Skip to main content
Log in

Fractal electrodynamics. Scaling of the fractal antennas based on ring structures and multiscale frequency-selective 3D media and fractal sandwiches: Transition to fractal nanostructures

  • Electrodynamics and Wave Propagation
  • Published:
Journal of Communications Technology and Electronics Aims and scope Submit manuscript

Abstract

Computer simulation is employed to simulate the electrodynamic parameters of new fractal antennas and frequency-selective surfaces based on such antennas in the frequency range up to 20 GHz. The analysis of the original fractal antennas is supplemented with the study of the fractal frequency-selective 3D media or fractal sandwiches (i.e., radioelectronic fractal micro/nanostructures that contain no less than two layers. The efficiency of the fractal antennas and the fractal frequency-selective 3D media is demonstrated. The methods to create new passive electron components and elements for modern broadband and multifrequency radio systems based on such media are proposed

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. The Antenna Engineering Handbook, 4th Ed., Ed. by J. L. Volakis (McGraw Hill, New York, 2007).

    Google Scholar 

  2. B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley, New York, 2000).

    Book  Google Scholar 

  3. V. H. Rumsey, Frequency Independent Antennas (Academic, New York, 1966; Mir, Moscow, 1968).

    Google Scholar 

  4. S. A. Podosenov, A. A. Potapov, and A. A. Sokolov, Pulsed Electrodynamics of Broadband Radio Systems and Fields of Coupled Structures, Ed. by A. A. Potapov (Radiotekhnika, Moscow, 2003) [in Russian].

    Google Scholar 

  5. A. A. Potapov, Fractals in Radio Physics and Radars (Logos, Moscow, 2002) [in Russian].

    Google Scholar 

  6. A. A. Potapov, Fractals in Radio Physics and Radars: Topology of a Sample (Universitetskaya Kniga, Moscow, 2005) [in Russian].

    Google Scholar 

  7. A. A. Potapov and V. A. Chernykh, Fractional Letnikov Calculus, Fractal Theory, and Scaling, Ed. by A. A. Pota- pov (Fizmatlit, Moscow, 2010) [in Russian].

    Google Scholar 

  8. D. L. Jaggard, Recent Advances in Electromagnetic Theory, Ed. by H. N. Kritikos and D. L. Jaggard (Springer, New York, 1990), p. 183.

    Google Scholar 

  9. D. L. Jaggard, Directions in Electromagnetic Wave Modeling, Ed. by H. L. Bertoni and L. B. Felsen (Plenum, New York, 1991), p. 435.

    Google Scholar 

  10. D. L. Jaggard, Electromagnetic Symmetry, Ed. by C. Baum and H. N. Kritikos (Taylor & Francis, London, 1995), p. 231.

    Google Scholar 

  11. D. L. Jaggard, Fractals in Engineering, Ed. by J. Levy-Vehel (Springer-Verlag, Berlin, 1997), p. 204.

    Google Scholar 

  12. D. L. Jaggard, Frontiers in Electromagnetics, Ed. by D. H. Werner and R. Mittra (IEEE, New York, 2000), p. 2.

    Google Scholar 

  13. A. A. Potapov, Fractals and Chaos as a Base of New Breakthrough Technologies in Modern Radio Systems, in: R. M. Crownover, Introduction to Fractals and Chaos (Tekhnosfera, Moscow, 2006) [in Russian].

    Google Scholar 

  14. A. A. Potapov, Irreversible Processes in Nature and Technology, Ed. by V. S. Gorelik and A. N. Morozov (Bauman MGTU, Moscow, 2008) [in Russian].

    Google Scholar 

  15. A. A. Potapov, Yu. V. Gulyaev, S. A. Nikitov, et al., Newest Methods of Image Processing, Ed. by A. A. Potapov (Fizmatlit, Moscow, 2008) [in Russian].

    Google Scholar 

  16. A. A. Potapov, et al., Fluctuations and Noise in Complex Systems of Living and Nonliving Nature, Ed. by R. M. Yul’-met’ev (Ministerstvo Obrazovan. Nauki Resp. Tatarstan, Kazan, 2008) [in Russian].

    Google Scholar 

  17. A. A. Potapov, A. Kh. Gil’mutdinov, and P. A. Ushakov, Fractal Elements and Radio Systems: Physical Aspects, Ed. by A. A. Potapov (Radiotekhnika, Moscow, 2009) [in Russian].

    Google Scholar 

  18. O. I. Antipov, V. A. Neganov, and A. A. Potapov, Deterministic Chaos and Fractals in Discrete-Nonlinear Systems, Ed. by Yu. V. Gulyaev and S. A. Nikitov (Radio-tekhnika, Moscow, 2009) [in Russian].

    Google Scholar 

  19. A. A. Potapov, Proc. SPIE 7374, 73740E–1 (2009).

    Google Scholar 

  20. A. N. Bogolyubov, A. A. Potapov, and S. Sh. Rekhviashvili, Vestn. Leningr Univ., Ser. 3: Fiz., Astron., No. 4, 9 (2009).

  21. Y. Kim and D. L. Jaggard, Proc. IEEE 74, 1278 (1986).

    Article  Google Scholar 

  22. C. Puente, J. Romeu, R. Pous, and A. Cardama, Fractals in Engineering, Ed. by J. Levy-Vehel (Springer, Berlin, 1997), p. 222.

    Google Scholar 

  23. C. Puente, J. Romeu, and A. Cardama, in Frontiers in Electromagnetics, Ed. by D. H. Werner and R. Mittra (IEEE, New York, 2000), pp. 48–93.

    Google Scholar 

  24. D. H. Werner, P. L. Werner, D. L. Jaggard, et al., Frontiers in Electromagnetics, Ed. by D. H. Werner and R. Mittra (IEEE, New York, 2000), p. 94.

    Google Scholar 

  25. D. Werner, J. S. Petko, and T. G. Spence, The Antenna Engineering Handbook, Ed. by J. L. Volakis (McGraw-Hill, New York, 2007).

    Google Scholar 

  26. R. L. Haupt and D. H. Werner, Genetic Algorithms in Electromagnetics (IEEE Press, New York, 2007).

    Book  Google Scholar 

  27. A. A. Potapov, Doctoral Dissertation in Mathematics and Physics (IRE RAN, Moscow, 1994).

    Google Scholar 

  28. http://www.tsc.upc.edu/fractalcoms; http://www.tsc.upc.es/fractalcoms

  29. A. A. Potapov, in Day on Diffraction — 2006 (Abstracts Int. Conf., St. Petersburg, May 30–June 2, 2006) (S.-Peterb. Gos. Univ., St. Petersburg, 2006), p. 84.

    Google Scholar 

  30. X. Liang, W. Zhensen, W. Wenbing, J. Xidiun Univer. 21(5), 80 (1994).

    Google Scholar 

  31. A. Boag, A. Boag, E. Michielssen, and R. Mittra, IEEE Trans. Antennas Propag. 44, 687 (1996).

    Article  Google Scholar 

  32. N. Cohen, Communications Quarterly 6(3), 53 (1996).

    Google Scholar 

  33. C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama, IEEE Trans. Antennas Propag. 46, 517 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  34. R. Hohlfeld and N. Cohen, Fractals 7(1), 79 (1999).

    Article  Google Scholar 

  35. K. Harigaya, Chem. Phys. Lett. 300(1), 33 (1999).

    Article  Google Scholar 

  36. J. Romeu and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 48, 1097 (2000).

    Article  Google Scholar 

  37. K. J. Vinoy and V. K. Varadan, Smart Mater. Struct. 10, 1211 (2001).

    Article  Google Scholar 

  38. S. R. Best, IEEE Antennas Wireless Propag. Lett. 1(1), 39 (2002).

    Article  Google Scholar 

  39. D. H. Werner and S. Ganguly, IEEE Antennas Propagation. Magazine 45(1), 38 (2003).

    Article  Google Scholar 

  40. B.-L. Ooi, IEEE Trans. Antennas Propag. 52, 1286 (2004).

    Article  Google Scholar 

  41. F. Frezza, L. Pajewski, and G. Schettini, IEEE Trans. Microwave Theory Tech. 52, 220 (2004).

    Article  MathSciNet  Google Scholar 

  42. G. Konstantatos, Electromagnetics 24(1–2), 81 (2004).

    Article  Google Scholar 

  43. A. A. Potapov, in Proc. 28th ESA Antenna Workshop on Space Antenna Systems and Technologies, Noordwijk, The Netherlands, May 31–June 3, 2005) (ESTEC, Noordwijk, 2005), part 2, p. 1047.

    Google Scholar 

  44. H. A. Ghali, A. Tarek, and T. A. Moselhy, IEEE Trans. Microwave Theory Tech. 53, 1946 (2005).

    Article  Google Scholar 

  45. Yu. V. Gulyaev, S. A. Nikitov, A. A. Potapov, and A.G. Davydov, Radiotekh. Elektron. (Moscow) 50, 1070 (2005) [J. Commun. Technol. Electron. 50, 988 (2005)].

    Google Scholar 

  46. S. Shinya Tada, M. Haneisih, and Y. Kimura, Electron. Commun. Jpn., Part 2: Electron. 88(7), 1 (2005).

    Article  Google Scholar 

  47. D. E. Anagnostou, G. Zheng, M. T. Chryssomallis, et al., IEEE Trans. Antennas Propag. 54, 422 (2006).

    Article  Google Scholar 

  48. S. Shinya Tada, R. Chayono, Y. Shinohe, et al., Electron. Commun. Jpn., Part 1: Commun. 89(9), 10 (2006).

    Article  Google Scholar 

  49. A. A. Potapov, E. N. Matveev, V. A. Potapov, and A. V. Laktyunkin, in CD-ROM Proc. the Second European Conf. on Antennas and Propagation EuCAP 2007, Edinburgh, UK, 11–16 Nov. 2007 (Institution of Engineering and Technology & EurAAP AISBL, Edinburgh, 2007), ThPA.031.

    Google Scholar 

  50. J. S. Petko and D. H. Werner, IEEE Trans. Antennas Propag. 56, 97 (2008).

    Article  Google Scholar 

  51. A. A. Potapov, Tekhnol. Konstr. Elektron. Apparature, No. 5 (77), 3 (2008).

  52. J. J. Wang, Y. Z. Yin, and X. W. Dai, J. Electromagn. Waves Appl. 23, 1313 (2009).

    Article  Google Scholar 

  53. Guo Rui, Chen Xing, Huang Kama, Electromagnetics 29, 283 (2009).

    Article  Google Scholar 

  54. A. A. Potapov and E. N. Matveev, in Abstracts 2nd Int. Conf. on Chaotic Modeling, Simulation and Applications (CHAOS’ 2009), Chania, Greece, Jun. 01–05, 2009 (National and Kapodistrian Univ., Chania, 2009), P. 61.

    Google Scholar 

  55. E. N. Matveev and A. A. Potapov, in Proc. PIERS, Aug. 18–21, Moscow, 2009 (Electromagn. Acad., Cambridge, MA, 2009), p. 1933.

    Google Scholar 

  56. E. N. Matveev and A. A. Potapov, in Proc. 2009 Int. Radar Symp. (IRS — 2009), Hamburg, Sep. 09–11, 2009 (Hamburg Technical Univ., Hamburg, 2009), p. 465.

    Google Scholar 

  57. A. A. Potapov in Proc. Int. Conf. “Mode Conversion, Coherent Structures and Turbulence” (MSS-09), Moscow, Nov. 23–25, 2009 (URSS Publishing House, Moscow, 2009), p. 18.

    Google Scholar 

  58. Yiming Li, Math. Comput. Modelling 51, 944 (2010).

    Article  MATH  Google Scholar 

  59. E. N. Matveev, Extended Abstract of Candidate’s Dissertation in Mathematics and Physics (MFTI, Moscow, 2009).

    Google Scholar 

  60. A. A. Potapov, Problems of Non-Linear Analysis in Engineering Systems 14(1(29)), 145 (2008).

    Google Scholar 

  61. P. Xu, H. Tian, and Y. Ji, J. Opt. Soc. Am. B: Opt. Phys. 27, 640 (2010).

    Article  Google Scholar 

  62. J. P. Gianvittorio, J. Romeu, S. Blanch, and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 51, 3088 (2003).

    Article  Google Scholar 

  63. F. Frezza, L. Pajewski, and G. Schettini, IEEE Trans. Microwave Theory Tech. 52, 220 (2004).

    Article  MathSciNet  Google Scholar 

  64. V. A. Obukhovets and A. O. Kas’yanov, Microstrip Reflecting Antenna Arrays, Ed. by V. A. Obukhovets (Radiotekhnika, Moscow, 2006) [in Russian].

    Google Scholar 

  65. K. Sarabandi and N. Nader Behdad, IEEE Trans. Antennas Propag. 55, 1239 (2007).

    Article  Google Scholar 

  66. G. Stojanovic, M. Radovanovic, and V. Radonic, A new fractal-based design of stacked integrated transformers, Active and Passive Electronic Components, Hindawi 2008 Article ID 134805 (2008).

  67. Y. Xiang, X. Dai, S. Wen, and D. Fan, Opt. Lett. 33, 1255 (2008).

    Article  Google Scholar 

  68. B. Ghosh, S. N. Sinha, and M. V. Kartikeyan, Int. J. RF and Microwave Comput.-Aided Engineering 20(2), 209 (2010).

    Google Scholar 

  69. B. Hou, X. Q. Liao, and J. K. S. Poon, Opt. Express 18, 3946 (2010).

    Article  Google Scholar 

  70. T. L. Thomas, Smart Skins Program Boeing Military Airplanes (Boeing Company, Seattle, 1989), p. 131.

    Google Scholar 

  71. Yu. K. Evdokimov, A. A. Potapov, and D. V. Shakhturin, Nelineinyi Mir 6, 444 (2008).

    Google Scholar 

  72. M. S. Dresselhaus, Nature 432(7020), 959 (2004).

    Article  Google Scholar 

  73. M. V. Shuba, G. Ya. Slepyan, S. A. Maksimenko, et al., Phys. Rev. 79, 155403 (2009).

    Article  Google Scholar 

  74. Y. Lan, B. Zeng, H. Zhang, et al., Int. J. of Infrared and Millimeter Waves 27, 871 (2006).

    Article  Google Scholar 

  75. G. Hanson, IEEE Antennas Propagation Magazine 50(3), 66 (2008).

    Article  Google Scholar 

  76. Y. Huang, W.-Y. Yin, and Q. H. Liu, IEEE Trans. Nano 7, 331 (2008).

    Article  Google Scholar 

  77. A. M. Attiya, Prog. Electromagn. Res. 94, 419 (2009).

    Article  Google Scholar 

  78. Yu. N. Luponosov, S. A. Ponomarenko, N. M. Surin, et al., Chem. Mater. 21, 447 (2009).

    Article  Google Scholar 

  79. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424(6950), 824 (2003).

    Article  Google Scholar 

  80. C. Genet and T. W. Ebbesen, Nature 445(7123), 39 (2007).

    Article  Google Scholar 

  81. Z. Ruan and M. Qiu, Phys. Rev. Lett. 96, 233901 (2006).

    Article  Google Scholar 

  82. C. Huang, Q. Wang, and Y. Zhu, Phys. Rev. B 75, 245421 (2007).

    Article  Google Scholar 

  83. W. Wen, L. Zhou, B. Hou, et al., Phys. Rev. 72, 153406 (2005).

    Article  Google Scholar 

  84. L. Lin, L. B. Hande, and A. Roberts, Appl. Phys. Lett. 95, 201116 (2009).

    Article  Google Scholar 

  85. E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, 1985).

    Google Scholar 

  86. R. Gordon and A. G. Brolo, Opt. Express 13, 1933 (2005).

    Article  Google Scholar 

  87. S. Collin, F. Pardo, and J. L. Pelouard, Opt. Express 15, 4310 (2007).

    Article  Google Scholar 

  88. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305(5685), 847 (2004).

    Article  Google Scholar 

  89. A. Agrawal, Z. V. Vardeny, and A. Nahata, Opt. Express 16, 9601 (2008).

    Article  Google Scholar 

  90. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).

    Article  Google Scholar 

  91. T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, Phys. Rev. E 68, 065602 (2003).

    Article  Google Scholar 

Download references

Authors

Additional information

Original Russian Text © A.A. Potapov, E.N. Matveev, 2010, published in Radiotekhnika i Elektronika, 2010, Vol. 55, No. 10, pp. 1157–1177.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Potapov, A.A., Matveev, E.N. Fractal electrodynamics. Scaling of the fractal antennas based on ring structures and multiscale frequency-selective 3D media and fractal sandwiches: Transition to fractal nanostructures. J. Commun. Technol. Electron. 55, 1083–1101 (2010). https://doi.org/10.1134/S1064226910100013

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064226910100013

Keywords

Navigation