Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities

Optics Express

Volumn 10, Issue 16, 2002, Pages 752-776

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

^a Yale University   (United States)

^b Princeton University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ABERRATIONS; CAVITY RESONATORS; GEOMETRICAL OPTICS; HAMILTONIANS; LIGHT REFLECTION; OPTICAL RESONATORS; QUANTUM THEORY; REFRACTIVE INDEX;

DIELECTRIC MICRO-CAVITIES; ORBIT RESONANCES; PARABOLIC EQUATIONS; WAVEVECTOR QUANTIZATION;

MICROOPTICS;

EID: 1042267896     PISSN: 10944087     EISSN: None     Source Type: Journal    
DOI: 10.1364/OE.10.000752     Document Type: Article

References (46)

1. R. K. Chang, A. K. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
2. H. Yokoyama, "Physics and device applications of optical microcavities," Science 256, 66-70 (1992).
3. A. D. Stone, "Wave-chaotic optical resonators and lasers," Phys. Scr. T90, 248-262 (2001).
4. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
5. J. U. Nöckel and A. D. Stone, "Ray and wave chaos in asymmetric resonant optical cavities," Nature 385, 45-47 (1997).
6. A. J. Campillo, J. D. Eversole, and H. B. Lin, "Cavity quantum electrodynamic enhancement of stimulated-emission in microdroplets," Phys. Rev. Lett. 67, 437-440 (1991).
7. H. B. Lin, J. D. Eversole, and A. J. Campillo, "Spectral properties of lasing microdroplets," J. Opt. Soc. Am. B 9, 43-50 (1992).
8. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow- threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-623 (2002).
9. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photonics Technol. Lett. 10, 549-551 (1998).
10. S. X. Qian, J. B. Snow, H. M. Tzeng, and R. K. Chang, "Lasing droplets - highlighting the liquid-air interface by laser-emission," Science 231, 486-488 (1986).
11. A. W. Poon, F. Courvoisier, and R. K. Chang, "Multimode resonances in square-shaped optical microcavities," Opt. Lett. 26, 632-634 (2001).
12. I. Braun, G. Ihlein, F. Laeri, J. U. Nöckel, G. Schulz-Ekloff, F. Schuth, U. Vietze, O. Weiss, and D. Wohrle, "Hexagonal microlasers based ou organic dyes in nanoporous crystals," Appl. Phys. B-Lasers Opt. 70, 335-343 (2000).
13. A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, and R. K. Chang, "Ray chaos and q spoiling in lasing droplets," Phys. Rev. Lett. 75, 2682-2685 (1995).
14. J. U. Nöckel, A. D. Stone, G. Chen, H. L. Grossman, and R. K. Chang, "Directional emission from asymmetric resonant cavities," Opt. Lett. 21, 1609-1611 (1996).
15. S. Gianordoli, L. Hvozdara, G. Strasser, W. Schrenk, J. Faist, and E. Gornik, "Long-wavelength λ = 10μm quadrupolar-shaped GaAs-AlGaAs microlasers," IEEE J. Quantum Electron. 36, 458-464 (2000).
16. S. Chang, R. K. Chang, A. D. Stone, and J. U. Nöckel, "Observation of emission from chaotic lasing modes in deformed microspheres: displacement by the stable-orbit modes," J. Opt. Soc. Am. B-Opt. Phys. 17, 1828-1834 (2000).
17. N. B. Rex, H. E. Tureci, H. G. L. Schwefel, R. K. Chang, and A. D. Stone, "Fresnel filtering in lasing emission from scarred modes of wave-chaotic optical resonators," Phys. Rev. Lett. 88, art. no.094102 (2002).
18. N. B. Rex, Regular and chaotic orbit Gallium Nitride microcavity lasers, Ph.D. thesis, Yale University (2001).
19. C. Gmachl, E. E. Narimanov, F. Capasso, J. N. Baillargeon, and A. Y. Cho. "Kolmogorov-Arnold-Moser transition and laser action on scar modes in semiconductor diode lasers with deformed resonators," Opt. Lett. 27, 824-826 (2002).
20. S. B. Lee, J. H. Lee, J. S. Chang, H. J. Moon, S. W. Kim, and K. An, "Observation of scarred modes in asymmetrically deformed microcylinder lasers," Phys. Rev. Lett. 88, art. no.033903 (2002).
21. E. J. Heller, "Bound-state eigenfunctions of classically chaotic hamiltonian-systems - Scars of periodic orbits," Phys. Rev. Lett. 53, 1515-1518 (1984).
22. H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, and A. D. Stone, "Dramatic shape sensitivity of emission patterns for similarly deformed cylindrical polymer lasers," in QELS 2002 Technical Digest, (Baltimore, MD, 2002), pp. 24-25.
23. M. V. Berry, "Regularity and chaos in classical mechanics, illustrated by three deformations of a circular billiard," Eur. J. Phys. 2, 91-102 (1981).
24. B. Li and M. Robnik, "Geometry of high-lying eigenfunctions in a plane billiard system having mixed type classical dynamics," J. Phys. A 28, 2799-2818 (1995).
25. J. B. Keller and S. I. Rubinow, "Asymptotic Solution of Eigenvalue Problems," Ann. Phys. 9, 24-75 (1960).
26. M. C. Gutzwiller, Chaos in classical and quantum mechanics (Springer, New York, USA. 1990).
27. W. H. Miller, "Semiclassical quantization of nonseparable systems: A new look at periodic orbit theory," J. Chem. Phys. 63, 996-999 (1975).
28. S. D. Frischat and E. Doron, "Quantum phase-space structures in classically mixed systems: A scattering approach," J. Phys. A-Math. Gen. 30, 3613-3634 (1997).
29. O. A. Starykh, P. R. J. Jacquod, E. E. Narimanov, and A. D. Stone, "Signature of dynamical localization in the resonance width distribution of wave-chaotic dielectric cavities," Phys. Rev. E 62, 2078-2084 (2000).
30. J. U. Nöckel, "Angular momentum localization in oval billiards," Phys. Scr. T90, 263-267 (2001).
31. V. M. Babič and V. S. Buldyrev, Asymptotic Methods in Shortwave Diffraction Problems (Springer, New York, USA, 1991).
32. F. Laeri and J. U. Nöckel, "Nanoporous compound materials for optical applications - Microlasers and microresonators," in Handbook of Advanced Electronic and Photonic Materials, H. S. Nalwa, ed. (Academic Press, San Diego, 2001).
33. A. E. Siegman, Lasers (University Science Books, Mill Valley, California, 1986).
34. V. P. Maslov and M. V. Fedoriuk, Semiclassical Approximations in Quantum Mechanics (Reidel, Boston, USA, 1981).
35. N. A. Chernikov, "System whose hamiltonian is a time-dependent quadratic form in x and p," Sov Phys-Jetp EngI Trans 26, 603-808 (1968).
36. E. S. C. Ching, P. T. Leung, A. Maassen van den Brink, W. M. Suen, T. S. S., and K. Young, "Quasinormal-mode expansion for waves in open systems," Rev. Mod. Phys. 70, 1545-1554 (1998).
37. J. W. Ra, H. L. Bertoni, and L. B. Felsen, "Reflection and transmission of beams at a dielectric interface," SIAM J. Appl. Math 24, 396-413 (1973).
38. J. M. Robbins, "Discrete symmetries in periodic-orbit theory," Phys. Rev. A. 40, 2128-2136 (1989).
39. M. J. Davis and E. J. Heller, "Multidimensional wave functions from classical trajectories," J. Chem. Phys. 75, 246 (1981).
40. O. Bohigas, S. Tomsovic, and D. Ullmo, "Manifestations of classical phase space structures in quantum mechanics," Phys. Rep. 223, 45 (1993).
41. S. D. Frischat and E. Doron, "Semiclassical description of tunneling in mixed systems: case of the annular billiard," Phys. Rev. Lett. 75, 3661 (1995).
42. F. Leyvraz and D. Ullmo, "The level splitting distribution in chaos-assisted tunneling," J. Phys. A 29, 2529 (1996).
43. E. E. Narimanov, unpublished.
44. M. V. Berry, "Regular and irregular semiclassical wavefunctions," J. Phys. A 10, 2083 (1977).
45. H. E. Tureci and A. D. Stone, "Deviation from Snell's law for beams transmitted near the critical angle: application to microcavity lasers," Opt. Lett. 27, 7-9 (2002).
46. E. E. Narimanov, G. Hackenbroich, P. Jacquod, and A. D. Stone, "Semiclassical theory of the emission properties of wave-chaotic resonant cavities," Phys. Rev. Lett. 83, 4991-4994 (1999).