Abstract

We investigate the impact of local dynamics on chaos-assisted tunneling in a highly deformed microcavity whose classical ray dynamics exhibits a small measure of trapezoidal-shaped orbit (TSO) stability islands in a main chaotic sea. These two classically completely decomposed regions in phase space can support resonance modes of their own respectively. Using numerical ray and wave analyses, we show that the emission characteristics of the TSO resonance mode are determined by local ray dynamics near TSO islands. The emission characteristics of the other high-Q resonance modes, on the other hand, are governed by usual ray-wave correspondence. We experimentally demonstrate that the TSO emission mode can be lased without selective excitations by devising a half-moon shaped highly deformed cavity. And we also show that the emission characteristics of the TSO lasing modes are well explained by numerical ray and wave analyses.

© 2013 Optical Society of America

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  1. K. Vahala, Optical Microcavities (World Scientific: New York, 1999).
  2. R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific: New York, 1996).
  3. M. J. Davis and E. J. Heller, “Quantum dynamical tunneling in bound states,” J. Chem. Phys.75, 246–254 (1981).
    [CrossRef]
  4. O. Bohigas, S. Tomsovic, and D. Ullmo, “Manifestations of classical phase space structures in quantum mechanics,” Phys. Rep.223, 1–91 (1993).
  5. C. Dembowski, H.-D. Gräf, A. Heine, R. Hofferbert, H. Rehfeld, and A. Ritcher, “First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard” Phys. Rev. Lett.84, 867–870 (2000).
    [CrossRef] [PubMed]
  6. A. Bäcker, R. Ketzmerick, S. Löck, G. Vidmar, R. Höhmann, U. Kuhl, and H. J. Stöckmann, “Dynamical Tunneling in Mushroom Billiards,” Phys. Rev. Lett.100, 174103 (2008).
    [CrossRef] [PubMed]
  7. D. A. Stech, W. H. Oskay, and M. G. Raizen, “Observation of Chaos-Assisted Tunneling Between Islands of Stability,” Science293, 274–278 (2001).
    [CrossRef]
  8. W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
    [CrossRef] [PubMed]
  9. J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature385, 45–47 (1997).
    [CrossRef]
  10. V. A. Podolskiy and E. E. Narimanov, “Chaos-assisted tunneling in dielectric microcavities,” Opt. Lett.30, 474–476 (2005)
    [CrossRef] [PubMed]
  11. E. E. Narimanov and V. A. Podolskiy, “Chaos-assisted tunneling and dynamical localization in dielectric microdisk resonators,” IEEE J. Sel. Top. Quantum Electron.12, 40–51 (2006).
    [CrossRef]
  12. S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-Assisted Directional Light Emission from Microcavity Lasers,” Phys. Rev. Lett.104, 163902(2010).
    [CrossRef] [PubMed]
  13. S. Shinohara, T. Harayama, T. Fukushima, S. Sunada, and E. E. Narimanov, “Chaos-assisted emission from asymmetric resonant cavity microlasers,” Phys. Rev. A83, 053837 (2011).
    [CrossRef]
  14. A. D. Stone, “Nonlinear dynamics: Chaotic billiard lasers,” Nature465, 696–697 (2010)
    [CrossRef] [PubMed]
  15. M.-W. Kim, K.-W. Park, C.-H. Yi, and C.-M. Kim, “Directional and low-divergence emission in a rounded half-moon shaped microcavity,” Appl. Phys. Lett.98, 241110 (2011).
    [CrossRef]
  16. J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A5, 53–60 (2003).
    [CrossRef]
  17. S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Ray and wave dynamical properties of a spiral-shaped dielectric microcavity,” J. Phys. A: Math. Theor.41, 275102 (2008).
    [CrossRef]
  18. J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, “Survival probability time distribution in dielectric cavities,” Phys. Rev. E73, 036207 (2006).
    [CrossRef]
  19. J. Wiersig and M. Hentschel, “Combining Directional Light Output and Ultralow Loss in Deformed Microdisks,” Phys. Rev. Lett.100, 033901 (2008).
    [CrossRef] [PubMed]
  20. S. Shinohara and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
    [CrossRef]
  21. C.-H. Yi, S.-H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A84, 041803 (2011).
    [CrossRef]

2011 (3)

S. Shinohara, T. Harayama, T. Fukushima, S. Sunada, and E. E. Narimanov, “Chaos-assisted emission from asymmetric resonant cavity microlasers,” Phys. Rev. A83, 053837 (2011).
[CrossRef]

M.-W. Kim, K.-W. Park, C.-H. Yi, and C.-M. Kim, “Directional and low-divergence emission in a rounded half-moon shaped microcavity,” Appl. Phys. Lett.98, 241110 (2011).
[CrossRef]

C.-H. Yi, S.-H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A84, 041803 (2011).
[CrossRef]

2010 (2)

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-Assisted Directional Light Emission from Microcavity Lasers,” Phys. Rev. Lett.104, 163902(2010).
[CrossRef] [PubMed]

A. D. Stone, “Nonlinear dynamics: Chaotic billiard lasers,” Nature465, 696–697 (2010)
[CrossRef] [PubMed]

2008 (3)

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Ray and wave dynamical properties of a spiral-shaped dielectric microcavity,” J. Phys. A: Math. Theor.41, 275102 (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]

A. Bäcker, R. Ketzmerick, S. Löck, G. Vidmar, R. Höhmann, U. Kuhl, and H. J. Stöckmann, “Dynamical Tunneling in Mushroom Billiards,” Phys. Rev. Lett.100, 174103 (2008).
[CrossRef] [PubMed]

2007 (1)

S. Shinohara and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
[CrossRef]

2006 (2)

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, “Survival probability time distribution in dielectric cavities,” Phys. Rev. E73, 036207 (2006).
[CrossRef]

E. E. Narimanov and V. A. Podolskiy, “Chaos-assisted tunneling and dynamical localization in dielectric microdisk resonators,” IEEE J. Sel. Top. Quantum Electron.12, 40–51 (2006).
[CrossRef]

2005 (1)

2003 (1)

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A5, 53–60 (2003).
[CrossRef]

2001 (2)

D. A. Stech, W. H. Oskay, and M. G. Raizen, “Observation of Chaos-Assisted Tunneling Between Islands of Stability,” Science293, 274–278 (2001).
[CrossRef]

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
[CrossRef] [PubMed]

2000 (1)

C. Dembowski, H.-D. Gräf, A. Heine, R. Hofferbert, H. Rehfeld, and A. Ritcher, “First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard” Phys. Rev. Lett.84, 867–870 (2000).
[CrossRef] [PubMed]

1997 (1)

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

1993 (1)

O. Bohigas, S. Tomsovic, and D. Ullmo, “Manifestations of classical phase space structures in quantum mechanics,” Phys. Rep.223, 1–91 (1993).

1981 (1)

M. J. Davis and E. J. Heller, “Quantum dynamical tunneling in bound states,” J. Chem. Phys.75, 246–254 (1981).
[CrossRef]

Bäcker, A.

A. Bäcker, R. Ketzmerick, S. Löck, G. Vidmar, R. Höhmann, U. Kuhl, and H. J. Stöckmann, “Dynamical Tunneling in Mushroom Billiards,” Phys. Rev. Lett.100, 174103 (2008).
[CrossRef] [PubMed]

Bohigas, O.

O. Bohigas, S. Tomsovic, and D. Ullmo, “Manifestations of classical phase space structures in quantum mechanics,” Phys. Rep.223, 1–91 (1993).

Browaeys, A.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
[CrossRef] [PubMed]

Campillo, A. J.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific: New York, 1996).

Chang, R. K.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific: New York, 1996).

Cho, J.

C.-H. Yi, S.-H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A84, 041803 (2011).
[CrossRef]

Choi, M.

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Ray and wave dynamical properties of a spiral-shaped dielectric microcavity,” J. Phys. A: Math. Theor.41, 275102 (2008).
[CrossRef]

Davis, M. J.

M. J. Davis and E. J. Heller, “Quantum dynamical tunneling in bound states,” J. Chem. Phys.75, 246–254 (1981).
[CrossRef]

Dembowski, C.

C. Dembowski, H.-D. Gräf, A. Heine, R. Hofferbert, H. Rehfeld, and A. Ritcher, “First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard” Phys. Rev. Lett.84, 867–870 (2000).
[CrossRef] [PubMed]

Dunlop, H. R.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
[CrossRef] [PubMed]

Fukushima, T.

S. Shinohara, T. Harayama, T. Fukushima, S. Sunada, and E. E. Narimanov, “Chaos-assisted emission from asymmetric resonant cavity microlasers,” Phys. Rev. A83, 053837 (2011).
[CrossRef]

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-Assisted Directional Light Emission from Microcavity Lasers,” Phys. Rev. Lett.104, 163902(2010).
[CrossRef] [PubMed]

Gräf, H.-D.

C. Dembowski, H.-D. Gräf, A. Heine, R. Hofferbert, H. Rehfeld, and A. Ritcher, “First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard” Phys. Rev. Lett.84, 867–870 (2000).
[CrossRef] [PubMed]

Häffner, H.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
[CrossRef] [PubMed]

Harayama, T.

S. Shinohara, T. Harayama, T. Fukushima, S. Sunada, and E. E. Narimanov, “Chaos-assisted emission from asymmetric resonant cavity microlasers,” Phys. Rev. A83, 053837 (2011).
[CrossRef]

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-Assisted Directional Light Emission from Microcavity Lasers,” Phys. Rev. Lett.104, 163902(2010).
[CrossRef] [PubMed]

S. Shinohara and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
[CrossRef]

Heckenberg, N. R.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
[CrossRef] [PubMed]

Heine, A.

C. Dembowski, H.-D. Gräf, A. Heine, R. Hofferbert, H. Rehfeld, and A. Ritcher, “First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard” Phys. Rev. Lett.84, 867–870 (2000).
[CrossRef] [PubMed]

Heller, E. J.

M. J. Davis and E. J. Heller, “Quantum dynamical tunneling in bound states,” J. Chem. Phys.75, 246–254 (1981).
[CrossRef]

Hensinger, W. K.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
[CrossRef] [PubMed]

Hentschel, M.

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-Assisted Directional Light Emission from Microcavity Lasers,” Phys. Rev. Lett.104, 163902(2010).
[CrossRef] [PubMed]

J. Wiersig and M. Hentschel, “Combining Directional Light Output and Ultralow Loss in Deformed Microdisks,” Phys. Rev. Lett.100, 033901 (2008).
[CrossRef] [PubMed]

Hofferbert, R.

C. Dembowski, H.-D. Gräf, A. Heine, R. Hofferbert, H. Rehfeld, and A. Ritcher, “First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard” Phys. Rev. Lett.84, 867–870 (2000).
[CrossRef] [PubMed]

Höhmann, R.

A. Bäcker, R. Ketzmerick, S. Löck, G. Vidmar, R. Höhmann, U. Kuhl, and H. J. Stöckmann, “Dynamical Tunneling in Mushroom Billiards,” Phys. Rev. Lett.100, 174103 (2008).
[CrossRef] [PubMed]

Ketzmerick, R.

A. Bäcker, R. Ketzmerick, S. Löck, G. Vidmar, R. Höhmann, U. Kuhl, and H. J. Stöckmann, “Dynamical Tunneling in Mushroom Billiards,” Phys. Rev. Lett.100, 174103 (2008).
[CrossRef] [PubMed]

Kim, C.-M.

C.-H. Yi, S.-H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A84, 041803 (2011).
[CrossRef]

M.-W. Kim, K.-W. Park, C.-H. Yi, and C.-M. Kim, “Directional and low-divergence emission in a rounded half-moon shaped microcavity,” Appl. Phys. Lett.98, 241110 (2011).
[CrossRef]

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Ray and wave dynamical properties of a spiral-shaped dielectric microcavity,” J. Phys. A: Math. Theor.41, 275102 (2008).
[CrossRef]

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, “Survival probability time distribution in dielectric cavities,” Phys. Rev. E73, 036207 (2006).
[CrossRef]

Kim, M.-W.

C.-H. Yi, S.-H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A84, 041803 (2011).
[CrossRef]

M.-W. Kim, K.-W. Park, C.-H. Yi, and C.-M. Kim, “Directional and low-divergence emission in a rounded half-moon shaped microcavity,” Appl. Phys. Lett.98, 241110 (2011).
[CrossRef]

Kuhl, U.

A. Bäcker, R. Ketzmerick, S. Löck, G. Vidmar, R. Höhmann, U. Kuhl, and H. J. Stöckmann, “Dynamical Tunneling in Mushroom Billiards,” Phys. Rev. Lett.100, 174103 (2008).
[CrossRef] [PubMed]

Kwon, T.-Y.

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Ray and wave dynamical properties of a spiral-shaped dielectric microcavity,” J. Phys. A: Math. Theor.41, 275102 (2008).
[CrossRef]

Lee, J.

C.-H. Yi, S.-H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A84, 041803 (2011).
[CrossRef]

Lee, S.-H.

C.-H. Yi, S.-H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A84, 041803 (2011).
[CrossRef]

Lee, S.-Y.

C.-H. Yi, S.-H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A84, 041803 (2011).
[CrossRef]

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Ray and wave dynamical properties of a spiral-shaped dielectric microcavity,” J. Phys. A: Math. Theor.41, 275102 (2008).
[CrossRef]

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, “Survival probability time distribution in dielectric cavities,” Phys. Rev. E73, 036207 (2006).
[CrossRef]

Löck, S.

A. Bäcker, R. Ketzmerick, S. Löck, G. Vidmar, R. Höhmann, U. Kuhl, and H. J. Stöckmann, “Dynamical Tunneling in Mushroom Billiards,” Phys. Rev. Lett.100, 174103 (2008).
[CrossRef] [PubMed]

Mckenzie, C.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
[CrossRef] [PubMed]

Milburn, G. J.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
[CrossRef] [PubMed]

Narimanov, E. E.

S. Shinohara, T. Harayama, T. Fukushima, S. Sunada, and E. E. Narimanov, “Chaos-assisted emission from asymmetric resonant cavity microlasers,” Phys. Rev. A83, 053837 (2011).
[CrossRef]

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-Assisted Directional Light Emission from Microcavity Lasers,” Phys. Rev. Lett.104, 163902(2010).
[CrossRef] [PubMed]

E. E. Narimanov and V. A. Podolskiy, “Chaos-assisted tunneling and dynamical localization in dielectric microdisk resonators,” IEEE J. Sel. Top. Quantum Electron.12, 40–51 (2006).
[CrossRef]

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

Nöckel, J. U.

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

Oskay, W. H.

D. A. Stech, W. H. Oskay, and M. G. Raizen, “Observation of Chaos-Assisted Tunneling Between Islands of Stability,” Science293, 274–278 (2001).
[CrossRef]

Park, K.-W.

M.-W. Kim, K.-W. Park, C.-H. Yi, and C.-M. Kim, “Directional and low-divergence emission in a rounded half-moon shaped microcavity,” Appl. Phys. Lett.98, 241110 (2011).
[CrossRef]

Park, Y.-J.

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, “Survival probability time distribution in dielectric cavities,” Phys. Rev. E73, 036207 (2006).
[CrossRef]

Philips, W. D.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
[CrossRef] [PubMed]

Podolskiy, V. A.

E. E. Narimanov and V. A. Podolskiy, “Chaos-assisted tunneling and dynamical localization in dielectric microdisk resonators,” IEEE J. Sel. Top. Quantum Electron.12, 40–51 (2006).
[CrossRef]

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

Raizen, M. G.

D. A. Stech, W. H. Oskay, and M. G. Raizen, “Observation of Chaos-Assisted Tunneling Between Islands of Stability,” Science293, 274–278 (2001).
[CrossRef]

Rehfeld, H.

C. Dembowski, H.-D. Gräf, A. Heine, R. Hofferbert, H. Rehfeld, and A. Ritcher, “First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard” Phys. Rev. Lett.84, 867–870 (2000).
[CrossRef] [PubMed]

Rim, S.

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Ray and wave dynamical properties of a spiral-shaped dielectric microcavity,” J. Phys. A: Math. Theor.41, 275102 (2008).
[CrossRef]

Ritcher, A.

C. Dembowski, H.-D. Gräf, A. Heine, R. Hofferbert, H. Rehfeld, and A. Ritcher, “First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard” Phys. Rev. Lett.84, 867–870 (2000).
[CrossRef] [PubMed]

Rolston, S. L.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, C. Mckenzie, G. J. Milburn, W. D. Philips, S. L. Rolston, H. R. Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature412, 52–55 (2001).
[CrossRef] [PubMed]

Ryu, J.-W.

S.-Y. Lee, S. Rim, J.-W. Ryu, T.-Y. Kwon, M. Choi, and C.-M. Kim, “Ray and wave dynamical properties of a spiral-shaped dielectric microcavity,” J. Phys. A: Math. Theor.41, 275102 (2008).
[CrossRef]

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, “Survival probability time distribution in dielectric cavities,” Phys. Rev. E73, 036207 (2006).
[CrossRef]

Sasaki, T.

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-Assisted Directional Light Emission from Microcavity Lasers,” Phys. Rev. Lett.104, 163902(2010).
[CrossRef] [PubMed]

Shinohara, S.

S. Shinohara, T. Harayama, T. Fukushima, S. Sunada, and E. E. Narimanov, “Chaos-assisted emission from asymmetric resonant cavity microlasers,” Phys. Rev. A83, 053837 (2011).
[CrossRef]

S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-Assisted Directional Light Emission from Microcavity Lasers,” Phys. Rev. Lett.104, 163902(2010).
[CrossRef] [PubMed]

S. Shinohara and T. Harayama, “Signature of ray chaos in quasibound wave functions for a stadium-shaped dielectric cavity,” Phys. Rev. E75, 036216 (2007).
[CrossRef]

Stech, D. A.

D. A. Stech, W. H. Oskay, and M. G. Raizen, “Observation of Chaos-Assisted Tunneling Between Islands of Stability,” Science293, 274–278 (2001).
[CrossRef]

Stöckmann, H. J.

A. Bäcker, R. Ketzmerick, S. Löck, G. Vidmar, R. Höhmann, U. Kuhl, and H. J. Stöckmann, “Dynamical Tunneling in Mushroom Billiards,” Phys. Rev. Lett.100, 174103 (2008).
[CrossRef] [PubMed]

Stone, A. D.

A. D. Stone, “Nonlinear dynamics: Chaotic billiard lasers,” Nature465, 696–697 (2010)
[CrossRef] [PubMed]

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

Sunada, S.

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Appl. Phys. Lett. (1)

M.-W. Kim, K.-W. Park, C.-H. Yi, and C.-M. Kim, “Directional and low-divergence emission in a rounded half-moon shaped microcavity,” Appl. Phys. Lett.98, 241110 (2011).
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IEEE J. Sel. Top. Quantum Electron. (1)

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Phys. Rev. A (2)

S. Shinohara, T. Harayama, T. Fukushima, S. Sunada, and E. E. Narimanov, “Chaos-assisted emission from asymmetric resonant cavity microlasers,” Phys. Rev. A83, 053837 (2011).
[CrossRef]

C.-H. Yi, S.-H. Lee, M.-W. Kim, J. Cho, J. Lee, S.-Y. Lee, J. Wiersig, and C.-M. Kim, “Light emission of a scarlike mode with assistance of quasiperiodicity,” Phys. Rev. A84, 041803 (2011).
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Phys. Rev. Lett. (4)

J. Wiersig and M. Hentschel, “Combining Directional Light Output and Ultralow Loss in Deformed Microdisks,” Phys. Rev. Lett.100, 033901 (2008).
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S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-Assisted Directional Light Emission from Microcavity Lasers,” Phys. Rev. Lett.104, 163902(2010).
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Figures (4)

Fig. 1
Fig. 1

(a) Ray dynamics of a half-moon shaped billiard in BSOS (s, p). The dashed line indicates the critical line for TIR given by pc (sinχc) = ±1/n. There are two island chains in mainly chaotic sea and the centers of islands for each chain correspond to the TSO (solid line) and V-shaped orbit (dotted line), respectively, as shown on the right. Here, we show only the upper half of the BSOS due to the symmetry. (b) Geometry of a half-moon shaped cavity. The cavity boundary is composed of three circular arcs and one linear section as shown in gray. (c) The logarithmic intensity pattern of the typical TSO resonance mode supported by the corresponding classical TSO islands chain.

Fig. 2
Fig. 2

(a) SPD and the main escape regions below the critical line are labeled as A and B, respectively. The husimi functions obtained by averaging over 40 high-Q resonances and 2 TSO resonances are shown in (b) and (d), respectively. The eight solid curves in (b) correspond to the outer boundary of localized spots in (d). (c) FFPs of the ray (dotted line) and wave (solid line) calculations. The angle of the FFP is defined in the inset. The FFP is calculated at 12R to compare with experimental results. In each panel, the solid line indicates the critical line for TIR.

Fig. 3
Fig. 3

Ray trajectories starting from the initial ensemble of the beach area marked by 1 are superimposed onto the logarithmic husimi function (Fig. 2(d)). Then the ensemble of rays marked 2, 3, and 4 are propagated along the TSO islands during 3 iterations. After that the trajectories marked 5, 6, and 7 follows the chaotic ray dynamics and finally cross the critical line at 6 iterations. Here, we consider the only clockwise directionally propagating ensemble of rays due to the symmetry. The dotted line indicate the critical line for TIR. Inset shows the FFPs obtained by local ray dynamics (dashed line) and TSO resonance (solid line), respectively.

Fig. 4
Fig. 4

(a) Optical spectrum. The average mode spacing of 2.8 nm and 2.7 nm correspond to the TSO and WG-type mode, respectively. (b) FFPs of the lasing mode in experiment (dotted line) and that of the TSO resonance (solid line). Inset shows the photograph of the fabricated half-moon shaped microcavity laser. The experimental results of (a) and (b) are obtained at 70 mA injection current for 0.9 μsec pulse width. Because of the symmetry, the emission direction from 0° to 180° is shown. (c) Outside intensity pattern of the numerically obtained TSO resonance shows the emission directions more clearly.

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