Influence of diffraction on the spectrum and wave functions of an open system

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

Volumn 62, Issue 4, 2000, Pages 4873-4888

  Hersch, J S ^a   Haggerty, M R ^a   Heller, E J ^b  

^a HARVARD UNIVERSITY   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROMAGNETIC WAVE DIFFRACTION; LIGHT TRANSMISSION; MICROWAVE DEVICES;

OPEN MICROWAVE BILLIARDS;

OPTICAL SYSTEMS;

EID: 0034294217     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.4873     Document Type: Article

References (24)

1. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, Berlin, 1990).
2. G. Vattay, A. Wirzba, and P. E. Rosenqvist, Phys. Rev. Lett. 73, 2304 (1994).
3. N. Pavloff and C. Schmit, Phys. Rev. Lett. 75, 61 (1995).
4. M. Sieber, N. Pavloff, and C. Schmit, Phys. Rev. E 55, 2279 (1997).
5. N. Whelan, Phys. Rev. E 51, 3778 (1995).
6. J. S. Hersch, M. R. Haggerty, and E. J. Heller, Phys. Rev. Lett. 83, 5342 (1999).
7. J. S. Hersch, Ph.D. thesis, Harvard University, 1999. Available at http://monsoon.harvard.edu.
8. J. A. Katine , Phys. Rev. Lett. 79, 4806 (1997).
9. E. J. Heller and S. Tomsovic, Phys. Today 46(7), 38 (1993).
10. J. D. Edwards, Ph.D. thesis, Harvard University, 1998. Available at http://monsoon.harvard.edu.
11. R. M. Westervelt (private communication).
12. S. Gokirmak, D. H. Wu, J. S. A. Bridgewater, and S. M. Anlage, Rev. Sci. Instrum. 69, 3410 (1998).
13. S. Sridhar, D. Hogenboomq, and B. A. Willemsen, J. Stat. Phys. 68, 239 (1992).
14. J. Stein and H. J. Stöckmann, Phys. Rev. Lett. 68, 2867 (1992).
15. H. J. Stöckmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990).
16. L. C. Maier and J. C. Slater, J. Appl. Phys. 23, 68 (1954).
17. G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves (Peregrinus, Stevenage, England, 1976), p. 115.
18. Note that the expression given in Ref. 17 is the complex conjugate of the expression above, because the convention for the time dependence of the fields taken in Ref. 17 is (Formula presented), whereas we take the opposite convention, (Formula presented).
19. R. G. Kouyoumjian and P. H. Pathak, Proc. IEEE 62, 1448 (1974).
20. J. B. Keller, J. Opt. Soc. Am. 52, 116 (1962).
21. The reason for the difference in the argument of the Fresnel integral is that in the half-line case the incident wave was plane (Formula presented), whereas in the present case the incident wave is a cylindrical wave emanating from the QPC.
22. Y. S. Chan and E. J. Heller, Phys. Rev. Lett. 78, 2570 (1997).
23. M. F. Crommie, C. P. Lutz, D. M. Eigler, and E. J. Heller, Physica D 83, 98 (1995).
24. Strictly speaking, there is diffraction in the lemon and stadium billiards, although it is of a different nature than in the corresponding open system. In the lemon billiard, it occurs at the point where the two arcs meet, and there is a discontinuity of slope. In the stadium, it occurs at the point where the arcs meet the straight wall sections, and there is a discontinuity of curvature. Since the discontinuities are of higher order, diffraction is weaker than in the open system.