Fractal Electrodynamics: From Super Antennas to Superlattices
We provide a selected overview of fractal electrodynamics by examining the properties of fractal antennas, arrays and apertures; and investigating the nature of electromagnetic wave scattering from fractal surfaces and superlattices.
Fractals offer an ideal blend of order and disorder that can be used in the design of robust antenna arrays with low or moderate side lobes. More recently, fractal geometry has also been used to design individual antenna elements suitable for multiband operation. We also investigate and review the diffraction of electromagnetic waves by fractal apertures.
Finally, we examine and review the scattering of electromagnetic waves from fractal surfaces and fractal superlattices. In each case fractals imprint their distinctive symmetry on interrogating waves. In this way fractal descriptors of an object are embedded in the scattered wave in such a way that they can often be extracted.
KeywordsFractal Dimension Antenna Array Fractal Structure Fractal Aperture Diffract Field
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- 1.Jaggard, D.L. (1990): On Fractal Electrodynamics. In Recent Advances in Electromagnetic Theory, H.N. Kritikos and D.L. Jaggard, editors, Springer-Verlag, New York, 183–224.Google Scholar
- 2.Jaggard, D.L. (1991): Fractal Electrodynamics and Modeling. In Directions in Electromagnetic Wave Modeling, H.L. Bertoni and L.B. Felsen, editors, Plenum Publishing Co., New York, 435–446.Google Scholar
- 3.Jaggard, D.L. (1995): Fractal Electrodynamics: Wave Interactions with Discretely Self-Similar Structures. In Electromagnetic Symmetry, C. Baum and H. Kritikos, eds., Taylor and Francis Publishers, Washington, D.C., 231–281.Google Scholar
- 8.Jakeman, E. (1983): Fraunhofer Scattering by a Sub-Fractal Diffuser. Opt. Acta 30, 1207–1212.Google Scholar
- 9.Jakeman, E. (1986): Scattering by Fractals. In Fractals in Physics, L.Pietronero and E. Tosatti, editors, Elsevier Science Publishers B.V., New York, 55–60.Google Scholar
- 10.Allain, C, Cloitre, M. (1986): Optical Fourier Transforms of Fractals. In Fractals in Physics, L. Pietronero and E. Tosatti, editors, Elsevier Science Publishers B.V., New York, 61–64.Google Scholar
- 16.Teixeira, T. (1986): Experimental Methods for Studying Fractal Aggregates. In On Growth and Form: Fractal and Non-Fractal Patterns in Physics, H.E. Stanley and N. Ostrowsky, editors, M. Nijhoff, Boston, MA, 145–162.Google Scholar
- 17.Rarity, J.G., Pusey, P.N. (1986): Light Scattering from Aggregating Systems: Static, Dynamic (QELS) and Number Fluctuations. In H. E. Stanley and N. Ostrowsky, editors, On Growth and Form: Fractal and Non-Fractal Patterns in Physics, Martinus Nijhoff Publishers, Boston, MA, 218–221.Google Scholar
- 18.Kaye, B.H. (1986): Fractal Dimension and Signature Waveform Characterization of Fine Particle Shape. American Laboratory, 55–63.Google Scholar
- 19.Chen, Z., Sheng, P., Weitz, D.A., Lindsay, H.M., Lin, M.Y., Meakin, P. (1988): Optical Properties of Aggregate Clusters. Phys. Rev. B37, 5232–5235.Google Scholar
- 20.Rarity, J.G., Seabrook, R.N., Carr, R.J.G. (1989): Light-Scattering Studies of Aggregation. In Fractals in the Natural Sciences, M. Fleischmann, D.J. Tildesley, and R.C Ball, editors, Princeton University Press, Princeton, NJ, 89–101.Google Scholar
- 21.Lin, M.Y., Lindsay, H.M., Weitz, D.A., Ball, R.C, Klein, R., Meakin, P. (1989): Universality of Fractal Aggregates as Probed by Light Scattering. In Fractals in the Natural Sciences, M. Fleischmann, D. J. Tildesley, and R. C. Ball, editors, Princeton University Press, Princeton, NJ, 71–87.Google Scholar
- 28.Puente, C. (Dec. 1993): Fractal Design of Multiband Antenna Arrays. Departmenet of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, ECE 477 Term Project.Google Scholar
- 29.Cohen, N. (Summer 1995): Fractal Antennas Part 1. Comm. Quart., 7–22.Google Scholar
- 30.Cohen, N. (Summer 1996): Fractal Antennas Part 2. Comm. Quart., 53–66.Google Scholar
- 31.Cohen, N., Hohfeld, R.G. (Winter 1996): Fractal Loops and the Small Loop Approximation. Comm. Quart. 77–81.Google Scholar
- 36.Jaggard, D.L., Spielman, T., Sun, X¿ (June 24–27, 1991): Diffraction by Cantor Targets”, presented at the 1991 AP-S/URSI Meeting, London, Ontario.Google Scholar
- 37.Kim, Y., Grebel, H., Jaggard, D.L. (1991): Diffraction by Fractally Serrated Apertures. J. Opt. Soc. A8, 20–26.Google Scholar
- 38.Spielman, T., Jaggard, D.L. (July 20–25, 1992): Diffraction by Cantor Targets: Theory and Experiment, presented at the 1992 AP-S/URSI Meeting, Chicago, IL.Google Scholar
- 40.Jaggard, D.L., Spielman, T., Dempsey, M. (June 28–July 2, 1993): Diffraction by Two-Dimensional Cantor Apertures. Presented at the 1993 AP-S/URSI Meeting, Ann Arbor, MI.Google Scholar
- 41.Jaggard, D.L., Jaggard, A.D. (July 13–18, 1997): Fractal Apertures: The Effect of Lacunarity. to be presented at the 1997 AP-S/URSI Meeting, Montreal.Google Scholar
- 42.Jaggard, D.L., Sun, X. (1990): Scattering by Fractally Corrugated Surfaces. J. Opt. Soc. A7, 1131–1139.Google Scholar
- 53.Jaggard, A.D., Jaggard, D.L. (July 13–18, 1997): Fractal Superlattices and Scattering: Lacunarity, Fractal Dimension, and Stage of Growth. To be pre¬sented at the 1997 AP-S/URSI Meeting, Montreal; also Jaggard, A.D., Jaggard, D.L. (1997): Scattering from Fractal Superlattices with Variable Lacunarity. In preparation.Google Scholar
- 54.Mandelbrot, B.B. (1983): The Fractal Geometry of Nature. W. H. Freeman and Comapny, New York.Google Scholar
- 56.Voss, R. (1985): Random Fractals: Characterization and Measurement. In Scaling Phenomena in Disordered Systems, NATO ASI Series, R. Pynn and A. Skjeltorp, editors, Plenum Press, New York, 1–11.Google Scholar