Comptes Rendus
Wave chaos techniques to analyze a modeled reverberation chamber
Comptes Rendus. Physique, Volume 10 (2009) no. 1, pp. 42-53.

A Reverberation Chamber (RC) is analyzed with techniques issued from the wave chaos domain. The first 200 modes are determined numerically: their cumulated number is separated into a smooth part, predicted by the Weyl formula, and an oscillating part, interpreted in term of periodic orbits. The technique of the nearest-neighbor spacing distribution is also presented, showing the signature of chaos. Eigenfield distributions are examined for two RC geometries and compared to the Gaussian ideal case. Finally, the notion of avoided crossing is illustrated for an almost chaotic RC, leading to a statement for frequency sweeps induced by the stirrer displacement.

Une chambre réverbérante (CR) est étudiée grâce à quelques techniques du chaos ondulatoire. Ses 200 premiers modes, déterminés numériquement, permettent de vérifier que la statistique des écarts entre fréquences de résonance voisines dépend du caractère chaotique de la CR, et que les fluctuations du nombre cumulé de modes sont associées aux orbites périodiques. En outre les distributions des champs propres sont étudiées et comparées au cas idéal gaussien pour deux géométries de CR. Enfin la notion de croisement évité est illustrée, propriété des systèmes chaotiques ayant une importante conséquence sur les perturbations provoquées par le brasseur sur les fréquences de résonance.

Published online:
DOI: 10.1016/j.crhy.2009.01.001
Keywords: Reverberation chamber, Modal finite element method, Quantum chaos, Electromagnetic cavity
Mot clés : Chambre réverbérante, Analyse modale, Méthode des éléments finis, Chaos quantique, Cavité électromagnétique

Gérard Orjubin 1; Elodie Richalot 2; Odile Picon 2; Olivier Legrand 3

1 Université française d'Egypte, ville de Chorouq, Km 37 autoroute Le Caire-Ismaïlia, B.P. 21, Le Caire, Egypte
2 Université Paris-Est, ESYCOM, EA2552, bâtiment Copernic, 5, boulevard Descartes, 77454 Marne-la-Vallée, France
3 Laboratoire de physique de la matière condensée, CNRS-UMR 6622, Université de Nice-Sophia Antipolis, parc Valrose, 06108 Nice cedex 2, France
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Gérard Orjubin; Elodie Richalot; Odile Picon; Olivier Legrand. Wave chaos techniques to analyze a modeled reverberation chamber. Comptes Rendus. Physique, Volume 10 (2009) no. 1, pp. 42-53. doi : 10.1016/j.crhy.2009.01.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2009.01.001/

[1] D.A. Hill Plane wave integral representation for fields in reverberation chambers, IEEE Trans. Electromag. Compat., Volume 40 (1998), pp. 209-217

[2] C.F. Bunting et al. A two-dimensional finite-element analysis of reverberation chambers, IEEE Trans. Electromag. Compat., Volume 41 (1999), pp. 280-289

[3] G. Cerri et al. Investigation of the antenna factor behavior of a dipole operating inside a resonant cavity, IEEE Trans. Electromag. Compat., Volume 50 (2008), pp. 89-96

[4] G. Orjubin et al. On the FEM modal approach for a reverberation chamber analysis, IEEE Trans. Electromag. Compat., Volume 49 (2007), pp. 76-85

[5] H.-J. Stöckmann Quantum Chaos. An Introduction, Cambridge University Press, Cambridge, 1999

[6] H.J. Stöckmann; J. Stein Quantum chaos in billiards studied by microwave absorption, Phys. Rev. Lett., Volume 64 (1990), pp. 2215-2218

[7] S. Sridhar Experimental observation of scarred eigenfunctions of chaotic microwaves cavities, Phys. Rev. Lett., Volume 67 (1991), pp. 785-788

[8] J. Barthélemy; O. Legrand; F. Mortessagne Complete S matrix in a microwave cavity at room temperature, Phys. Rev. E, Volume 71 (2005), p. 016205

[9] S. Deus; P.M. Koch; L. Sirko Statistical properties of the eigenfrequency distribution of the three-dimensional microwave cavities, Phys. Rev. E, Volume 52 (1995), pp. 1146-1155

[10] U. Dörr et al. Scarred and chaotic field distributions in a three-dimensional Sinai microwave resonator, Phys. Rev. Lett., Volume 80 (1998), pp. 1030-1033

[11] L.R. Arnaut Operation of electromagnetic reverberation chambers with wave diffractors at relatively low frequencies, IEEE Trans. Electromagn. Compat., Volume 43 (2001), pp. 637-653

[12] B.H. Liu, D.C. Chang, M.T. Ma, Eigenmodes and the composite quality factor of a reverberating chamber, Nat. Bur. Stand. (U.S.) (1983), Tech. Note 1066

[13] V. Galdi; I.M. Pinto; L.B. Felsen Wave propagation in ray-chaotic enclosures: Paradigms, oddities and examples, IEEE Antennas and Propagation Magazine, Volume 47 (2005), pp. 62-81

[14] R. Balian; B. Duplantier Electromagnetic waves near perfect conductors. I. Multiple scattering expansions. Distribution of modes, Ann. Phys., Volume 104 (1977), pp. 300-335

[15] H.P. Baltes Asymptotic eigenvalue distribution for the wave equation in a cylinder of arbitrary cross section, Phys. Rev. A, Volume 6 (1972), pp. 2252-2257

[16] M.V. Berry Regular and irregular semiclassical wavefunctions, J. Phys. A, Volume 10 (1977), pp. 2083-2091

[17] C. Dembowski et al. Experimental test of a trace formula for a chaotic three-dimensional microwave cavity, Phys. Rev. Lett., Volume 89 (2002), p. 064101

[18] G. Orjubin et al. Chaoticity of a reverberation chamber assessed from the analysis of modal distributions obtained by FEM, IEEE Trans. Electromag. Compat., Volume 49 (2007), pp. 732-771

[19] IEC 61000-4-21 Electromagnetic Compatibility: Reverberation Chamber Test Methods, Intern. Electrotech. Commission (IEC), Geneva, 2003

[20] J.P. Royston An extension of Shapiro and Wilk's W test for normality to large samples, Appl. Statist., Volume 31 (1982), pp. 115-124

[21] D.I. Wu; D.C. Chang The effect of an electrically large stirrer in a mode-stirred chamber, IEEE Trans. Electromag. Compat., Volume 31 (1989), pp. 164-169

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