Modes of wave-chaotic dielectric resonators

Progress in Optics

Volumn 47, Issue , 2005, Pages 75-137

  Tureci H E ^a   Schwefel, H G L ^a   Jacquod, Ph ^b   Stone, A Douglas ^a  

^a Yale University   (United States)

^b UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21844433523     PISSN: 00796638     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0079-6638(05)47002-X     Document Type: Chapter

References (72)

1. Abramovitz M., and Stegun I.A. Handbook of Mathematical Functions (1972), Dover, New York
2. Amiran E.Y. Integrable smooth planar billiards and evolutes. N.Y. J. Math. 3 (1997) 32-47
3. Arnold V.I. Mathematical Methods of Classical Mechanics (1989), Springer-Verlag, New York
4. Babič V.M., and Buldyrev V.S. Asymptotic Methods in Shortwave Diffraction Problems (1991), Springer-Verlag, New York
5. Barnett, A.H., 2000, Dissipation in deforming chaotic billiards, PhD thesis, Harvard University, Cambridge, MA
6. Bender C.M., and Orszag S.A. Advanced Mathematical Methods for Scientists and Engineers (1999), Springer-Verlag, New York
7. In: Berggren K.-F., and Åberg S. (Eds). Quantum Chaos Y2K Proceedings of Nobel Symposium. Phys. Scr. 116 (2000) Stockholm
8. Berry M.V. Waves and Thom's theorem. Adv. Phys. 25 (1976) 1-26
9. Birkhoff G.D. On the periodic motion of dynamical systems. Acta Math. 50 (1927) 359-379
10. Bleistein N., and Handelsman R.A. Asymptotic Expansion of Integrals (1986), Dover, New York
11. In: Chang R.K., and Campillo A.K. (Eds). Optical Processes in Microcavities (1996), World Scientific, Singapore
12. Chang S., Chang R.K., Stone A.D., and Nöckel J.U. Observation of emission from chaotic lasing modes in deformed microspheres: displacement by the stable-orbit modes. J. Opt. Soc. Am. B 17 (2000) 1828-1834
13. Chern G.D., Türeci H.E., Stone A.D., Chang R.K., Kneissl M., and Johnson N.M. Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars. Appl. Phys. Lett. 83 (2003) 1710-1712
14. Ching E.S.C., Leung P.T., van den Brink A.M., Suen W.M., Tong S.S., and Young K. Quasinormal-mode expansion for waves in open systems. Rev. Mod. Phys. 70 (1998) 1545-1554
15. Collot L., Lefevreseguin V., Brune M., Raimond J.M., and Haroche S. Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres. Europhys. Lett. 23 (1993) 327-334
16. Crespi B., Perez G., and Chang S.J. Quantum Poincaré sections for 2-dimensional billiards. Phys. Rev. E 47 (1993) 986-991
17. Dietz B., Eckmann J.P., Pillet C.A., Smilansky U., and Ussishkin I. Inside-outside duality for planar billiards - a numerical study. Phys. Rev. E 51 (1995) 4222-4231
18. Doron E., and Smilansky U. Semiclassical quantization of chaotic billiards - a scattering-theory approach. Nonlinearity 5 (1992) 1055-1084
19. Eckmann J.P., and Pillet C.A. Spectral duality for planar billiards. Commun. Math. Phys. 170 (1995) 283-313
20. Einstein A. Zum Quantensatz von Sommerfeld und Epstein. Verhandl. Dtsch. Physik. Ges. 19 (1917) 82-92
21. Frischat S.D., and Doron E. Quantum phase-space structures in classically mixed systems: a scattering approach. J. Phys. A 30 (1997) 3613-3634
22. Fukushima T., Biellak S.A., Sun Y., and Siegman A.E. Beam propagation behavior in a quasi-stadium laser diode. Opt. Exp. 2 (1998) 21-28
23. In: Giannoni M.J., Voros A., and Zinn-Justin J. (Eds). Les Houches Lecture Series, Session LII (1989), North-Holland, Amsterdam
24. Gianordoli S., Hvozdara L., Strasser G., Schrenk W., Faist J., and Gornik E. Long-wavelength λ = 10 μm quadrupolar-shaped GaAs-AlGaAs microlasers. IEEE J. Quantum Electron. 36 (2000) 458-464
25. Gmachl C., Capasso F., Narimanov E.E., Nöckel J.U., Stone A.D., Faist J., Sivco D.L., and Cho A.Y. High-power directional emission from microlasers with chaotic resonators. Science 280 (1998) 1556-1564
26. Gmachl C., Narimanov E.E., Capasso F., Baillargeon J.N., and Cho A.Y. Kolmogorov-Arnold-Moser transition and laser action on scar modes in semiconductor diode lasers with deformed resonators. Opt. Lett. 27 (2002) 824-826
27. Goodman J.W. Introduction to Fourier Optics (1996), McGraw-Hill, New York
28. Gutzwiller M.C. Chaos in Classical and Quantum Mechanics (1990), Springer-Verlag, New York
29. Haake F. Quantum Signatures of Chaos (2000), Springer-Verlag, Berlin
30. Hackenbroich G., and Nöckel J.U. Dynamical tunneling in optical cavities. Europhys. Lett. 39 (1997) 371-376
31. Heller E.J. Bound-state eigenfunctions of classically chaotic Hamiltonian systems - scars of periodic-orbits. Phys. Rev. Lett. 53 (1984) 1515-1518
32. Heller E.J. Wavepacket Dynamics and Quantum Chaology (1989), North-Holland, Amsterdam pp. 547-663
33. Hentschel M., and Richter K. Quantum chaos in optical systems: the annular billiard. Phys. Rev. E 66 (2002) Art. no. 056207
34. Husimi K. Some formal properties of the density matrix. Proc. Phys. Math. Soc. Jpn. 22 (1940) 264-314
35. Jackson J.D. Classical Electrodynamics (1998), Wiley, New York
36. Johnson B.R. Theory of morphology-dependent resonances - shape resonances and width formulas. J. Opt. Soc. Am. A 10 (1993) 343-352
37. Kaplan L. Scars in quantum chaotic wavefunctions. Nonlinearity 12 (1999) R1-R40
38. In: Keller J.B., Papanicolau G., and McLaughlin D. (Eds). Asymptotic Methods for Partial Differential Equations: The Reduced Wave Equation and Maxwell's Equations (1995), Plenum, New York
39. Keller J.B., and Rubinow S.I. Asymptotic solution of eigenvalue problems. Ann. Phys. 9 (1960) 24-75
40. Klakow D., and Smilansky U. Wavefunctions, expectation values and scars on Poincaré sections - a scattering approach. J. Phys. A 29 (1996) 3213-3231
41. Kravtsov Y.A., and Orlov Y.I. Caustics, Catastrophes and Wave Fields (1999), Springer-Verlag, Berlin
42. Lazutkin V.F. KAM Theory and Semiclassical Approximations to Eigenfunctions (1993), Springer-Verlag, New York
43. Lee S.B., Lee J.H., Chang J.S., Moon H.J., Kim S.W., and An K. Observation of scarred modes in asymmetrically deformed microcylinder lasers. Phys. Rev. Lett. 8803 (2002) Art. no. 033903
44. Leung P.T., Liu S.Y., and Young K. Completeness and orthogonality of quasi-normal modes in leaky optical cavities. Phys. Rev. A 49 (1994) 3057-3067
45. Levi A.F.J., Slusher R.E., McCall S.L., Tanbunek T., Coblentz D.L., and Pearton S.J. Electrically pumped, room-temperature microdisk semiconductor lasers with submilliampere threshold currents. IEEE Trans. Electron Devices 39 (1992) 2651
46. Lichtenberg A.J., and Lieberman M.A. Regular and Chaotic Dynamics (1992), Springer-Verlag, New York
47. Manenkov A.B. Radiation modes of a fiber. 1. Construction and properties. IEE Proc. Optoelectron. 141 (1994) 287-295
48. McCall S.L., Levi A.F.J., Slusher R.E., Pearton S.J., and Logan R.A. Whispering-gallery mode microdisk lasers. Appl. Phys. Lett. 60 (1992) 289-291
49. Mekis A., Nöckel J.U., Chen G., Stone A.D., and Chang R.K. Ray chaos and q spoiling in lasing droplets. Phys. Rev. Lett. 75 (1995) 2682-2685
50. Narimanov E.E., Hackenbroich G., Jacquod P., and Stone A.D. Semiclassical theory of the emission properties of wave-chaotic resonant cavities. Phys. Rev. Lett. 83 (1999) 4991-4994
51. Nöckel, J.U., 1997, Resonances in nonintegrable open systems, PhD thesis, Yale University, New Haven, CT
52. Nöckel J.U., and Stone A.D. Ray and wave chaos in asymmetric resonant optical cavities. Nature 385 (1997) 45-47
53. Nöckel J.U., Stone A.D., and Chang R.K. Q-spoiling and directionality in deformed ring cavities. Opt. Lett. 19 (1994) 1693-1695
54. Nöckel J.U., Stone A.D., Chen G., Grossman H.L., and Chang R.K. Directional emission from asymmetric resonant cavities. Opt. Lett. 21 (1996) 1609-1611
55. Nussenzveig H.M. Diffraction Effects in Semiclassical Scattering (1992), Cambridge University Press, Cambridge
56. Poincaré H. Sur le problème des trois corps et les équations de la dynamique. Acta Math. 13 (1890) 67
57. Poritsky H. The billiard ball problem on a table with convex boundary - an illustrative dynamical problem. Ann. Math. 51 (1950) 446-470
58. Ralston J.V. Construction of quasimodes associated with stable periodic orbits. Commun. Math. Phys. 51 (1976) 219-242
59. Rayleigh L. On the dynamical theory of gratings. Proc. R. Soc. London Ser. A 79 (1907) 399-416
60. Reichl L.E. The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations (1992), Springer-Verlag, New York
61. Rex, N.B., 2001, Regular and chaotic orbit gallium nitride microcavity lasers, PhD thesis, Yale University, New Haven, CT
62. Rex N.B., Chang R.K., and Guido L.J. Threshold lowering in GaN micropillar lasers by means of spatially selective optical pumping. IEEE Photonics Technol. Lett. 13 (2001) 1-3
63. Rex N.B., Türeci H.E., Schwefel H.G.L., Chang R.K., and Stone A.D. Fresnel filtering in lasing emission from scarred modes of wave-chaotic optical resonators. Phys. Rev. Lett. 88 (2002) Art. no. 094102
64. Robnik M., and Berry M.V. Classical billiards in magnetic fields. J. Phys. A 18 (1985) 1361-1378
65. Schwefel H.G.L., Rex N.B., Türeci H.E., Chang R.K., Stone A.D., and Zyss J. Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers. J. Opt. Soc Am. B 21 (2003) 923-934
66. Siegman A.E. Lasers (1986), University Science Books, Mill Valley, CA
67. Slusher R.E., Levi A.F.J., Mohideen U., McCall S.L., Pearton S.J., and Logan R.A. Threshold characteristics of semiconductor microdisk lasers. Appl. Phys. Lett. 63 (1993) 1310-1312
68. Türeci, H.E., 2003, Wave chaos in dielectric resonators: asymptotic and numerical approaches, PhD thesis, Yale University, New Haven, CT
69. Türeci H.E., Schwefel H.G.L., Stone A.D., and Narimanov E.E. Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities. Opt. Exp. 10 (2002) 752-776
70. van den Berg P.M., and Fokkema J.T. The Rayleigh hypothesis in the theory of diffraction by a perturbation in a plane surface. Radio Sci. 15 (1980) 723-732
71. Wigner E. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40 (1932) 749-759
72. Yamamoto Y., and Slusher R.E. Optical processes in microcavities. Phys. Today 46 (1993) 66-73