Skip to main content
SpringerLink
Log in

Time-Domain Mapping of Electromagnetic Ray Movement Inside 2D Anisotropic Region

  • Published:
International Journal of Infrared and Millimeter Waves Aims and scope Submit manuscript

Abstract

The paper presents the extension of the time-domain mapping method applied to 2D billiard problem inside an anisotropic region bounded by ellipse [1]. In this paper, it has been considered the ray movement inside 2D anisotropic region bounded by arbitrary differentiable curve. It has been proved that the problem can be one-to-one mapped onto 2D mathemeatical billiard problem inside the region possessing isotropic properties by linear transformation of group velocity hodograph and boundary with the same coefficient, which is equal to anisotropy of the ray group velocity, simultaneously. The main features of the ray movement inside 2D anistropic region are discussed.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Biber A., Golick A., Tomak M., Optical Ray Movement inside Dielectric Sphere, Int'l.J.Inf&MMW, vol22,no7, pp.1019-1035.

  2. Weinstein L.V., Open Resonators and Open Waveguides, Boulder, CO: Golem, 1969.

    Google Scholar 

  3. Kornfeld, I.P., Sinai, Y.G., Fomin, S.V. Theory of ergodicity. Moscow, Nauka, 1980 pp. 1-383; (Ergodicheskaja teorija; in Russian).

    Google Scholar 

  4. Birkhoff G.D. Dynamical systems. AMS, Providence, Rhode Island, 1966 pp. 1-305.

    Google Scholar 

  5. Golick, A.V. The time invariant for the propagation of plane waves in solids. Sol St. Comm. 1984, v.52,No 11, pp. 917-919.

    Google Scholar 

  6. Mason, W.P., Multiple Reflection Ultrasonic Delay Lines, Physical Acoustics. Principles and Methods, vol1, part A, Academic Press, 1964.

  7. Golick, A.V., Korolyuk, A.P., Matsakov, L. Ya., Multireflection Ultrasound Delay Line, USSR Patent No: 1364207, 1986.

  8. Born, M., Wolf, E., Principles of optics. Pergamon Press, 1965 pp. 1-808.

  9. Landau, L.D., Lifshitz, E. M. Theory of elasticity. Butterworth-Heinemann, 1995 pp. 1-187.

  10. Lazutkin, V.F. Existence of caustics for billiard problem inside convex region. Izvest. Acad. Nauk SSSR, Math. Series, 1973, v.37, No 1, pp. 186-216; (Suschestvovanie kaustik dlja billiardnoj zadachi v vypukloj oblasti; in Russian).

  11. Lazutkin V. Convex billiard and eigen function of Laplas operator. Publishing House of Leningrad State University, 1981, pp. 1-196; (Vypuklyj billiard i sobstvennye funkcii operatora Laplasa; in Russian).

  12. Kolmogorov, A.N. New metric invariant of transitive dynamical systems and Lebeg space automorphisms. Dokl. Acad. Nauk SSSR, 1958, vol.119, No 5, pp. 861-864; (Novyj metricheskij invariant tranzitivnyh dinamicheskih sistem i avtomorfizmov prostranstva Lebega; in Russian).

  13. Kolmogorov A.N. About entropy per time unit as a metric invariant of automorphisms. Dokl. Acad. Nauk SSSR, 1959, vol.124, No 4 pp. 754-755; (Ob entropii na edinicu vremeni kak metricheskom invariante avtomorfizmov; in Russian).

  14. Sinai, Y.G. About conception of entropy of dynamical system. Dokl. Acad. Nauk SSSR, 1959, vol.124, No 4 pp. 768-771; (O ponjatii entropii dinamicheskoj sistemy; in Russian).

  15. Bunimovich, L.A. About billiards close to scattering. Math. Sbornik, 1974 vol.94 (136), No 1(5), pp. 49-73; (O bil'jardah, blizkih k rasseivajuschim; in Russian).

  16. Bunimovich, L.A. About ergodic properties of some billiards. Func.anal. i ego prilozh. (Func. Analysis and its Application), 1974, vol.8, No 3, pp. 73-74; (Ob ergodicheskih svojstvah nekotoryh bil'jardov; in Russian).

  17. Zaslavsky, G.M. Stochasticity in Quantum Systems. Phys Reports, 1980, v.80, No 3, pp. 157-250.

  18. Ganapolskii E.M. Electromagnetic K-system for long time keeping of SHF-signal energy, Dokl. Acad.Nauk SSSR, 1991, vol.319, No 5, pp.1128-1131; (Elektromagnitnaja K-sistema s dlitel'nym uderzhaniem energii SVCh signala; in Russian).

  19. Ganapolskii E.M., Eremenko Z.E. Quantum chaos in 3D electromagnetic microwave system similar to Bunimovich billiard. Proc. of MSMW'2001, Kharkov, Ukraine, June 4–9, 2001, pp. 290-292

Download references

Authors
  1. A. Biber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Golick
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Tomak
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Biber, A., Golick, A. & Tomak, M. Time-Domain Mapping of Electromagnetic Ray Movement Inside 2D Anisotropic Region. International Journal of Infrared and Millimeter Waves 23, 919–930 (2002). https://doi.org/10.1023/A:1015755403064

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015755403064

Search

Navigation