Toward a Full-Wave-Based Electromagnetics Approach to Chaotic Footprints in a Complex Deterministic Environment: A Test Model With Coupled Floquet-Type and Ducted-Type Mode Characteristics

  • Giuseppe Castaldi
  • Vincenzo Fiumara
  • Vincenzo Galdi
  • Vincenzo Pierro
  • Innocenzo M. Pinto
  • Leopold B. Felsen
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 96)


Deterministic chaos has gradually emerged as an ubiquitous natural phenomenon. Basically, it consists of exponentially increasing separation between nearby phase-space trajectories describing the (e.g., time) evolution of a (even feebly) nonlinear dynamic system with sufficiently many degrees of freedom, resulting in long-time algorithmic unpredictability and random-like behavior [1]. Despite the pervasiveness of chaos in physics, chaotic phenomena have been studied relatively little in connection with applied elect romagnetics (EM). Most published studies refer to optical-wavelength systems where chaos usu ally stems from the nonlinear EM constitutive properties of material medi a. However, during the last decade there has been a growing interest in linear EM propagation environments featuring ray-chaotic behavior. Apart from intrinsic theoretical aspects (ray theory describes wave dynamics in the zero-wavelength limit), this interest is motivated by the possibility of designing novel devices and components (microlasers, resonators, etc.) where ray chaos has been demonstrated to playa key role (see, e.g., [2]).


Deterministic Chaos Exit Angle Dielectric Slab Linear Wave Equation IEEE Trans Antenna 
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  1. 1.
    Ott E (1993) Chaos in dynamical systems. Cambridge University Press, Cambridge, UKzbMATHGoogle Scholar
  2. 2.
    Gmachl C, et al. (1998) Science 280: 1556–1564CrossRefGoogle Scholar
  3. 3.
    Berry MV (1987) Proc Roy Soc London A413:183–198CrossRefGoogle Scholar
  4. 4.
    Sinai YG (1970) Russian Math Surveys 25:137–189MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bunimovich LA (1991) Chaos 1:187–193MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Kottos T, Smilansky U, Fortuny J, Nesti G (1999) Radio Science 34:747–758CrossRefGoogle Scholar
  7. 7.
    Fiumara V, Galdi V, Pierro V, Pinto IM (2000) Bouncing ray chaos for smart media. In: Proc 2000 IEEE Antenn as and Propagat Int Symp, Salt Lake City, UT, USA, July 16–21, 2000, pp. 682–684.Google Scholar
  8. 8.
    Castaldi G, Fiumara V, Galdi V, Pierro V, Pinto IM (2002). Submitted to Phys Rev Lett (Preprint at arXiv:nlin.CD/0208017 v1)Google Scholar
  9. 9.
    Harayama T, Gaspard P (2001), Phys Rev E 64: 036215CrossRefGoogle Scholar
  10. 10.
    Abramowitz M, Stegun IE (1972) Handbook of mathematical functions. Dover, New YorkGoogle Scholar
  11. 11.
    Prudnikov AP, Brychkov YA, Marichev OI (1986) Integrals and series. Gordon and Breach, New YorkGoogle Scholar
  12. 12.
    Golub GH, Van Loan CF (1996) Matrix computations, 3rd ed. The John Hopkins University Press, Baltimore, MDzbMATHGoogle Scholar
  13. 13.
    Wolfram S (1999) The MATHEMATICA book. Cambridge University Press, Cambridge, UKzbMATHGoogle Scholar
  14. 14.
    Felsen LB (1984) IEEE Tr ans Antennas Propagat AP32:775–796MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Neviere M, Cadilhac M, Petit R (1973) IEEE Trans Antennas Propagat AP21:37–46CrossRefGoogle Scholar
  16. 16.
    Berry MV (1977) J Phys A10:2083–2091MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Giuseppe Castaldi
    • 1
  • Vincenzo Fiumara
    • 2
  • Vincenzo Galdi
    • 1
  • Vincenzo Pierro
    • 1
  • Innocenzo M. Pinto
    • 1
  • Leopold B. Felsen
    • 3
    • 4
  1. 1.Waves Group, Department of EngineeringUniversity of SannioBeneventoItaly
  2. 2.D.I.I.I.E.University of SalernoFisciano (SA)Italy
  3. 3.Department of Aerospace and Mechanical EngineeringBoston UniversityBostonUSA
  4. 4.Polytechnic UniversityBrooklynUSA

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