Abstract

Theoretical study of free space coupling to high-Q whispering gallery modes (WGMs) are presented in circular and deformed microcavities. Both analytical solutions and asymptotic formulas are derived for a circular cavity. The coupling efficiencies at different coupling regimes for cylindrical incoming wave are discussed, and the maximum efficiency is estimated for the practical Gaussian beam excitation. In the case of a deformed cavity, the coupling efficiency can be higher than the circular cavity if the excitation beam can match the intrinsic emission which can be tuned by adjusting the degree of deformation. Employing an abstract model of slightly deformed cavity, we find that the asymmetric and peak like line shapes instead of the Lorentz-shape dip are universal in transmission spectra due to multi-wave interference, and the coupling efficiency cannot be estimated from the absolute depth of the dip. Our results provide guidelines for free space coupling in experiments, suggesting that the high-Q asymmetric resonator cavities (ARCs) can be efficiently excited through free space which will stimulate further experiments and applications of WGMs based on free space coupling.

© 2013 OSA

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  1. Lord Rayleigh, “The problem of the whispering gallery,” Phil. Mag.20, 1001–1004 (1910).
  2. R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys.10, 391–398 (1939).
    [CrossRef]
  3. I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A74, 063806 (2006).
    [CrossRef]
  4. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nature Methods5, 591–596 (2008).
    [CrossRef] [PubMed]
  5. L. He, S. K. Ozdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photon. Rev.7, 60–82 (2013).
    [CrossRef]
  6. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
    [CrossRef]
  7. T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
    [CrossRef] [PubMed]
  8. Y. S. Park and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat. Phys.5, 489–493 (2009).
    [CrossRef]
  9. V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett.107, 133601 (2011).
    [CrossRef] [PubMed]
  10. E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature482, 63–67 (2012).
    [CrossRef] [PubMed]
  11. G. Mie, “Beiträge zur optik trüber Medien, speziell kolloidaler metallösungen,” Ann. Phys. (Leipzig)330, 377–445 (1908).
    [CrossRef]
  12. H. Moyses Nussenzveig, “The Science of the Glory,” Sci. Am.306(1), 68–73 (2012)
    [CrossRef] [PubMed]
  13. S. X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets highlighting the liquid-air interface by laser emission,” Science231, 486–488 (1986)
    [CrossRef] [PubMed]
  14. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
    [CrossRef]
  15. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett.60, 289–291 (1992).
    [CrossRef]
  16. H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett.85, 3161–3164 (2000).
    [CrossRef] [PubMed]
  17. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
    [CrossRef] [PubMed]
  18. M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun.113, 133–143 (1994).
    [CrossRef]
  19. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
    [CrossRef] [PubMed]
  20. Y.-Z. Yan, C.-L. Zou, S.-B. Yan, F.-W. Sun, Z. Ji, J. Liu, Y.-G. Zhang, L. Wang, C.-Y. Xue, and W.-D. Zhang, “Packaged silica microsphere-taper coupling system for robust thermal sensing application,” Opt. Express19, 5753–5759 (2011).
    [CrossRef] [PubMed]
  21. F.-J. Shu, C.-L. Zou, and F.-W. Sun, “Perpendicular coupler for whispering-gallery resonators,” Opt. Lett.37, 3123–3125 (2012).
    [CrossRef] [PubMed]
  22. B. E. Little, J. P. Laine, and H. A. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol.17, 704–715 (1999).
    [CrossRef]
  23. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett.36, 321–322 (2000).
    [CrossRef]
  24. C.-L. Zou, Y. Yang, C.-H. Dong, Y.-F. Xiao, X.-W. Wu, Z.-F. Han, and G.-C. Guo, “Taper-microsphere coupling with numerical calculation of coupled-mode theory,” J. Opt. Soc. Am. B25, 1895–1898 (2008)
    [CrossRef]
  25. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analogue of electromagnetically induced transparency,” Phys. Rev. Lett.93, 233903 (2004).
    [CrossRef] [PubMed]
  26. K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett.98, 213904 (2007).
    [CrossRef] [PubMed]
  27. C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B42, 215401 (2009).
    [CrossRef]
  28. B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
    [CrossRef]
  29. B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
    [CrossRef]
  30. A. Chiba, H. Fujiwara, J.-I. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett.86, 261106 (2005).
    [CrossRef]
  31. C.-H. Dong, C.-L. Zou, J.-M. Cui, Y. Yang, Z.-F. Han, and G.-C. Guo, “Ringing phenomenon in silica microspheres,” Chin. Opt. Lett.7, 299–301 (2009).
    [CrossRef]
  32. 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).
    [CrossRef] [PubMed]
  33. 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,” Science280, 1556–1564 (1998).
    [CrossRef] [PubMed]
  34. 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, 033903 (2002).
    [CrossRef] [PubMed]
  35. S. Lacey, H. Wang, D. H. Foster, and J. U. Nöckel, “Directional tunneling escape from nearly spherical optical resonators,” Phys. Rev. Lett.91, 033902(2003).
    [CrossRef] [PubMed]
  36. Y.-F. Xiao, C.-H. Dong, Z.-F. Han, G.-C. Guo, and Y.-S. Park, “Directional escape from a high-Q deformed microsphere induced by short CO2 laser pulses,” Opt. Lett.32, 644–646 (2007).
    [CrossRef] [PubMed]
  37. T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, “Lasing on scar modes in fully chaotic microcavities,” Phys. Rev. E67, 015207 (2003).
    [CrossRef]
  38. W. Fang, A. Yamilov, and H. Cao, “Analysis of high-quality modes in open chaotic microcavities,” Phys. Rev. A72, 023815 (2005).
    [CrossRef]
  39. M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, “Highly directional stadium-shaped polymer microlasers,” Appl. Phys. Lett.88, 031108 (2006).
    [CrossRef]
  40. Y.-F. Xiao, C.-H. Dong, C.-L. Zou, Z.-F. Han, L. Yang, and G.-C. Guo, “Low-threshold microlaser in a high-Q asymmetrical microcavity,” Opt. Lett.34, 509–511 (2009).
    [CrossRef] [PubMed]
  41. J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature385, 45–47 (1997).
    [CrossRef]
  42. H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B21, 923–934 (2004).
    [CrossRef]
  43. V. A. Podolskiy and E. E. Narimanov, “Chaos-assisted tunneling in dielectric microcavities,” Opt. Lett.30, 474–476 (2005).
    [CrossRef] [PubMed]
  44. S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A77, 033807 (2008).
    [CrossRef]
  45. S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
    [CrossRef]
  46. J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A73, 031802 (2006).
    [CrossRef]
  47. J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett.100, 033901 (2008).
    [CrossRef] [PubMed]
  48. Q. Song, W. Fang, B. Liu, S.-T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A80, 041807 (2009).
    [CrossRef]
  49. C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
    [CrossRef]
  50. S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limacon-shaped semiconductor microcavities,” Phys. Rev. A80, 031801 (2009).
    [CrossRef]
  51. C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “High Q and unidirectional emission whispering gallery modes: principles and design,” IEEE J. Sel. Top. Quantum Electron., In press (2013).
  52. X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
    [CrossRef] [PubMed]
  53. Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
    [CrossRef] [PubMed]
  54. Y.-S. Park and H. Wang, “Radiation pressure driven mechanical oscillation in deformed silica microspheres via free-space evanescent excitation,” Opt. Express15, 16471–16477 (2007).
    [CrossRef] [PubMed]
  55. J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
    [CrossRef]
  56. J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, and K. An, “Observation of resonance effects in the pump transmission of a chaotic microcavity,” Opt. Express18, 26141–26148 (2010).
    [CrossRef] [PubMed]
  57. J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
    [CrossRef] [PubMed]
  58. D. Q. Chowdhury, S. C. Hill, and Md. Mohiuddin Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption.” IEEE J. Quant. Electron.29, 2553–2561 (1993).
    [CrossRef]
  59. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-VerlagBerlin Heidelberg, 2008 ).
  60. A. Serpengüzel, S. Arnold, G. Griffel, and J.A. Lock, “Enhanced coupling to microsphere resonances with optical fibers,” J. Opt. Soc. Am. B14, 790–795 (1997).
    [CrossRef]
  61. H.-B. Lin, J.D. Eversole, A.J. Campillo, and J.P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett.23, 1921–1923 (1998).
    [CrossRef]
  62. S. C. Creagh, “Directional emission from weakly eccentric resonators,” Phys. Rev. Lett.98, 153901 (2007).
    [CrossRef] [PubMed]
  63. M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express17, 19160–19165 (2009).
    [CrossRef]
  64. S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).
  65. S. Tomsovic and D. Ullmo, “Chaos-assisted tunneling,” Phys. Rev. E50, 145–162 (1994).
    [CrossRef]
  66. D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science293, 274–278 (2001).
    [CrossRef] [PubMed]

2013 (2)

L. He, S. K. Ozdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photon. Rev.7, 60–82 (2013).
[CrossRef]

C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “High Q and unidirectional emission whispering gallery modes: principles and design,” IEEE J. Sel. Top. Quantum Electron., In press (2013).

2012 (5)

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

F.-J. Shu, C.-L. Zou, and F.-W. Sun, “Perpendicular coupler for whispering-gallery resonators,” Opt. Lett.37, 3123–3125 (2012).
[CrossRef] [PubMed]

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature482, 63–67 (2012).
[CrossRef] [PubMed]

H. Moyses Nussenzveig, “The Science of the Glory,” Sci. Am.306(1), 68–73 (2012)
[CrossRef] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
[CrossRef]

2011 (3)

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
[CrossRef]

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett.107, 133601 (2011).
[CrossRef] [PubMed]

Y.-Z. Yan, C.-L. Zou, S.-B. Yan, F.-W. Sun, Z. Ji, J. Liu, Y.-G. Zhang, L. Wang, C.-Y. Xue, and W.-D. Zhang, “Packaged silica microsphere-taper coupling system for robust thermal sensing application,” Opt. Express19, 5753–5759 (2011).
[CrossRef] [PubMed]

2010 (3)

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, and K. An, “Observation of resonance effects in the pump transmission of a chaotic microcavity,” Opt. Express18, 26141–26148 (2010).
[CrossRef] [PubMed]

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
[CrossRef] [PubMed]

2009 (9)

Q. Song, W. Fang, B. Liu, S.-T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A80, 041807 (2009).
[CrossRef]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limacon-shaped semiconductor microcavities,” Phys. Rev. A80, 031801 (2009).
[CrossRef]

S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).

Y.-F. Xiao, C.-H. Dong, C.-L. Zou, Z.-F. Han, L. Yang, and G.-C. Guo, “Low-threshold microlaser in a high-Q asymmetrical microcavity,” Opt. Lett.34, 509–511 (2009).
[CrossRef] [PubMed]

C.-H. Dong, C.-L. Zou, J.-M. Cui, Y. Yang, Z.-F. Han, and G.-C. Guo, “Ringing phenomenon in silica microspheres,” Chin. Opt. Lett.7, 299–301 (2009).
[CrossRef]

M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express17, 19160–19165 (2009).
[CrossRef]

Y. S. Park and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat. Phys.5, 489–493 (2009).
[CrossRef]

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B42, 215401 (2009).
[CrossRef]

2008 (5)

S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A77, 033807 (2008).
[CrossRef]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nature Methods5, 591–596 (2008).
[CrossRef] [PubMed]

C.-L. Zou, Y. Yang, C.-H. Dong, Y.-F. Xiao, X.-W. Wu, Z.-F. Han, and G.-C. Guo, “Taper-microsphere coupling with numerical calculation of coupled-mode theory,” J. Opt. Soc. Am. B25, 1895–1898 (2008)
[CrossRef]

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
[CrossRef]

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett.100, 033901 (2008).
[CrossRef] [PubMed]

2007 (6)

S. C. Creagh, “Directional emission from weakly eccentric resonators,” Phys. Rev. Lett.98, 153901 (2007).
[CrossRef] [PubMed]

Y.-F. Xiao, C.-H. Dong, Z.-F. Han, G.-C. Guo, and Y.-S. Park, “Directional escape from a high-Q deformed microsphere induced by short CO2 laser pulses,” Opt. Lett.32, 644–646 (2007).
[CrossRef] [PubMed]

Y.-S. Park and H. Wang, “Radiation pressure driven mechanical oscillation in deformed silica microspheres via free-space evanescent excitation,” Opt. Express15, 16471–16477 (2007).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
[CrossRef]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett.98, 213904 (2007).
[CrossRef] [PubMed]

2006 (4)

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A73, 031802 (2006).
[CrossRef]

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, “Highly directional stadium-shaped polymer microlasers,” Appl. Phys. Lett.88, 031108 (2006).
[CrossRef]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A74, 063806 (2006).
[CrossRef]

2005 (3)

A. Chiba, H. Fujiwara, J.-I. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett.86, 261106 (2005).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, “Chaos-assisted tunneling in dielectric microcavities,” Opt. Lett.30, 474–476 (2005).
[CrossRef] [PubMed]

W. Fang, A. Yamilov, and H. Cao, “Analysis of high-quality modes in open chaotic microcavities,” Phys. Rev. A72, 023815 (2005).
[CrossRef]

2004 (2)

2003 (3)

S. Lacey, H. Wang, D. H. Foster, and J. U. Nöckel, “Directional tunneling escape from nearly spherical optical resonators,” Phys. Rev. Lett.91, 033902(2003).
[CrossRef] [PubMed]

T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, “Lasing on scar modes in fully chaotic microcavities,” Phys. Rev. E67, 015207 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

2002 (1)

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, 033903 (2002).
[CrossRef] [PubMed]

2001 (1)

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science293, 274–278 (2001).
[CrossRef] [PubMed]

2000 (3)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett.36, 321–322 (2000).
[CrossRef]

H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett.85, 3161–3164 (2000).
[CrossRef] [PubMed]

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (2)

H.-B. Lin, J.D. Eversole, A.J. Campillo, and J.P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett.23, 1921–1923 (1998).
[CrossRef]

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,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

1997 (2)

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature385, 45–47 (1997).
[CrossRef]

A. Serpengüzel, S. Arnold, G. Griffel, and J.A. Lock, “Enhanced coupling to microsphere resonances with optical fibers,” J. Opt. Soc. Am. B14, 790–795 (1997).
[CrossRef]

1995 (1)

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).
[CrossRef] [PubMed]

1994 (2)

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun.113, 133–143 (1994).
[CrossRef]

S. Tomsovic and D. Ullmo, “Chaos-assisted tunneling,” Phys. Rev. E50, 145–162 (1994).
[CrossRef]

1993 (1)

D. Q. Chowdhury, S. C. Hill, and Md. Mohiuddin Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption.” IEEE J. Quant. Electron.29, 2553–2561 (1993).
[CrossRef]

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett.60, 289–291 (1992).
[CrossRef]

1989 (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
[CrossRef]

1986 (1)

S. X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets highlighting the liquid-air interface by laser emission,” Science231, 486–488 (1986)
[CrossRef] [PubMed]

1939 (1)

R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys.10, 391–398 (1939).
[CrossRef]

1910 (1)

Lord Rayleigh, “The problem of the whispering gallery,” Phil. Mag.20, 1001–1004 (1910).

1908 (1)

G. Mie, “Beiträge zur optik trüber Medien, speziell kolloidaler metallösungen,” Ann. Phys. (Leipzig)330, 377–445 (1908).
[CrossRef]

Aida, T.

T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, “Lasing on scar modes in fully chaotic microcavities,” Phys. Rev. E67, 015207 (2003).
[CrossRef]

An, K.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, and K. An, “Observation of resonance effects in the pump transmission of a chaotic microcavity,” Opt. Express18, 26141–26148 (2010).
[CrossRef] [PubMed]

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
[CrossRef] [PubMed]

S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
[CrossRef]

S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
[CrossRef]

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, 033903 (2002).
[CrossRef] [PubMed]

H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett.85, 3161–3164 (2000).
[CrossRef] [PubMed]

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nature Methods5, 591–596 (2008).
[CrossRef] [PubMed]

A. Serpengüzel, S. Arnold, G. Griffel, and J.A. Lock, “Enhanced coupling to microsphere resonances with optical fibers,” J. Opt. Soc. Am. B14, 790–795 (1997).
[CrossRef]

Barbour, R.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett.107, 133601 (2011).
[CrossRef] [PubMed]

Barton, J.P.

Belkin, M. A.

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

Ben-Messaoud, T.

Bowen, W. P.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
[CrossRef]

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
[CrossRef] [PubMed]

Campillo, A.J.

Cao, H.

Q. Song, W. Fang, B. Liu, S.-T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A80, 041807 (2009).
[CrossRef]

W. Fang, A. Yamilov, and H. Cao, “Analysis of high-quality modes in open chaotic microcavities,” Phys. Rev. A72, 023815 (2005).
[CrossRef]

Capasso, F.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

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,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Carmon, T.

Chang, J.-S.

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, 033903 (2002).
[CrossRef] [PubMed]

Chang, R. K.

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B21, 923–934 (2004).
[CrossRef]

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).
[CrossRef] [PubMed]

S. X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets highlighting the liquid-air interface by laser emission,” Science231, 486–488 (1986)
[CrossRef] [PubMed]

Chen, G.

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).
[CrossRef] [PubMed]

Chen, Y.-L.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
[CrossRef]

Chiba, A.

A. Chiba, H. Fujiwara, J.-I. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett.86, 261106 (2005).
[CrossRef]

Cho, A. Y.

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,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Chough, Y. T.

H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett.85, 3161–3164 (2000).
[CrossRef] [PubMed]

Chowdhury, D. Q.

D. Q. Chowdhury, S. C. Hill, and Md. Mohiuddin Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption.” IEEE J. Quant. Electron.29, 2553–2561 (1993).
[CrossRef]

Creagh, S. C.

S. C. Creagh, “Directional emission from weakly eccentric resonators,” Phys. Rev. Lett.98, 153901 (2007).
[CrossRef] [PubMed]

Cui, J.-M.

C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “High Q and unidirectional emission whispering gallery modes: principles and design,” IEEE J. Sel. Top. Quantum Electron., In press (2013).

C.-H. Dong, C.-L. Zou, J.-M. Cui, Y. Yang, Z.-F. Han, and G.-C. Guo, “Ringing phenomenon in silica microspheres,” Chin. Opt. Lett.7, 299–301 (2009).
[CrossRef]

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B42, 215401 (2009).
[CrossRef]

Dao, T. T. A.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
[CrossRef] [PubMed]

Davis, P.

T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, “Lasing on scar modes in fully chaotic microcavities,” Phys. Rev. E67, 015207 (2003).
[CrossRef]

Dayan, B.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Del’Haye, P.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Deleglise, S.

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature482, 63–67 (2012).
[CrossRef] [PubMed]

Diehl, L.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

Dong, C.-H.

C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “High Q and unidirectional emission whispering gallery modes: principles and design,” IEEE J. Sel. Top. Quantum Electron., In press (2013).

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B42, 215401 (2009).
[CrossRef]

C.-H. Dong, C.-L. Zou, J.-M. Cui, Y. Yang, Z.-F. Han, and G.-C. Guo, “Ringing phenomenon in silica microspheres,” Chin. Opt. Lett.7, 299–301 (2009).
[CrossRef]

Y.-F. Xiao, C.-H. Dong, C.-L. Zou, Z.-F. Han, L. Yang, and G.-C. Guo, “Low-threshold microlaser in a high-Q asymmetrical microcavity,” Opt. Lett.34, 509–511 (2009).
[CrossRef] [PubMed]

C.-L. Zou, Y. Yang, C.-H. Dong, Y.-F. Xiao, X.-W. Wu, Z.-F. Han, and G.-C. Guo, “Taper-microsphere coupling with numerical calculation of coupled-mode theory,” J. Opt. Soc. Am. B25, 1895–1898 (2008)
[CrossRef]

Y.-F. Xiao, C.-H. Dong, Z.-F. Han, G.-C. Guo, and Y.-S. Park, “Directional escape from a high-Q deformed microsphere induced by short CO2 laser pulses,” Opt. Lett.32, 644–646 (2007).
[CrossRef] [PubMed]

Edamura, T.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

Eversole, J.D.

Faist, J.

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,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Fan, S.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analogue of electromagnetically induced transparency,” Phys. Rev. Lett.93, 233903 (2004).
[CrossRef] [PubMed]

Fang, W.

Q. Song, W. Fang, B. Liu, S.-T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A80, 041807 (2009).
[CrossRef]

W. Fang, A. Yamilov, and H. Cao, “Analysis of high-quality modes in open chaotic microcavities,” Phys. Rev. A72, 023815 (2005).
[CrossRef]

Fiore, V.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett.107, 133601 (2011).
[CrossRef] [PubMed]

Foster, D. H.

S. Lacey, H. Wang, D. H. Foster, and J. U. Nöckel, “Directional tunneling escape from nearly spherical optical resonators,” Phys. Rev. Lett.91, 033902(2003).
[CrossRef] [PubMed]

Fujiwara, H.

A. Chiba, H. Fujiwara, J.-I. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett.86, 261106 (2005).
[CrossRef]

Fukushima, T.

S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A77, 033807 (2008).
[CrossRef]

T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, “Lasing on scar modes in fully chaotic microcavities,” Phys. Rev. E67, 015207 (2003).
[CrossRef]

Gmachl, C.

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,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Gong, Q.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
[CrossRef]

Gorodetsky, M. L.

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun.113, 133–143 (1994).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
[CrossRef]

Griffel, G.

Grudinin, I. S.

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A74, 063806 (2006).
[CrossRef]

Guo, G.-C.

Han, Z.-F.

Harayama, T.

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limacon-shaped semiconductor microcavities,” Phys. Rev. A80, 031801 (2009).
[CrossRef]

S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A77, 033807 (2008).
[CrossRef]

T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, “Lasing on scar modes in fully chaotic microcavities,” Phys. Rev. E67, 015207 (2003).
[CrossRef]

Haus, H. A.

He, L.

L. He, S. K. Ozdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photon. Rev.7, 60–82 (2013).
[CrossRef]

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Hentschel, M.

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limacon-shaped semiconductor microcavities,” Phys. Rev. A80, 031801 (2009).
[CrossRef]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett.100, 033901 (2008).
[CrossRef] [PubMed]

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A73, 031802 (2006).
[CrossRef]

Hierle, R.

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, “Highly directional stadium-shaped polymer microlasers,” Appl. Phys. Lett.88, 031108 (2006).
[CrossRef]

Hill, S. C.

D. Q. Chowdhury, S. C. Hill, and Md. Mohiuddin Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption.” IEEE J. Quant. Electron.29, 2553–2561 (1993).
[CrossRef]

Ho, S.-T.

Q. Song, W. Fang, B. Liu, S.-T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A80, 041807 (2009).
[CrossRef]

Holzwarth, R.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Hotta, J.-I.

A. Chiba, H. Fujiwara, J.-I. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett.86, 261106 (2005).
[CrossRef]

Ilchenko, V. S.

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A74, 063806 (2006).
[CrossRef]

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun.113, 133–143 (1994).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
[CrossRef]

Ji, Z.

Jiang, X.-F.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
[CrossRef]

Kan, H.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

Kim, S. W.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
[CrossRef] [PubMed]

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, and K. An, “Observation of resonance effects in the pump transmission of a chaotic microcavity,” Opt. Express18, 26141–26148 (2010).
[CrossRef] [PubMed]

S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
[CrossRef]

S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
[CrossRef]

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, 033903 (2002).
[CrossRef] [PubMed]

Kimble, H. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Kippenberg, T. J.

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature482, 63–67 (2012).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

Kobayashi, N.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett.98, 213904 (2007).
[CrossRef] [PubMed]

Kuzyk, M. C.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett.107, 133601 (2011).
[CrossRef] [PubMed]

Lacey, S.

S. Lacey, H. Wang, D. H. Foster, and J. U. Nöckel, “Directional tunneling escape from nearly spherical optical resonators,” Phys. Rev. Lett.91, 033902(2003).
[CrossRef] [PubMed]

Laine, J. P.

Lauret, J. S.

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, “Highly directional stadium-shaped polymer microlasers,” Appl. Phys. Lett.88, 031108 (2006).
[CrossRef]

Lebental, M.

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, “Highly directional stadium-shaped polymer microlasers,” Appl. Phys. Lett.88, 031108 (2006).
[CrossRef]

Lee, H. W.

S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
[CrossRef]

Lee, J. H.

S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
[CrossRef]

Lee, J.-H.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
[CrossRef] [PubMed]

S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
[CrossRef]

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, 033903 (2002).
[CrossRef] [PubMed]

Lee, S. B.

S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
[CrossRef]

Lee, S.-B.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, and K. An, “Observation of resonance effects in the pump transmission of a chaotic microcavity,” Opt. Express18, 26141–26148 (2010).
[CrossRef] [PubMed]

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
[CrossRef] [PubMed]

S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
[CrossRef]

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, 033903 (2002).
[CrossRef] [PubMed]

Lee, S.-Y.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, and K. An, “Observation of resonance effects in the pump transmission of a chaotic microcavity,” Opt. Express18, 26141–26148 (2010).
[CrossRef] [PubMed]

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
[CrossRef] [PubMed]

S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
[CrossRef]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett.60, 289–291 (1992).
[CrossRef]

Li, B.-B.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
[CrossRef]

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
[CrossRef]

Li, Y.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
[CrossRef]

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
[CrossRef]

Lin, H.-B.

Little, B. E.

Liu, B.

Q. Song, W. Fang, B. Liu, S.-T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A80, 041807 (2009).
[CrossRef]

Liu, J.

Liu, Y.-C.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
[CrossRef]

Lock, J.A.

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett.60, 289–291 (1992).
[CrossRef]

Maleki, L.

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A74, 063806 (2006).
[CrossRef]

Mazumder, Md. Mohiuddin

D. Q. Chowdhury, S. C. Hill, and Md. Mohiuddin Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption.” IEEE J. Quant. Electron.29, 2553–2561 (1993).
[CrossRef]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett.60, 289–291 (1992).
[CrossRef]

Mekis, A.

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).
[CrossRef] [PubMed]

Mie, G.

G. Mie, “Beiträge zur optik trüber Medien, speziell kolloidaler metallösungen,” Ann. Phys. (Leipzig)330, 377–445 (1908).
[CrossRef]

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-VerlagBerlin Heidelberg, 2008 ).

Miyasaka, T.

T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, “Lasing on scar modes in fully chaotic microcavities,” Phys. Rev. E67, 015207 (2003).
[CrossRef]

Moon, H. J.

H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett.85, 3161–3164 (2000).
[CrossRef] [PubMed]

Moon, H.-J.

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, 033903 (2002).
[CrossRef] [PubMed]

Moon, S.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, and K. An, “Observation of resonance effects in the pump transmission of a chaotic microcavity,” Opt. Express18, 26141–26148 (2010).
[CrossRef] [PubMed]

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
[CrossRef] [PubMed]

S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
[CrossRef]

S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
[CrossRef]

Moyses Nussenzveig, H.

H. Moyses Nussenzveig, “The Science of the Glory,” Sci. Am.306(1), 68–73 (2012)
[CrossRef] [PubMed]

Narimanov, E. E.

V. A. Podolskiy and E. E. Narimanov, “Chaos-assisted tunneling in dielectric microcavities,” Opt. Lett.30, 474–476 (2005).
[CrossRef] [PubMed]

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,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Nishimura, T.

T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, “Lasing on scar modes in fully chaotic microcavities,” Phys. Rev. E67, 015207 (2003).
[CrossRef]

Nöckel, J. U.

S. Lacey, H. Wang, D. H. Foster, and J. U. Nöckel, “Directional tunneling escape from nearly spherical optical resonators,” Phys. Rev. Lett.91, 033902(2003).
[CrossRef] [PubMed]

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,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature385, 45–47 (1997).
[CrossRef]

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).
[CrossRef] [PubMed]

Oskay, W. H.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science293, 274–278 (2001).
[CrossRef] [PubMed]

Ozdemir, S. K.

L. He, S. K. Ozdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photon. Rev.7, 60–82 (2013).
[CrossRef]

Painter, O.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
[CrossRef] [PubMed]

Park, Y. S.

Y. S. Park and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat. Phys.5, 489–493 (2009).
[CrossRef]

Park, Y.-S.

Parkins, A. S.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett.60, 289–291 (1992).
[CrossRef]

Pflugl, C.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

Podolskiy, V. A.

Qian, S. X.

S. X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets highlighting the liquid-air interface by laser emission,” Science231, 486–488 (1986)
[CrossRef] [PubMed]

Raizen, M. G.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science293, 274–278 (2001).
[CrossRef] [PubMed]

Rayleigh, Lord

Lord Rayleigh, “The problem of the whispering gallery,” Phil. Mag.20, 1001–1004 (1910).

Rex, N. B.

Richtmyer, R. D.

R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys.10, 391–398 (1939).
[CrossRef]

Sasaki, K.

A. Chiba, H. Fujiwara, J.-I. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett.86, 261106 (2005).
[CrossRef]

Sasaki, T.

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limacon-shaped semiconductor microcavities,” Phys. Rev. A80, 031801 (2009).
[CrossRef]

Schliesser, A.

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature482, 63–67 (2012).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Schwefel, H. G. L.

Serpengüzel, A.

Shim, J. B.

S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
[CrossRef]

Shim, J.-B.

S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
[CrossRef]

Shinohara, S.

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limacon-shaped semiconductor microcavities,” Phys. Rev. A80, 031801 (2009).
[CrossRef]

S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A77, 033807 (2008).
[CrossRef]

Shu, F.-J.

C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “High Q and unidirectional emission whispering gallery modes: principles and design,” IEEE J. Sel. Top. Quantum Electron., In press (2013).

F.-J. Shu, C.-L. Zou, and F.-W. Sun, “Perpendicular coupler for whispering-gallery resonators,” Opt. Lett.37, 3123–3125 (2012).
[CrossRef] [PubMed]

Sivco, D. L.

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,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett.60, 289–291 (1992).
[CrossRef]

Snow, J. B.

S. X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets highlighting the liquid-air interface by laser emission,” Science231, 486–488 (1986)
[CrossRef] [PubMed]

Solomon, G. S.

Q. Song, W. Fang, B. Liu, S.-T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A80, 041807 (2009).
[CrossRef]

Song, Q.

Q. Song, W. Fang, B. Liu, S.-T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A80, 041807 (2009).
[CrossRef]

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

Steck, D. A.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science293, 274–278 (2001).
[CrossRef] [PubMed]

Stone, A. D.

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B21, 923–934 (2004).
[CrossRef]

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,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature385, 45–47 (1997).
[CrossRef]

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).
[CrossRef] [PubMed]

Suh, W.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analogue of electromagnetically induced transparency,” Phys. Rev. Lett.93, 233903 (2004).
[CrossRef] [PubMed]

Sun, F.-W.

C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “High Q and unidirectional emission whispering gallery modes: principles and design,” IEEE J. Sel. Top. Quantum Electron., In press (2013).

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
[CrossRef]

F.-J. Shu, C.-L. Zou, and F.-W. Sun, “Perpendicular coupler for whispering-gallery resonators,” Opt. Lett.37, 3123–3125 (2012).
[CrossRef] [PubMed]

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Y.-Z. Yan, C.-L. Zou, S.-B. Yan, F.-W. Sun, Z. Ji, J. Liu, Y.-G. Zhang, L. Wang, C.-Y. Xue, and W.-D. Zhang, “Packaged silica microsphere-taper coupling system for robust thermal sensing application,” Opt. Express19, 5753–5759 (2011).
[CrossRef] [PubMed]

Takeuchi, S.

A. Chiba, H. Fujiwara, J.-I. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett.86, 261106 (2005).
[CrossRef]

Tian, L.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett.107, 133601 (2011).
[CrossRef] [PubMed]

Tomes, M.

Tomita, M.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett.98, 213904 (2007).
[CrossRef] [PubMed]

Tomsovic, S.

S. Tomsovic and D. Ullmo, “Chaos-assisted tunneling,” Phys. Rev. E50, 145–162 (1994).
[CrossRef]

Totsuka, K.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett.98, 213904 (2007).
[CrossRef] [PubMed]

Tureci, H. E.

Tzeng, H.-M.

S. X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets highlighting the liquid-air interface by laser emission,” Science231, 486–488 (1986)
[CrossRef] [PubMed]

Ullmo, D.

S. Tomsovic and D. Ullmo, “Chaos-assisted tunneling,” Phys. Rev. E50, 145–162 (1994).
[CrossRef]

Unterhinninghofen, J.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

Vaccaro, P. O.

T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, “Lasing on scar modes in fully chaotic microcavities,” Phys. Rev. E67, 015207 (2003).
[CrossRef]

Vahala, K. J.

M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express17, 19160–19165 (2009).
[CrossRef]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
[CrossRef] [PubMed]

Verhagen, E.

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature482, 63–67 (2012).
[CrossRef] [PubMed]

Vollmer, F.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nature Methods5, 591–596 (2008).
[CrossRef] [PubMed]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-VerlagBerlin Heidelberg, 2008 ).

Wang, H.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett.107, 133601 (2011).
[CrossRef] [PubMed]

Y. S. Park and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat. Phys.5, 489–493 (2009).
[CrossRef]

Y.-S. Park and H. Wang, “Radiation pressure driven mechanical oscillation in deformed silica microspheres via free-space evanescent excitation,” Opt. Express15, 16471–16477 (2007).
[CrossRef] [PubMed]

S. Lacey, H. Wang, D. H. Foster, and J. U. Nöckel, “Directional tunneling escape from nearly spherical optical resonators,” Phys. Rev. Lett.91, 033902(2003).
[CrossRef] [PubMed]

Wang, L.

Wang, Q. J.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

Wang, Z.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analogue of electromagnetically induced transparency,” Phys. Rev. Lett.93, 233903 (2004).
[CrossRef] [PubMed]

Weis, S.

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature482, 63–67 (2012).
[CrossRef] [PubMed]

Wiersig, J.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limacon-shaped semiconductor microcavities,” Phys. Rev. A80, 031801 (2009).
[CrossRef]

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett.100, 033901 (2008).
[CrossRef] [PubMed]

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A73, 031802 (2006).
[CrossRef]

Wilcut, E.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Wu, X.-W.

C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “High Q and unidirectional emission whispering gallery modes: principles and design,” IEEE J. Sel. Top. Quantum Electron., In press (2013).

C.-L. Zou, Y. Yang, C.-H. Dong, Y.-F. Xiao, X.-W. Wu, Z.-F. Han, and G.-C. Guo, “Taper-microsphere coupling with numerical calculation of coupled-mode theory,” J. Opt. Soc. Am. B25, 1895–1898 (2008)
[CrossRef]

Xiao, Y.-F.

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
[CrossRef]

Y.-F. Xiao, C.-H. Dong, C.-L. Zou, Z.-F. Han, L. Yang, and G.-C. Guo, “Low-threshold microlaser in a high-Q asymmetrical microcavity,” Opt. Lett.34, 509–511 (2009).
[CrossRef] [PubMed]

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B42, 215401 (2009).
[CrossRef]

C.-L. Zou, Y. Yang, C.-H. Dong, Y.-F. Xiao, X.-W. Wu, Z.-F. Han, and G.-C. Guo, “Taper-microsphere coupling with numerical calculation of coupled-mode theory,” J. Opt. Soc. Am. B25, 1895–1898 (2008)
[CrossRef]

Y.-F. Xiao, C.-H. Dong, Z.-F. Han, G.-C. Guo, and Y.-S. Park, “Directional escape from a high-Q deformed microsphere induced by short CO2 laser pulses,” Opt. Lett.32, 644–646 (2007).
[CrossRef] [PubMed]

Xue, C.-Y.

Yamanishi, M.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

Yamilov, A.

W. Fang, A. Yamilov, and H. Cao, “Analysis of high-quality modes in open chaotic microcavities,” Phys. Rev. A72, 023815 (2005).
[CrossRef]

Yan, C.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

Yan, S.-B.

Yan, Y.-Z.

Yang, J.

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, and K. An, “Observation of resonance effects in the pump transmission of a chaotic microcavity,” Opt. Express18, 26141–26148 (2010).
[CrossRef] [PubMed]

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
[CrossRef] [PubMed]

S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
[CrossRef]

S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
[CrossRef]

Yang, L.

L. He, S. K. Ozdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photon. Rev.7, 60–82 (2013).
[CrossRef]

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Y.-F. Xiao, C.-H. Dong, C.-L. Zou, Z.-F. Han, L. Yang, and G.-C. Guo, “Low-threshold microlaser in a high-Q asymmetrical microcavity,” Opt. Lett.34, 509–511 (2009).
[CrossRef] [PubMed]

Yang, Y.

C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “High Q and unidirectional emission whispering gallery modes: principles and design,” IEEE J. Sel. Top. Quantum Electron., In press (2013).

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett.107, 133601 (2011).
[CrossRef] [PubMed]

C.-H. Dong, C.-L. Zou, J.-M. Cui, Y. Yang, Z.-F. Han, and G.-C. Guo, “Ringing phenomenon in silica microspheres,” Chin. Opt. Lett.7, 299–301 (2009).
[CrossRef]

C.-L. Zou, Y. Yang, C.-H. Dong, Y.-F. Xiao, X.-W. Wu, Z.-F. Han, and G.-C. Guo, “Taper-microsphere coupling with numerical calculation of coupled-mode theory,” J. Opt. Soc. Am. B25, 1895–1898 (2008)
[CrossRef]

Yanik, M. F.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analogue of electromagnetically induced transparency,” Phys. Rev. Lett.93, 233903 (2004).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett.36, 321–322 (2000).
[CrossRef]

Yu, N.

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

Zhang, W.-D.

Zhang, Y.-G.

Zou, C.-L.

C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “High Q and unidirectional emission whispering gallery modes: principles and design,” IEEE J. Sel. Top. Quantum Electron., In press (2013).

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
[CrossRef]

F.-J. Shu, C.-L. Zou, and F.-W. Sun, “Perpendicular coupler for whispering-gallery resonators,” Opt. Lett.37, 3123–3125 (2012).
[CrossRef] [PubMed]

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Y.-Z. Yan, C.-L. Zou, S.-B. Yan, F.-W. Sun, Z. Ji, J. Liu, Y.-G. Zhang, L. Wang, C.-Y. Xue, and W.-D. Zhang, “Packaged silica microsphere-taper coupling system for robust thermal sensing application,” Opt. Express19, 5753–5759 (2011).
[CrossRef] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
[CrossRef]

Y.-F. Xiao, C.-H. Dong, C.-L. Zou, Z.-F. Han, L. Yang, and G.-C. Guo, “Low-threshold microlaser in a high-Q asymmetrical microcavity,” Opt. Lett.34, 509–511 (2009).
[CrossRef] [PubMed]

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B42, 215401 (2009).
[CrossRef]

C.-H. Dong, C.-L. Zou, J.-M. Cui, Y. Yang, Z.-F. Han, and G.-C. Guo, “Ringing phenomenon in silica microspheres,” Chin. Opt. Lett.7, 299–301 (2009).
[CrossRef]

C.-L. Zou, Y. Yang, C.-H. Dong, Y.-F. Xiao, X.-W. Wu, Z.-F. Han, and G.-C. Guo, “Taper-microsphere coupling with numerical calculation of coupled-mode theory,” J. Opt. Soc. Am. B25, 1895–1898 (2008)
[CrossRef]

Zyss, J.

Adv. Mater. (1)

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly Unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater.24, OP260–OP264 (2012).
[CrossRef] [PubMed]

Ann. Phys. (Leipzig) (1)

G. Mie, “Beiträge zur optik trüber Medien, speziell kolloidaler metallösungen,” Ann. Phys. (Leipzig)330, 377–445 (1908).
[CrossRef]

Appl. Phys. Lett. (7)

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98, 021116 (2011).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett.100, 021108 (2012).
[CrossRef]

A. Chiba, H. Fujiwara, J.-I. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett.86, 261106 (2005).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett.60, 289–291 (1992).
[CrossRef]

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, “Highly directional stadium-shaped polymer microlasers,” Appl. Phys. Lett.88, 031108 (2006).
[CrossRef]

C. Yan, Q. J. Wang, L. Diehl, M. Hentschel, J. Wiersig, N. Yu, C. Pflugl, F. Capasso, M. A. Belkin, T. Edamura, M. Yamanishi, and H. Kan, “Directional emission and universal far-field behavior from semiconductor lasers with limacon-shaped microcavity,” Appl. Phys. Lett.94, 251101 (2009).
[CrossRef]

J. Yang, S.-B. Lee, J.-B. Shim, S. Moon, S.-Y. Lee, S. W. Kim, J.-H. Lee, and K. An, “Enhanced nonresonant optical pumping based on turnstile transport in a chaotic microcavity laser,” Appl. Phys. Lett.93, 061101 (2008).
[CrossRef]

Chin. Opt. Lett. (1)

Electron. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett.36, 321–322 (2000).
[CrossRef]

IEEE J. Quant. Electron. (1)

D. Q. Chowdhury, S. C. Hill, and Md. Mohiuddin Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption.” IEEE J. Quant. Electron.29, 2553–2561 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C.-L. Zou, F.-W. Sun, C.-H. Dong, F.-J. Shu, X.-W. Wu, J.-M. Cui, Y. Yang, G.-C. Guo, and Z.-F. Han, “High Q and unidirectional emission whispering gallery modes: principles and design,” IEEE J. Sel. Top. Quantum Electron., In press (2013).

International Conference on Transparent Optical Networks (1)

S.-B. Lee, J. Yang, S.-Y. Lee, S. Moon, J.-B. Shim, S. W. Kim, J.-H. Lee, and K. An, “Evolution of emission mechanism in deformed microcavities,” International Conference on Transparent Optical Networks, Paper no. Tu.P.16 (2009).

J. Appl. Phys. (1)

R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys.10, 391–398 (1939).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

J. Phys. B (1)

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B42, 215401 (2009).
[CrossRef]

Laser Photon. Rev. (1)

L. He, S. K. Ozdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photon. Rev.7, 60–82 (2013).
[CrossRef]

Nat. Phys. (1)

Y. S. Park and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat. Phys.5, 489–493 (2009).
[CrossRef]

Nature (5)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature482, 63–67 (2012).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature385, 45–47 (1997).
[CrossRef]

Nature Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nature Methods5, 591–596 (2008).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun.113, 133–143 (1994).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Phil. Mag. (1)

Lord Rayleigh, “The problem of the whispering gallery,” Phil. Mag.20, 1001–1004 (1910).

Phys. Lett. A (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
[CrossRef]

Phys. Rev. A (7)

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A74, 063806 (2006).
[CrossRef]

S. Shinohara, T. Fukushima, and T. Harayama, “Light emission patterns from stadium-shaped semiconductor microcavity lasers,” Phys. Rev. A77, 033807 (2008).
[CrossRef]

S. B. Lee, J. Yang, S. Moon, J. H. Lee, K. An, J. B. Shim, H. W. Lee, and S. W. Kim, “Universal output directionality of single modes in a deformed microcavity,” Phys. Rev. A75, 011802 (2007).
[CrossRef]

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A73, 031802 (2006).
[CrossRef]

W. Fang, A. Yamilov, and H. Cao, “Analysis of high-quality modes in open chaotic microcavities,” Phys. Rev. A72, 023815 (2005).
[CrossRef]

Q. Song, W. Fang, B. Liu, S.-T. Ho, G. S. Solomon, and H. Cao, “Chaotic microcavity laser with high quality factor and unidirectional output,” Phys. Rev. A80, 041807 (2009).
[CrossRef]

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, “Ray-wave correspondence in limacon-shaped semiconductor microcavities,” Phys. Rev. A80, 031801 (2009).
[CrossRef]

Phys. Rev. E (2)

S. Tomsovic and D. Ullmo, “Chaos-assisted tunneling,” Phys. Rev. E50, 145–162 (1994).
[CrossRef]

T. Harayama, T. Fukushima, P. Davis, P. O. Vaccaro, T. Miyasaka, T. Nishimura, and T. Aida, “Lasing on scar modes in fully chaotic microcavities,” Phys. Rev. E67, 015207 (2003).
[CrossRef]

Phys. Rev. Lett. (11)

J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett.100, 033901 (2008).
[CrossRef] [PubMed]

H. J. Moon, Y. T. Chough, and K. An, “Cylindrical microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett.85, 3161–3164 (2000).
[CrossRef] [PubMed]

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, 033903 (2002).
[CrossRef] [PubMed]

S. Lacey, H. Wang, D. H. Foster, and J. U. Nöckel, “Directional tunneling escape from nearly spherical optical resonators,” Phys. Rev. Lett.91, 033902(2003).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett.107, 133601 (2011).
[CrossRef] [PubMed]

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
[CrossRef] [PubMed]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analogue of electromagnetically induced transparency,” Phys. Rev. Lett.93, 233903 (2004).
[CrossRef] [PubMed]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett.98, 213904 (2007).
[CrossRef] [PubMed]

S. C. Creagh, “Directional emission from weakly eccentric resonators,” Phys. Rev. Lett.98, 153901 (2007).
[CrossRef] [PubMed]

J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, T. T. A. Dao, J.-H. Lee, and K. An, “Pump-induced dynamical tunneling in a deformed microcavity laser,” Phys. Rev. Lett.104, 243601 (2010).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Whispering-gallery mode resonators for highly unidirectional laser action,” Proc. Natl. Acad. Sci. USA107, 22407–22412 (2010).
[CrossRef] [PubMed]

Sci. Am. (1)

H. Moyses Nussenzveig, “The Science of the Glory,” Sci. Am.306(1), 68–73 (2012)
[CrossRef] [PubMed]

Science (3)

S. X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets highlighting the liquid-air interface by laser emission,” Science231, 486–488 (1986)
[CrossRef] [PubMed]

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,” Science280, 1556–1564 (1998).
[CrossRef] [PubMed]

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Observation of chaos-assisted tunneling between islands of stability,” Science293, 274–278 (2001).
[CrossRef] [PubMed]

Other (1)

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-VerlagBerlin Heidelberg, 2008 ).

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Figures (4)

Fig. 1
Fig. 1

(a) Electric field distribution for a cylinder cavity critical coupling with m = 30 cylinder wave, and detuning δ = 0. (b) The normalized reflectivity and the total Q factor against the angular number m, with the refractive index n = 1.45+0.000117i. (c) and (d) are the intensity and phase of outgoing field for different coupling conditions, with κ1/κ0 = 0.2 (Red Dotted lines), 1.0 (Blue Dashed lines) and 5.0 (Black Solid lines).

Fig. 2
Fig. 2

(a) Schematic illustration of a Gaussian beam incident to a circular microcavity. The direction of beam is defined by θ0, and the location of center is (r0, ϕ0) in the cylindrical coordinate. (b) The electric field intensity distribution when the incident Gaussian beam is resonant with the WGM, with krc = 30.10, r0 = 1.1rc, ϕ0 = π/2 and θ0 = 0.

Fig. 3
Fig. 3

(a) Field distribution of directional emission of anti-clockwise WGM in a near circular cavity (The field is shown in Logarithm scale, and the intracavity field is not shown since the exact boundary shape is not known in our abstract model). The emission is in the form of Gaussian beam with dt = 1.2rc, wt = 0.1rc and direction is shown by arrows. (b) Field distribution when an on-resonance Gaussian beam coupling to the cavity in the over coupling regime with κ1 = 0.1κ0, d = 1.2, w = 0.2rc and direction is shown by arrows. (c) Beam matching parameters against the d for different w. (d) The far field intensity of outgoing wave when a Gaussian beam incident to a cylinder, for excitation frequency off-resonance and on-resonance at difference coupling conditions. (e), (f) and (g) are spectra detected at different angle (ϕ) in far field.

Fig. 4
Fig. 4

(a) Field distribution of directional emission of anti-clockwise WGM in a near circular cavity (The field is shown in normal scale, and the intracavity field is not shown since the exact boundary shape is not known in our abstract model). The emission is in the form of Gaussian beam with dr = 0.9rc, wr = 0.1rc and direction is shown by arrows. (b) The field distribution when an on-resonance Gaussian beam coupling to the cavity in the over coupling regime with κ1 = 0.1κ0, d = 0.9, w = 0.2rc and direction is shown by arrows. (c) The far field intensity of outgoing wave when a Gaussian beam is incident to the ARC with Gaussian beam emission, for off-resonance and on-resonance under different coupling conditions.

Equations (34)

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a m = H m ( 1 ) ( z ) H m ( 2 ) ( z ) H m ( 1 ) ( z ) H m ( 2 ) z n p J m ( n z ) H m ( 1 ) ( z ) J m ( n z ) H m ( 1 ) ( z ) c m ,
b m = n p J m ( n z ) H m ( 2 ) ( z ) J m ( n z ) H m ( 2 ) ( z ) n p J m ( n z ) H m ( 1 ) ( z ) J m ( n z ) H m ( 1 ) ( z ) c m ,
n p J m ( n z 0 ) H m ( 1 ) ( z 0 ) J m ( n z 0 ) H m ( 1 ) ( z 0 ) = 0 .
n p J m ( n z ) H m ( 1 ) ( k z ) J m ( n z ) H m ( 1 ) ( z ) F ( z 0 ) Δ ,
a m ( δ ) = 1 i δ + κ 0 + κ 1 4 π z 0 r F ( z 0 r ) c m ,
b m ( δ ) = i δ κ 0 + κ 1 i δ + κ 0 + κ 1 F * ( z 0 r ) F ( z 0 r ) c m .
d d t E m = ( i δ κ 0 κ 1 ) E m + 2 κ 0 E m in ,
E m = 2 κ 0 i δ + κ 0 + κ 1 E m in ,
E m out = i δ κ 0 + κ 1 i δ + κ 0 + κ 1 E m in .
E m = 2 κ ext i δ + κ int + κ ext E m in ,
G ( x 0 , y ) = e ( y y 0 ) 2 w 2
G ˜ ( θ ) = 1 2 π e i y k sin θ e y 2 w 2 d y = w 2 π e k 2 w 2 4 sin 2 θ ,
E ( r , ϕ ) = k k w 2 π e k 2 w 2 4 sin 2 θ e i k ( sin θ y + cos θ x ) d ( k sin θ ) ,
x = r cos ( ϕ + θ 0 ) r 0 cos ( ϕ 0 + θ 0 ) ,
y = r sin ( ϕ + θ 0 ) r 0 sin ( ϕ 0 + θ 0 ) .
e i k r cos ( ϕ + θ 0 θ ) = m = J m ( k r ) e i m [ π / 2 ( ϕ + θ 0 θ ) ] ,
c m = e i m ( π / 2 θ 0 ) i k q ( k r 0 d m ) 2 k 2 w 2 + i 2 k q 2 1 + i 2 q k w 2 ,
P G = π 2 k w 2 ω μ ,
P m = 2 ω μ .
η m = | c m | 2 P m P G .
η max = 2 π 1 k w .
= modes + int + pump .
modes = j h ¯ δ j ( A j , c A j , c + A j , a A j , a )
int = j k > j ( g j , k , c A j , c A k , c + g j , k , a A j , a A k , a + h . c . ) + j , k ( β j , k A j , c A k , a + h . c . ) ,
pump = j , k ( i h j , m , c A j , c u m in + i h j , m , a A j , a u m in + h . c . ) .
d d t A j , c = i k > j g j , k A k , c i k < j g k , j * A k , c χ j A j , c + m h j , m u m in ,
A j , c | j 2 = i g 1 , j * χ j A 1 , c + m = 1 h j , m χ j u m in .
d d t A 1 , c = χ ˜ 1 A 1 , c + m = 1 h ˜ 1 , m u m in .
< A 1 , c > = ξ | h | | u | / χ ˜ 1 ,
u m out = u m in + f m < A 1 , c > + j 2 m h j , m * h j , m χ j u m in ,
u h * / | h | .
h 1 , m = 𝔥 0 e i m π / 2 ( k d t m ) 2 k 2 w t 2 + i φ m ,
j 2 g 1 , j χ j h j , m e i φ m = 𝔥 e e i m π / 2 ( k d t m ) 2 k 2 w t 2 .
g 1 , m χ m h m , m = 𝔥 e e i m π / 2 ( k d t m ) 2 k 2 w t 2 + i φ m .

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