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Fractal Electrodynamics and Modeling

  • Dwight L. Jaggard

Abstract

Since nature has provided us with structures of almost infinite complexity and variety, it is apparent that some, and perhaps most, of these structures cannot be treated by traditional deterministic methods when modeling their interaction with electromagnetic waves. As one alternative, average properties of these interactions can be treated through statistical means and the use of averages and higher-order moments. These conventional methods are particularly successful when the scales of these structures are limited to modest ranges of variation or to the case of resonant interaction. However, certain types of wildly irregular, ramified, or variegated structures contain many scale sizes as demonstrated in the fractal surfaces of Fig. 1. It is often difficult to characterize the interaction of waves with these structures and in many cases it is not even easy to model these structures. It is just these complicated structures which are of interest to us here and which can often be modeled by the use of fractals. Thus, we blend fractal geometry and electromagnetics in a discipline we call fractal electrodynamics [1].

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Selected References

  1. [1]
    D. L. Jaggard, “On Fractal Electrodynamics,” in Recent Advances in Electromagnetic Theory, H. N. Kritikos and D. L. Jaggard, eds., Springer-Verlag, New York (1990).Google Scholar
  2. [2]
    Mandelbrot, B. B., The Fractal Geometry of Nature, W. H. Freeman and Company, San Francisco (1983).Google Scholar
  3. [3]
    This discussion is based, in part, on a lecture of Leo P. Kadanoff, “Measuring the Properties of Fractals,” presented at AT&T Bell Laboratories, Holmdel, NJ (Feb. 14, 1986); also see M. Barnsley, Fractals Everywhere, Academic Press, Boston (1988).Google Scholar
  4. [4]
    Berry, M. V. and Z. V. Lewis, Proc. R. Soc. London Ser. A370, 459–484 (1980).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    Jaggard, D. L. and Y. Kim, “Diffraction by Bandlimited Fractal Screens,” J. Opt. Soc. Am. A4, 1055–1062 (1987).ADSCrossRefMathSciNetGoogle Scholar
  6. [6]
    Kim, Y. and D. L. Jaggard, “A Bandlimited Fractal Model of Atmospheric Refractivity Fluctuation,” J. Opt. Soc. Am. A5, 475–480 (1988); orADSCrossRefGoogle Scholar
  7. [6a]
    Y. Kim and D. L. Jaggard, “Optical Beam Propagation in a Bandlimited Fractal Medium,” J. Opt. Soc. Am. A5, 1419–1426 (1988).ADSCrossRefGoogle Scholar
  8. [7]
    D. L. Jaggard and X. Sun, “Scattering by Fractally Corrugated Surfaces,” J. Opt. Soc. A7, 1131–1139(1990).ADSGoogle Scholar
  9. [8]
    X. Sun and D. L. Jaggard, “Wave Scattering from Non-Random Fractal Surfaces” to appear in Opt. Comm. (1990); or D. L. Jaggard and X. Sun, “Rough Surface Scattering: A Generalized Rayleigh Solution” to appear in J. Appl. Phy. (Dec. 1990).Google Scholar
  10. [9]
    Jaggard, D. L. and X. Sun, “Backscatter Cross-Section of Bandlimited Fractal Fibers,” IEEE Trans. Ant. and Propagat. AP-37, 1591–1597 (1989).ADSCrossRefGoogle Scholar
  11. [10]
    X. Sun and D. L. Jaggard, “Scattering from Fractally Fluted Cylinders,” J. Electromagnetic Wave Appl.4,599–611 (1990).Google Scholar
  12. [11]
    Y. Kim, H. Grebel and D. L. Jaggard, “Diffraction by Fractally Serrated Apertures,” to appear in J. Opt. Soc. A. (Nov. 1990).Google Scholar
  13. [12]
    Kim, Y. and D. L. Jaggard, “Fractal Random Arrays,” Proc. IEEE74, 1278–1280, (1986).ADSCrossRefGoogle Scholar
  14. [13]
    D. L. Jaggard and X. Sun, “Reflection from Fractal Multi-Layers,” to appear in Optics Lett. (Fall 1990).Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Dwight L. Jaggard
    • 1
  1. 1.Complex Media Laboratory, Moore School of Electrical EngineeringUniversity of PennsylvaniaPhiladelphiaUSA

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