Quantum chaos in optical systems: The annular billiard

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 5, 2002, Pages 13-

  Hentschel, Martina ^a   Richter, Klaus ^b  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^b UNIVERSITY OF REGENSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BILLIARD MATERIALS; HELMOHOLTZ EQUATIONS; OPTICAL CAVITIES; QUANTUM CHAOS;

ACOUSTIC RESONATORS; ELECTROMAGNETIC FIELDS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; MICROWAVES; OPTICAL COMMUNICATION EQUIPMENT; OPTICAL SYSTEMS; QUANTUM THEORY; SCATTERING; WAVE EQUATIONS;

CHAOS THEORY;

ARTICLE;

EID: 33646967567     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.056207     Document Type: Article

References (52)

1. H. J. Stöckmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990).
2. H.-D. Gräf, Phys. Rev. Lett. 69, 1296 (1992);
3. H. Alt, Phys. Rev. Lett. 79, 1026 (1996).
4. A. Andersen, Phys. Rev. E 63, 066204 (2001).
5. J. U. Nöckel, Ph.D. thesis, Yale University, 1997.
6. J. U. Nöckel and A. D. Stone, Nature (London) 385, 45 (1997).
7. J. A. Lock, Appl. Opt. 37, 1527 (1998).
8. P. B. Wilkinson, Phys. Rev. Lett. 86, 5466 (2001).
9. S.-B. Lee, Phys. Rev. Lett. 88, 033903 (2002).
10. V. Doya, Phys. Rev. Lett. 88, 014102 (2002).
11. S. Chang, J. Opt. Soc. Am. B 17, 1828 (2000).
12. S. A. Backes, J. Vac. Sci. Technol. B 16, 3817 (1998).
13. C. Gmachl, Science 280, 1556 (1998).
14. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 1975).
15. H.-J. Stöckmann, Quantum Chaos (Cambridge University Press, Cambridge, England, 1999).
16. O. Bohigas, D. Boosé, R. Egydio de Carvalho, and V. Marvulle, Nucl. Phys. A 560, 197 (1993).
17. S. D. Frischat and E. Doron, Phys. Rev. Lett. 75, 3661 (1995);
18. S. D. FrischatE. DoronPhys. Rev. E 57, 1421 (1998).
19. C. Dembowski, Phys. Rev. Lett. 84, 867 (2000).
20. A. Kohler and R. Blümel, Ann. Phys. (New York) 267, 249 (1998);
21. A. KohlerR. BlümelPhys. Lett. A 238, 271 (1998).
22. For such open annular billiards, questions concerning the doublet splitting addressed in 1516 are not of relevance because the splitting is masked by resonance broadening.
23. G. Hackenbroich and J.-U. Nöckel, Europhys. Lett. 39, 371 (1997).
24. G. Gouesbet, S. Meunier-Guttin-Cluzel, and G. Gréhan, Opt. Commun. 201, 223 (2002).
25. J. U. Nöckel and A. D. Stone, in Optical Processes in Microcavities, edited by R. K. Chang and A. J. Campillo (World Scientific, Singapore, 1996).
26. M. Hentschel and M. Vojta, Opt. Lett. 26, 1764 (2001).
27. The vector character of light requires one to distinguish between the two polarizations. In our planar systems, either the transverse magnetic (TM) or transverse electric (TE) field can lie in the system plane.
28. G. Gouesbet, S. Meunier-Guttin-Cluzel, and G. Gréhan, Phys. Rev. E 65, 016212 (2001).
29. S. G. Lipson, H. Lispon, and D. S. Tannhauser, Optical Physics (Cambridge University Press, Cambridge, England, 1995).
30. The first derivative in the first term can be eliminated by the substitution (Formula presented)
31. M. Hentschel and J. U. Nöckel, in Quantum Optics of Small Structures, edited by D. Lenstra, T. D. Visser, and K. A. H. van Leeuwen (Edita KNAW, Ammsterdam, 2000);e-print physics/0203064.
32. M. Hentschel and H. Schomerus, Phys. Rev. E 65, 045603R (2002).
33. F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947);
34. H. M. Lai, F. C. Cheng, and W. K. Tang, J. Opt. Soc. Am. A 3, 550 (1986);
35. H. K. V. Lotsch, Optik (Stuttgart) 32, 116 (1970);
36. Optik (Stuttgart)H. K. V. Lotsch32, 189 (1970);
37. Optik (Stuttgart)H. K. V. Lotsch32, 299 (1971);
38. Optik (Stuttgart)H. K. V. Lotsch32, 553 (1971).
39. E. Doron and U. Smilansky, Nonlinearity 5, 1055 (1992).
40. J. R. Taylor, Scattering Theory (Krieger, Malabar, FL, 1983).
41. U. Smilansky, in Mesoscopic Quantum Physics, Proceedings of the Les Houches Summer School of Theoretical Physics, Session LXI, 1994, edited by E. Akkermans, G. Montambaux, J. L. Pichard, and J. Zinn-Justin (Elsevier, Amsterdam, New York, 1995).
42. R. G. Newton, Scattering Theory of Waves and Particles (Springer, New York, 1982);
43. Y. V. Fyodorov and H.-J. Sommers, J. Math. Phys. 38, 1918 (1997).
44. For microlaser operation, resonances of intermediate width are of particular interest: For too broad resonances leakage stops the crossing of the lasing threshold, whereas very narrow resonances will fail to provide sufficient output power.
45. M. V. Berry, Eur. J. Phys. 2, 91 (1981).
46. The geometry parameters mainly studied here were chosen because of the particularly interesting phase space structure. Generalization of the results to other geometries is straightforward.
47. This applies to the families of WGMs with small (Formula presented) and depends on the size of the inner disk.
48. Having in mind the ratio of regular to chaotic regions in the corresponding Poincaré SOS, Fig. 55, regular modes appear to be over-represented for the (small) wave numbers considered here. One might even argue that smaller regular islands cannot be resolved. However, similar effects have been observed before, see, e.g., R. Ketzmerick, L. Hufnagel, F. Steinbach, and M. Weiss, Phys. Rev. Lett. 85, 1214 (2000).
49. B. Crespi, G. Perez, and S.-J. Chang, Phys. Rev. E 47, 986 (11993);A. M. Ozorio de Almeida, Hamiltonian Systems: Chaos and Quantization (Cambridge University Press, Cambridge, England, 1998).
50. We used the expressions valid for a refractive index boundary; see M. Hentschel, H. Schomerus, and R. Schubert (unpublished).
51. I. S. Gradshteyn and I. M. Ryzhik, in Table of Integrals, Series, and Products, edited by A. Jeffrey (Academic Press, San Diego, 1994).
52. M. Hentschel, Ph.D. thesis, Technical University of Dresden, 2001.