
  20. 20.
    R.W.P. King, The Loop Antenna for Transmission and Reception, vol. 7, 1st edn., Inter-University Electronic Series (McGraw-Hill, New York, 1969), pp. 458–482Google Scholar
  21. 21.
    T.T. Wu, in Antenna Theory Part 1, ed. by R.E. Collin, F.J. Zucker (McGraw-Hill, 1969), pp. 306–351Google Scholar
  22. 22.
    T. Do-Nhat, R.H. Macphie, IEEE Trans. Antennas Propag. 37(12), 1545 (1989).
  23. 23.
    P.J. Papakanellos, G. Fikioris, Prog. Electromagn. Res. 69, 77 (2007)CrossRefGoogle Scholar
  24. 24.
    G. Fikioris, P.J. Papakanellos, T.K. Mavrogordatos, N. Lafkas, D. Koulikas, SIAM J. Appl. Math. 71(2), 559 (2011).
  25. 25.
    I. Tastsoglou, G. Fikioris, IEEE Trans. Antennas Propag. 61(11), 5517 (2013).
  26. 26.
    I. Tastsoglou, G. Fikioris, IEEE Trans. Antennas Propag. 61(11), 5527 (2013).
  27. 27.
    G. Fikioris, P. Papakanellos, H. Anastassiu, IEEE Trans. Antennas Propag. 56(1), 151 (2008).
  28. 28.
    G. Fikioris, P. Papakanellos, H. Anastassiu, IEEE Trans. Antennas Propag. 58(10), 3436 (2010).
  29. 29.
    G. Zhou, G. Smith, IEEE Trans. Antennas Propag. 39(8), 1167 (1991).
  30. 30.
    C.A. Balanis, Antenna Theory, Analysis and Design, 4th edn. (Wiley, New York, 2016)Google Scholar
  31. 31.
    G. Fikioris, J. Lionas, C. Lioutas, IEEE Trans. Antennas Propag. 51(8), 1847 (2003).
  32. 32.
    K. Esselle, S. Stuchly, IEEE Trans. Antennas Propag. 38(7), 1123 (1990).

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.University College LondonLondonUK

Personalised recommendations