Abstract

For a fully chaotic two-dimensional (2D) microcavity laser, we present a theory that guarantees both the existence of a stable single-mode lasing state and the nonexistence of a stable multimode lasing state, under the assumptions that the cavity size is much larger than the wavelength and the external pumping power is sufficiently large. It is theoretically shown that these universal spectral characteristics arise from the synergistic effect of two different kinds of nonlinearities: deformation of the cavity shape and mode interaction due to a lasing medium. Our theory is based on the linear stability analysis of stationary states for the Maxwell–Bloch equations and accounts for single-mode lasing phenomena observed in real and numerical experiments of fully chaotic 2D microcavity lasers.

© 2017 Chinese Laser Press

Full Article  |  PDF Article
OSA Recommended Articles
Dependence of far-field characteristics on the number of lasing modes in stadium-shaped InGaAsP microlasers

Muhan Choi, Susumu Shinohara, and Takahisa Harayama
Opt. Express 16(22) 17554-17559 (2008)

Homoclinic orbits and chaos in the vibronic short-cavity standing-wave alexandrite laser

W. Gadomski and B. Ratajska-Gadomska
J. Opt. Soc. Am. B 17(2) 188-197 (2000)

Homoclinic orbits and chaos in a multimode laser

D. Y. Tang and N. R. Heckenberg
J. Opt. Soc. Am. B 14(11) 2930-2935 (1997)

References

  • View by:
  • |
  • |
  • |

  1. H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University, 1999).
  2. F. Haake, Quantum Signatures of Chaos (Springer, 2000).
  3. K. Nakamura and T. Harayama, Quantum Chaos and Quantum Dots (Oxford University, 2004).
  4. O. Bohigas, M. J. Giannoni, and C. Schmit, “Characterization of chaotic quantum spectra and universality of level fluctuation laws,” Phys. Rev. Lett. 52, 1–4 (1984).
    [Crossref]
  5. G. Casati, F. Valz-Gris, and I. Guarneri, “On the connection between quantization of nonintegrable systems and statistical theory of spectra,” Lett. Nuovo Cimento Soc. Ital. Fis. 28, 279–282 (1980).
    [Crossref]
  6. M. V. Berry, “Quantizing a classically ergodic system: Sinai’s billiard and the KKR method,” Ann. Phys. (N.Y.) 131, 163–216 (1981).
    [Crossref]
  7. M. V. Berry, “Semiclassical theory of spectral rigidity,” Proc. R. Soc. London Ser. A 400, 229–251 (1985).
    [Crossref]
  8. M. Sieber, “Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems,” J. Phys. A 35, L613–L619 (2002).
    [Crossref]
  9. S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, “Periodic-orbit theory of universality in quantum chaos,” Phys. Rev. Lett. 93, 014103 (2004).
    [Crossref]
  10. S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, “Periodic-orbit theory of level correlations,” Phys. Rev. Lett. 98, 044103 (2007).
    [Crossref]
  11. M. Sieber and K. Richter, “Correlations between periodic orbits and their role in spectral statistics,” Phys. Scr. T90, 128–133 (2001).
    [Crossref]
  12. R. A. Jalabert, H. U. Baranger, and A. D. Stone, “Conductance fluctuations in the ballistic regime: a probe of quantum chaos?” Phys. Rev. Lett. 65, 2442–2445 (1990).
    [Crossref]
  13. C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, “Conductance fluctuations and chaotic scattering in ballistic microstructures,” Phys. Rev. Lett. 69, 506–509 (1992).
    [Crossref]
  14. J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
    [Crossref]
  15. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
    [Crossref]
  16. 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]
  17. S.-Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
    [Crossref]
  18. 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. B 21, 923–934 (2004).
    [Crossref]
  19. V. A. Podolskiy, E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proc. Natl. Acad. Sci. USA 101, 10498–10500 (2004).
    [Crossref]
  20. J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
    [Crossref]
  21. J. Wiersig and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100, 033901 (2008).
    [Crossref]
  22. E. Bogomolny, R. Dubertrand, and C. Schmit, “Trace formula for dieletric cavities: I. General properties,” Phys. Rev. E 78, 056202 (2008).
    [Crossref]
  23. 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]
  24. Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108, 243902 (2012).
    [Crossref]
  25. R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
    [Crossref]
  26. H. Cao and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
    [Crossref]
  27. T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (2011).
    [Crossref]
  28. S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
    [Crossref]
  29. S. Sunada, S. Shinohara, T. Fukushima, and T. Harayama, “Signature of wave chaos in spectral characteristics of microcavity lasers,” Phys. Rev. Lett. 116, 203903 (2016).
    [Crossref]
  30. M. Fisher, “The renormalization group in the theory of critical behavior,” Rev. Mod. Phys. 46, 597–616 (1974).
    [Crossref]
  31. T. Harayama, P. Davis, and K. S. Ikeda, “Stable oscillations of a spatially chaotic wave function in a microstadium laser,” Phys. Rev. Lett. 90, 063901 (2003).
    [Crossref]
  32. T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
    [Crossref]
  33. H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
    [Crossref]
  34. H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
    [Crossref]
  35. W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, A1429–A1450 (1964).
    [Crossref]
  36. M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1974).
  37. M. Sargent, “Theory of a multimode quasiequilibrium semiconductor laser,” Phys. Rev. A 48, 717–726 (1993).
    [Crossref]
  38. T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
    [Crossref]
  39. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
    [Crossref]
  40. L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895–16902 (2008).
    [Crossref]
  41. H. E. Türeci, A. D. Stone, L. Ge, S. Rotter, and R. J. Tandy, “Ab initio self-consistent laser theory and random lasers,” Nonlinearity 22, C1–C18 (2009).
    [Crossref]
  42. L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
    [Crossref]
  43. A. Cerjan and A. D. Stone, “Steady-state ab initio theory of lasers with injected signals,” Phys. Rev. A 90, 013840 (2014).
    [Crossref]
  44. S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
    [Crossref]
  45. A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91, 063806 (2015).
    [Crossref]
  46. A. I. Shnirelman, “Ergodic properties of eigenfunctions,” Usp. Mat. Nauk 29, 181–182 (1974).
  47. Y. Colin de Verdie’re, “Ergodicité et fonctions propres du laplacien,” Commun. Math. Phys. 102, 497–502 (1985).
    [Crossref]
  48. S. Zelditch, “Uniform distribution of eigenfunctions on compact hyperbolic surfaces,” Duke Math. J. 55, 919–941 (1987).
    [Crossref]
  49. B. Helffer, A. Martinez, and D. Robert, “Ergodicité et limite semiclassique,” Commun. Math. Phys. 109, 313–326 (1987).
    [Crossref]
  50. S. Zelditch and M. Zworski, “Ergodicity of eigenfunctions for ergodic billiards,” Commun. Math. Phys. 175, 673–682 (1996).
    [Crossref]
  51. A. Bäcker, R. Schubert, and P. Stifter, “Rate of quantum ergodicity in Euclidean billiards,” Phys. Rev. E 57, 5425–5447 (1998).
    [Crossref]
  52. H. Schomerus and J. Tworzydlo, “Quantum-to-classical crossover of quasibound states in open quantum systems,” Phys. Rev. Lett. 93, 154102 (2004).
    [Crossref]
  53. S. Nonnenmacher and M. Zworski, “Fractal Weyl laws in discrete models of chaotic scattering,” J. Phys. A 38, 10683–10702 (2005).
    [Crossref]
  54. J. P. Keating, M. Novaes, S. D. Prado, and M. Sieber, “Semiclassical structure of chaotic resonance eigenfunctions,” Phys. Rev. Lett. 97, 150406 (2006).
    [Crossref]
  55. D. L. Shepelyansky, “Fractal Weyl law for quantum fractal eigenstates,” Phys. Rev. E 77, 015202(R) (2008).
    [Crossref]
  56. M. Novaes, “Resonances in open quantum maps,” J. Phys. A 46, 143001 (2013).
    [Crossref]
  57. T. Harayama and S. Shinohara, “Ray-wave correspondence in chaotic dielectric billiards,” Phys. Rev. E 92, 042916 (2015).
    [Crossref]
  58. E. G. Altmann, “Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics,” Phys. Rev. A 79, 013830 (2009).
    [Crossref]
  59. B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112, 1304–1309 (2015).
    [Crossref]
  60. M. Choi, S. Shinohara, and T. Harayama, “Dependence of far-field characteristics on the number of lasing modes in stadium-shaped InGaAsP microlasers,” Opt. Express 16, 17544–17559 (2008).
  61. A. Cerjan, B. Redding, L. Ge, S. F. Liew, H. Cao, and A. D. Stone, “Controlling mode competition by tailoring the spatial pump distribution in a laser: a resonance-based approach,” Opt. Express 24, 26006–26015 (2016).
    [Crossref]
  62. S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
    [Crossref]
  63. H. Fu and H. Haken, “Multifrequency operation in a short-cavity standing-wave laser,” Phys. Rev. A 43, 2446–2454 (1991).
    [Crossref]

2016 (2)

S. Sunada, S. Shinohara, T. Fukushima, and T. Harayama, “Signature of wave chaos in spectral characteristics of microcavity lasers,” Phys. Rev. Lett. 116, 203903 (2016).
[Crossref]

A. Cerjan, B. Redding, L. Ge, S. F. Liew, H. Cao, and A. D. Stone, “Controlling mode competition by tailoring the spatial pump distribution in a laser: a resonance-based approach,” Opt. Express 24, 26006–26015 (2016).
[Crossref]

2015 (5)

T. Harayama and S. Shinohara, “Ray-wave correspondence in chaotic dielectric billiards,” Phys. Rev. E 92, 042916 (2015).
[Crossref]

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112, 1304–1309 (2015).
[Crossref]

A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91, 063806 (2015).
[Crossref]

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

H. Cao and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

2014 (2)

A. Cerjan and A. D. Stone, “Steady-state ab initio theory of lasers with injected signals,” Phys. Rev. A 90, 013840 (2014).
[Crossref]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

2013 (2)

M. Novaes, “Resonances in open quantum maps,” J. Phys. A 46, 143001 (2013).
[Crossref]

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

2012 (1)

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108, 243902 (2012).
[Crossref]

2011 (1)

T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (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]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

2009 (2)

H. E. Türeci, A. D. Stone, L. Ge, S. Rotter, and R. J. Tandy, “Ab initio self-consistent laser theory and random lasers,” Nonlinearity 22, C1–C18 (2009).
[Crossref]

E. G. Altmann, “Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics,” Phys. Rev. A 79, 013830 (2009).
[Crossref]

2008 (6)

M. Choi, S. Shinohara, and T. Harayama, “Dependence of far-field characteristics on the number of lasing modes in stadium-shaped InGaAsP microlasers,” Opt. Express 16, 17544–17559 (2008).

D. L. Shepelyansky, “Fractal Weyl law for quantum fractal eigenstates,” Phys. Rev. E 77, 015202(R) (2008).
[Crossref]

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]

L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895–16902 (2008).
[Crossref]

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

E. Bogomolny, R. Dubertrand, and C. Schmit, “Trace formula for dieletric cavities: I. General properties,” Phys. Rev. E 78, 056202 (2008).
[Crossref]

2007 (2)

S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, “Periodic-orbit theory of level correlations,” Phys. Rev. Lett. 98, 044103 (2007).
[Crossref]

H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
[Crossref]

2006 (3)

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
[Crossref]

J. P. Keating, M. Novaes, S. D. Prado, and M. Sieber, “Semiclassical structure of chaotic resonance eigenfunctions,” Phys. Rev. Lett. 97, 150406 (2006).
[Crossref]

2005 (3)

S. Nonnenmacher and M. Zworski, “Fractal Weyl laws in discrete models of chaotic scattering,” J. Phys. A 38, 10683–10702 (2005).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
[Crossref]

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
[Crossref]

2004 (5)

S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, “Periodic-orbit theory of universality in quantum chaos,” Phys. Rev. Lett. 93, 014103 (2004).
[Crossref]

S.-Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref]

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. B 21, 923–934 (2004).
[Crossref]

V. A. Podolskiy, E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proc. Natl. Acad. Sci. USA 101, 10498–10500 (2004).
[Crossref]

H. Schomerus and J. Tworzydlo, “Quantum-to-classical crossover of quasibound states in open quantum systems,” Phys. Rev. Lett. 93, 154102 (2004).
[Crossref]

2003 (2)

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

T. Harayama, P. Davis, and K. S. Ikeda, “Stable oscillations of a spatially chaotic wave function in a microstadium laser,” Phys. Rev. Lett. 90, 063901 (2003).
[Crossref]

2002 (2)

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]

M. Sieber, “Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems,” J. Phys. A 35, L613–L619 (2002).
[Crossref]

2001 (1)

M. Sieber and K. Richter, “Correlations between periodic orbits and their role in spectral statistics,” Phys. Scr. T90, 128–133 (2001).
[Crossref]

1998 (2)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

A. Bäcker, R. Schubert, and P. Stifter, “Rate of quantum ergodicity in Euclidean billiards,” Phys. Rev. E 57, 5425–5447 (1998).
[Crossref]

1997 (1)

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
[Crossref]

1996 (1)

S. Zelditch and M. Zworski, “Ergodicity of eigenfunctions for ergodic billiards,” Commun. Math. Phys. 175, 673–682 (1996).
[Crossref]

1993 (1)

M. Sargent, “Theory of a multimode quasiequilibrium semiconductor laser,” Phys. Rev. A 48, 717–726 (1993).
[Crossref]

1992 (1)

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, “Conductance fluctuations and chaotic scattering in ballistic microstructures,” Phys. Rev. Lett. 69, 506–509 (1992).
[Crossref]

1991 (1)

H. Fu and H. Haken, “Multifrequency operation in a short-cavity standing-wave laser,” Phys. Rev. A 43, 2446–2454 (1991).
[Crossref]

1990 (1)

R. A. Jalabert, H. U. Baranger, and A. D. Stone, “Conductance fluctuations in the ballistic regime: a probe of quantum chaos?” Phys. Rev. Lett. 65, 2442–2445 (1990).
[Crossref]

1987 (2)

S. Zelditch, “Uniform distribution of eigenfunctions on compact hyperbolic surfaces,” Duke Math. J. 55, 919–941 (1987).
[Crossref]

B. Helffer, A. Martinez, and D. Robert, “Ergodicité et limite semiclassique,” Commun. Math. Phys. 109, 313–326 (1987).
[Crossref]

1985 (2)

Y. Colin de Verdie’re, “Ergodicité et fonctions propres du laplacien,” Commun. Math. Phys. 102, 497–502 (1985).
[Crossref]

M. V. Berry, “Semiclassical theory of spectral rigidity,” Proc. R. Soc. London Ser. A 400, 229–251 (1985).
[Crossref]

1984 (1)

O. Bohigas, M. J. Giannoni, and C. Schmit, “Characterization of chaotic quantum spectra and universality of level fluctuation laws,” Phys. Rev. Lett. 52, 1–4 (1984).
[Crossref]

1981 (1)

M. V. Berry, “Quantizing a classically ergodic system: Sinai’s billiard and the KKR method,” Ann. Phys. (N.Y.) 131, 163–216 (1981).
[Crossref]

1980 (1)

G. Casati, F. Valz-Gris, and I. Guarneri, “On the connection between quantization of nonintegrable systems and statistical theory of spectra,” Lett. Nuovo Cimento Soc. Ital. Fis. 28, 279–282 (1980).
[Crossref]

1974 (2)

M. Fisher, “The renormalization group in the theory of critical behavior,” Rev. Mod. Phys. 46, 597–616 (1974).
[Crossref]

A. I. Shnirelman, “Ergodic properties of eigenfunctions,” Usp. Mat. Nauk 29, 181–182 (1974).

1964 (1)

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, A1429–A1450 (1964).
[Crossref]

Adachi, M.

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

Altland, A.

S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, “Periodic-orbit theory of level correlations,” Phys. Rev. Lett. 98, 044103 (2007).
[Crossref]

S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, “Periodic-orbit theory of universality in quantum chaos,” Phys. Rev. Lett. 93, 014103 (2004).
[Crossref]

Altmann, E. G.

E. G. Altmann, “Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics,” Phys. Rev. A 79, 013830 (2009).
[Crossref]

An, K.

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]

Bäcker, A.

A. Bäcker, R. Schubert, and P. Stifter, “Rate of quantum ergodicity in Euclidean billiards,” Phys. Rev. E 57, 5425–5447 (1998).
[Crossref]

Baranger, H. U.

R. A. Jalabert, H. U. Baranger, and A. D. Stone, “Conductance fluctuations in the ballistic regime: a probe of quantum chaos?” Phys. Rev. Lett. 65, 2442–2445 (1990).
[Crossref]

Ben-Messaoud, T.

Berry, M. V.

M. V. Berry, “Semiclassical theory of spectral rigidity,” Proc. R. Soc. London Ser. A 400, 229–251 (1985).
[Crossref]

M. V. Berry, “Quantizing a classically ergodic system: Sinai’s billiard and the KKR method,” Ann. Phys. (N.Y.) 131, 163–216 (1981).
[Crossref]

Bogomolny, E.

E. Bogomolny, R. Dubertrand, and C. Schmit, “Trace formula for dieletric cavities: I. General properties,” Phys. Rev. E 78, 056202 (2008).
[Crossref]

Bohigas, O.

O. Bohigas, M. J. Giannoni, and C. Schmit, “Characterization of chaotic quantum spectra and universality of level fluctuation laws,” Phys. Rev. Lett. 52, 1–4 (1984).
[Crossref]

Braun, P.

S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, “Periodic-orbit theory of level correlations,” Phys. Rev. Lett. 98, 044103 (2007).
[Crossref]

S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, “Periodic-orbit theory of universality in quantum chaos,” Phys. Rev. Lett. 93, 014103 (2004).
[Crossref]

Cao, H.

A. Cerjan, B. Redding, L. Ge, S. F. Liew, H. Cao, and A. D. Stone, “Controlling mode competition by tailoring the spatial pump distribution in a laser: a resonance-based approach,” Opt. Express 24, 26006–26015 (2016).
[Crossref]

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112, 1304–1309 (2015).
[Crossref]

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

H. Cao and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108, 243902 (2012).
[Crossref]

V. A. Podolskiy, E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proc. Natl. Acad. Sci. USA 101, 10498–10500 (2004).
[Crossref]

Capasso, F.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

Casati, G.

G. Casati, F. Valz-Gris, and I. Guarneri, “On the connection between quantization of nonintegrable systems and statistical theory of spectra,” Lett. Nuovo Cimento Soc. Ital. Fis. 28, 279–282 (1980).
[Crossref]

Cerjan, A.

A. Cerjan, B. Redding, L. Ge, S. F. Liew, H. Cao, and A. D. Stone, “Controlling mode competition by tailoring the spatial pump distribution in a laser: a resonance-based approach,” Opt. Express 24, 26006–26015 (2016).
[Crossref]

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112, 1304–1309 (2015).
[Crossref]

A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91, 063806 (2015).
[Crossref]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

A. Cerjan and A. D. Stone, “Steady-state ab initio theory of lasers with injected signals,” Phys. Rev. A 90, 013840 (2014).
[Crossref]

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]

Chang, R. K.

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,” Science 280, 1556–1564 (1998).
[Crossref]

Choi, M.

M. Choi, S. Shinohara, and T. Harayama, “Dependence of far-field characteristics on the number of lasing modes in stadium-shaped InGaAsP microlasers,” Opt. Express 16, 17544–17559 (2008).

S.-Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref]

Choma, M. A.

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112, 1304–1309 (2015).
[Crossref]

Chong, Y. D.

A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91, 063806 (2015).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

Colin de Verdie’re, Y.

Y. Colin de Verdie’re, “Ergodicité et fonctions propres du laplacien,” Commun. Math. Phys. 102, 497–502 (1985).
[Crossref]

Collier, B.

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]

Davis, P.

T. Harayama, P. Davis, and K. S. Ikeda, “Stable oscillations of a spatially chaotic wave function in a microstadium laser,” Phys. Rev. Lett. 90, 063901 (2003).
[Crossref]

Dubertrand, R.

E. Bogomolny, R. Dubertrand, and C. Schmit, “Trace formula for dieletric cavities: I. General properties,” Phys. Rev. E 78, 056202 (2008).
[Crossref]

Esterhazy, S.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

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,” Science 280, 1556–1564 (1998).
[Crossref]

Fang, W.

V. A. Podolskiy, E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proc. Natl. Acad. Sci. USA 101, 10498–10500 (2004).
[Crossref]

Fisher, M.

M. Fisher, “The renormalization group in the theory of critical behavior,” Rev. Mod. Phys. 46, 597–616 (1974).
[Crossref]

Fu, H.

H. Fu and H. Haken, “Multifrequency operation in a short-cavity standing-wave laser,” Phys. Rev. A 43, 2446–2454 (1991).
[Crossref]

Fukushima, T.

S. Sunada, S. Shinohara, T. Fukushima, and T. Harayama, “Signature of wave chaos in spectral characteristics of microcavity lasers,” Phys. Rev. Lett. 116, 203903 (2016).
[Crossref]

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[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]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

Ge, L.

A. Cerjan, B. Redding, L. Ge, S. F. Liew, H. Cao, and A. D. Stone, “Controlling mode competition by tailoring the spatial pump distribution in a laser: a resonance-based approach,” Opt. Express 24, 26006–26015 (2016).
[Crossref]

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108, 243902 (2012).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

H. E. Türeci, A. D. Stone, L. Ge, S. Rotter, and R. J. Tandy, “Ab initio self-consistent laser theory and random lasers,” Nonlinearity 22, C1–C18 (2009).
[Crossref]

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]

L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895–16902 (2008).
[Crossref]

H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
[Crossref]

Giannoni, M. J.

O. Bohigas, M. J. Giannoni, and C. Schmit, “Characterization of chaotic quantum spectra and universality of level fluctuation laws,” Phys. Rev. Lett. 52, 1–4 (1984).
[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,” Science 280, 1556–1564 (1998).
[Crossref]

Gossard, A. C.

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, “Conductance fluctuations and chaotic scattering in ballistic microstructures,” Phys. Rev. Lett. 69, 506–509 (1992).
[Crossref]

Guarneri, I.

G. Casati, F. Valz-Gris, and I. Guarneri, “On the connection between quantization of nonintegrable systems and statistical theory of spectra,” Lett. Nuovo Cimento Soc. Ital. Fis. 28, 279–282 (1980).
[Crossref]

Haake, F.

S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, “Periodic-orbit theory of level correlations,” Phys. Rev. Lett. 98, 044103 (2007).
[Crossref]

S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, “Periodic-orbit theory of universality in quantum chaos,” Phys. Rev. Lett. 93, 014103 (2004).
[Crossref]

F. Haake, Quantum Signatures of Chaos (Springer, 2000).

Haken, H.

H. Fu and H. Haken, “Multifrequency operation in a short-cavity standing-wave laser,” Phys. Rev. A 43, 2446–2454 (1991).
[Crossref]

Harayama, T.

S. Sunada, S. Shinohara, T. Fukushima, and T. Harayama, “Signature of wave chaos in spectral characteristics of microcavity lasers,” Phys. Rev. Lett. 116, 203903 (2016).
[Crossref]

T. Harayama and S. Shinohara, “Ray-wave correspondence in chaotic dielectric billiards,” Phys. Rev. E 92, 042916 (2015).
[Crossref]

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (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]

M. Choi, S. Shinohara, and T. Harayama, “Dependence of far-field characteristics on the number of lasing modes in stadium-shaped InGaAsP microlasers,” Opt. Express 16, 17544–17559 (2008).

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
[Crossref]

T. Harayama, P. Davis, and K. S. Ikeda, “Stable oscillations of a spatially chaotic wave function in a microstadium laser,” Phys. Rev. Lett. 90, 063901 (2003).
[Crossref]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

K. Nakamura and T. Harayama, Quantum Chaos and Quantum Dots (Oxford University, 2004).

Helffer, B.

B. Helffer, A. Martinez, and D. Robert, “Ergodicité et limite semiclassique,” Commun. Math. Phys. 109, 313–326 (1987).
[Crossref]

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]

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

Heusler, S.

S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, “Periodic-orbit theory of level correlations,” Phys. Rev. Lett. 98, 044103 (2007).
[Crossref]

S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, “Periodic-orbit theory of universality in quantum chaos,” Phys. Rev. Lett. 93, 014103 (2004).
[Crossref]

Hopkins, P. F.

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, “Conductance fluctuations and chaotic scattering in ballistic microstructures,” Phys. Rev. Lett. 69, 506–509 (1992).
[Crossref]

Huang, X.

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112, 1304–1309 (2015).
[Crossref]

Ikeda, K. S.

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
[Crossref]

T. Harayama, P. Davis, and K. S. Ikeda, “Stable oscillations of a spatially chaotic wave function in a microstadium laser,” Phys. Rev. Lett. 90, 063901 (2003).
[Crossref]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

Jalabert, R. A.

R. A. Jalabert, H. U. Baranger, and A. D. Stone, “Conductance fluctuations in the ballistic regime: a probe of quantum chaos?” Phys. Rev. Lett. 65, 2442–2445 (1990).
[Crossref]

Johnson, S. G.

A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91, 063806 (2015).
[Crossref]

Keating, J. P.

J. P. Keating, M. Novaes, S. D. Prado, and M. Sieber, “Semiclassical structure of chaotic resonance eigenfunctions,” Phys. Rev. Lett. 97, 150406 (2006).
[Crossref]

Kim, C.-M.

S.-Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref]

Kim, S. W.

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]

Kwon, T. Y.

S.-Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref]

Lamb, W. E.

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, A1429–A1450 (1964).
[Crossref]

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1974).

Lee, J.-H.

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]

Lee, M. L.

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112, 1304–1309 (2015).
[Crossref]

Lee, S.-B.

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]

Lee, S.-Y.

S.-Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref]

Liertzer, M.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

Liew, S. F.

Liu, D.

A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91, 063806 (2015).
[Crossref]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

Makris, K. G.

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

Marcus, C. M.

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, “Conductance fluctuations and chaotic scattering in ballistic microstructures,” Phys. Rev. Lett. 69, 506–509 (1992).
[Crossref]

Martinez, A.

B. Helffer, A. Martinez, and D. Robert, “Ergodicité et limite semiclassique,” Commun. Math. Phys. 109, 313–326 (1987).
[Crossref]

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]

Müller, S.

S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, “Periodic-orbit theory of level correlations,” Phys. Rev. Lett. 98, 044103 (2007).
[Crossref]

S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, “Periodic-orbit theory of universality in quantum chaos,” Phys. Rev. Lett. 93, 014103 (2004).
[Crossref]

Nakamura, K.

K. Nakamura and T. Harayama, Quantum Chaos and Quantum Dots (Oxford University, 2004).

Narimanov, E.

V. A. Podolskiy, E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proc. Natl. Acad. Sci. USA 101, 10498–10500 (2004).
[Crossref]

Narimanov, E. E.

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]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

Nöckel, J. U.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
[Crossref]

Nonnenmacher, S.

S. Nonnenmacher and M. Zworski, “Fractal Weyl laws in discrete models of chaotic scattering,” J. Phys. A 38, 10683–10702 (2005).
[Crossref]

Novaes, M.

M. Novaes, “Resonances in open quantum maps,” J. Phys. A 46, 143001 (2013).
[Crossref]

J. P. Keating, M. Novaes, S. D. Prado, and M. Sieber, “Semiclassical structure of chaotic resonance eigenfunctions,” Phys. Rev. Lett. 97, 150406 (2006).
[Crossref]

Pick, A.

A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91, 063806 (2015).
[Crossref]

Podolskiy, V. A.

V. A. Podolskiy, E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proc. Natl. Acad. Sci. USA 101, 10498–10500 (2004).
[Crossref]

Prado, S. D.

J. P. Keating, M. Novaes, S. D. Prado, and M. Sieber, “Semiclassical structure of chaotic resonance eigenfunctions,” Phys. Rev. Lett. 97, 150406 (2006).
[Crossref]

Redding, B.

A. Cerjan, B. Redding, L. Ge, S. F. Liew, H. Cao, and A. D. Stone, “Controlling mode competition by tailoring the spatial pump distribution in a laser: a resonance-based approach,” Opt. Express 24, 26006–26015 (2016).
[Crossref]

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112, 1304–1309 (2015).
[Crossref]

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108, 243902 (2012).
[Crossref]

Rex, N. B.

Richter, K.

M. Sieber and K. Richter, “Correlations between periodic orbits and their role in spectral statistics,” Phys. Scr. T90, 128–133 (2001).
[Crossref]

Rim, S.

S.-Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref]

Rimberg, A. J.

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, “Conductance fluctuations and chaotic scattering in ballistic microstructures,” Phys. Rev. Lett. 69, 506–509 (1992).
[Crossref]

Robert, D.

B. Helffer, A. Martinez, and D. Robert, “Ergodicité et limite semiclassique,” Commun. Math. Phys. 109, 313–326 (1987).
[Crossref]

Rodriguez, A. W.

A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91, 063806 (2015).
[Crossref]

Rotter, S.

H. E. Türeci, A. D. Stone, L. Ge, S. Rotter, and R. J. Tandy, “Ab initio self-consistent laser theory and random lasers,” Nonlinearity 22, C1–C18 (2009).
[Crossref]

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]

Ryu, J. W.

S.-Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref]

Sargent, M.

M. Sargent, “Theory of a multimode quasiequilibrium semiconductor laser,” Phys. Rev. A 48, 717–726 (1993).
[Crossref]

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1974).

Sarma, R.

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[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]

Schmit, C.

E. Bogomolny, R. Dubertrand, and C. Schmit, “Trace formula for dieletric cavities: I. General properties,” Phys. Rev. E 78, 056202 (2008).
[Crossref]

O. Bohigas, M. J. Giannoni, and C. Schmit, “Characterization of chaotic quantum spectra and universality of level fluctuation laws,” Phys. Rev. Lett. 52, 1–4 (1984).
[Crossref]

Schomerus, H.

H. Schomerus and J. Tworzydlo, “Quantum-to-classical crossover of quasibound states in open quantum systems,” Phys. Rev. Lett. 93, 154102 (2004).
[Crossref]

Schubert, R.

A. Bäcker, R. Schubert, and P. Stifter, “Rate of quantum ergodicity in Euclidean billiards,” Phys. Rev. E 57, 5425–5447 (1998).
[Crossref]

Schwefel, H. G. L.

Scully, M. O.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1974).

Shepelyansky, D. L.

D. L. Shepelyansky, “Fractal Weyl law for quantum fractal eigenstates,” Phys. Rev. E 77, 015202(R) (2008).
[Crossref]

Shinohara, S.

S. Sunada, S. Shinohara, T. Fukushima, and T. Harayama, “Signature of wave chaos in spectral characteristics of microcavity lasers,” Phys. Rev. Lett. 116, 203903 (2016).
[Crossref]

T. Harayama and S. Shinohara, “Ray-wave correspondence in chaotic dielectric billiards,” Phys. Rev. E 92, 042916 (2015).
[Crossref]

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (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]

M. Choi, S. Shinohara, and T. Harayama, “Dependence of far-field characteristics on the number of lasing modes in stadium-shaped InGaAsP microlasers,” Opt. Express 16, 17544–17559 (2008).

Shnirelman, A. I.

A. I. Shnirelman, “Ergodic properties of eigenfunctions,” Usp. Mat. Nauk 29, 181–182 (1974).

Sieber, M.

J. P. Keating, M. Novaes, S. D. Prado, and M. Sieber, “Semiclassical structure of chaotic resonance eigenfunctions,” Phys. Rev. Lett. 97, 150406 (2006).
[Crossref]

M. Sieber, “Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems,” J. Phys. A 35, L613–L619 (2002).
[Crossref]

M. Sieber and K. Richter, “Correlations between periodic orbits and their role in spectral statistics,” Phys. Scr. T90, 128–133 (2001).
[Crossref]

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,” Science 280, 1556–1564 (1998).
[Crossref]

Song, Q.

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108, 243902 (2012).
[Crossref]

Stifter, P.

A. Bäcker, R. Schubert, and P. Stifter, “Rate of quantum ergodicity in Euclidean billiards,” Phys. Rev. E 57, 5425–5447 (1998).
[Crossref]

Stöckmann, H.-J.

H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University, 1999).

Stone, A. D.

A. Cerjan, B. Redding, L. Ge, S. F. Liew, H. Cao, and A. D. Stone, “Controlling mode competition by tailoring the spatial pump distribution in a laser: a resonance-based approach,” Opt. Express 24, 26006–26015 (2016).
[Crossref]

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112, 1304–1309 (2015).
[Crossref]

A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91, 063806 (2015).
[Crossref]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

A. Cerjan and A. D. Stone, “Steady-state ab initio theory of lasers with injected signals,” Phys. Rev. A 90, 013840 (2014).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

H. E. Türeci, A. D. Stone, L. Ge, S. Rotter, and R. J. Tandy, “Ab initio self-consistent laser theory and random lasers,” Nonlinearity 22, C1–C18 (2009).
[Crossref]

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]

L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895–16902 (2008).
[Crossref]

H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
[Crossref]

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]

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. B 21, 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,” Science 280, 1556–1564 (1998).
[Crossref]

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
[Crossref]

R. A. Jalabert, H. U. Baranger, and A. D. Stone, “Conductance fluctuations in the ballistic regime: a probe of quantum chaos?” Phys. Rev. Lett. 65, 2442–2445 (1990).
[Crossref]

Sunada, S.

S. Sunada, S. Shinohara, T. Fukushima, and T. Harayama, “Signature of wave chaos in spectral characteristics of microcavity lasers,” Phys. Rev. Lett. 116, 203903 (2016).
[Crossref]

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
[Crossref]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

Tandy, R. J.

H. E. Türeci, A. D. Stone, L. Ge, S. Rotter, and R. J. Tandy, “Ab initio self-consistent laser theory and random lasers,” Nonlinearity 22, C1–C18 (2009).
[Crossref]

L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895–16902 (2008).
[Crossref]

Tureci, H. E.

Türeci, H. E.

H. E. Türeci, A. D. Stone, L. Ge, S. Rotter, and R. J. Tandy, “Ab initio self-consistent laser theory and random lasers,” Nonlinearity 22, C1–C18 (2009).
[Crossref]

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]

L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895–16902 (2008).
[Crossref]

H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
[Crossref]

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]

Tworzydlo, J.

H. Schomerus and J. Tworzydlo, “Quantum-to-classical crossover of quasibound states in open quantum systems,” Phys. Rev. Lett. 93, 154102 (2004).
[Crossref]

Valz-Gris, F.

G. Casati, F. Valz-Gris, and I. Guarneri, “On the connection between quantization of nonintegrable systems and statistical theory of spectra,” Lett. Nuovo Cimento Soc. Ital. Fis. 28, 279–282 (1980).
[Crossref]

Westervelt, R. M.

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, “Conductance fluctuations and chaotic scattering in ballistic microstructures,” Phys. Rev. Lett. 69, 506–509 (1992).
[Crossref]

Wiersig, J.

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

H. Cao and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

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

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
[Crossref]

Zelditch, S.

S. Zelditch and M. Zworski, “Ergodicity of eigenfunctions for ergodic billiards,” Commun. Math. Phys. 175, 673–682 (1996).
[Crossref]

S. Zelditch, “Uniform distribution of eigenfunctions on compact hyperbolic surfaces,” Duke Math. J. 55, 919–941 (1987).
[Crossref]

Zworski, M.

S. Nonnenmacher and M. Zworski, “Fractal Weyl laws in discrete models of chaotic scattering,” J. Phys. A 38, 10683–10702 (2005).
[Crossref]

S. Zelditch and M. Zworski, “Ergodicity of eigenfunctions for ergodic billiards,” Commun. Math. Phys. 175, 673–682 (1996).
[Crossref]

Zyss, J.

Ann. Phys. (N.Y.) (1)

M. V. Berry, “Quantizing a classically ergodic system: Sinai’s billiard and the KKR method,” Ann. Phys. (N.Y.) 131, 163–216 (1981).
[Crossref]

Commun. Math. Phys. (3)

B. Helffer, A. Martinez, and D. Robert, “Ergodicité et limite semiclassique,” Commun. Math. Phys. 109, 313–326 (1987).
[Crossref]

S. Zelditch and M. Zworski, “Ergodicity of eigenfunctions for ergodic billiards,” Commun. Math. Phys. 175, 673–682 (1996).
[Crossref]

Y. Colin de Verdie’re, “Ergodicité et fonctions propres du laplacien,” Commun. Math. Phys. 102, 497–502 (1985).
[Crossref]

Duke Math. J. (1)

S. Zelditch, “Uniform distribution of eigenfunctions on compact hyperbolic surfaces,” Duke Math. J. 55, 919–941 (1987).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. A (3)

M. Sieber, “Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems,” J. Phys. A 35, L613–L619 (2002).
[Crossref]

S. Nonnenmacher and M. Zworski, “Fractal Weyl laws in discrete models of chaotic scattering,” J. Phys. A 38, 10683–10702 (2005).
[Crossref]

M. Novaes, “Resonances in open quantum maps,” J. Phys. A 46, 143001 (2013).
[Crossref]

Laser Photon. Rev. (1)

T. Harayama and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5, 247–271 (2011).
[Crossref]

Lett. Nuovo Cimento Soc. Ital. Fis. (1)

G. Casati, F. Valz-Gris, and I. Guarneri, “On the connection between quantization of nonintegrable systems and statistical theory of spectra,” Lett. Nuovo Cimento Soc. Ital. Fis. 28, 279–282 (1980).
[Crossref]

Nature (1)

J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385, 45–47 (1997).
[Crossref]

Nonlinearity (1)

H. E. Türeci, A. D. Stone, L. Ge, S. Rotter, and R. J. Tandy, “Ab initio self-consistent laser theory and random lasers,” Nonlinearity 22, C1–C18 (2009).
[Crossref]

Opt. Express (3)

Phys. Rev. A (12)

H. Fu and H. Haken, “Multifrequency operation in a short-cavity standing-wave laser,” Phys. Rev. A 43, 2446–2454 (1991).
[Crossref]

E. G. Altmann, “Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics,” Phys. Rev. A 79, 013830 (2009).
[Crossref]

M. Sargent, “Theory of a multimode quasiequilibrium semiconductor laser,” Phys. Rev. A 48, 717–726 (1993).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

A. Cerjan and A. D. Stone, “Steady-state ab initio theory of lasers with injected signals,” Phys. Rev. A 90, 013840 (2014).
[Crossref]

S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90, 023816 (2014).
[Crossref]

A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91, 063806 (2015).
[Crossref]

S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88, 013802 (2013).
[Crossref]

T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72, 013803 (2005).
[Crossref]

H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006).
[Crossref]

H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007).
[Crossref]

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, A1429–A1450 (1964).
[Crossref]

Phys. Rev. E (5)

E. Bogomolny, R. Dubertrand, and C. Schmit, “Trace formula for dieletric cavities: I. General properties,” Phys. Rev. E 78, 056202 (2008).
[Crossref]

A. Bäcker, R. Schubert, and P. Stifter, “Rate of quantum ergodicity in Euclidean billiards,” Phys. Rev. E 57, 5425–5447 (1998).
[Crossref]

T. Harayama and S. Shinohara, “Ray-wave correspondence in chaotic dielectric billiards,” Phys. Rev. E 92, 042916 (2015).
[Crossref]

D. L. Shepelyansky, “Fractal Weyl law for quantum fractal eigenstates,” Phys. Rev. E 77, 015202(R) (2008).
[Crossref]

S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in fully chaotic cavity lasers,” Phys. Rev. E 71, 046209 (2005).
[Crossref]

Phys. Rev. Lett. (17)

H. Schomerus and J. Tworzydlo, “Quantum-to-classical crossover of quasibound states in open quantum systems,” Phys. Rev. Lett. 93, 154102 (2004).
[Crossref]

J. P. Keating, M. Novaes, S. D. Prado, and M. Sieber, “Semiclassical structure of chaotic resonance eigenfunctions,” Phys. Rev. Lett. 97, 150406 (2006).
[Crossref]

T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91, 073903 (2003).
[Crossref]

T. Harayama, P. Davis, and K. S. Ikeda, “Stable oscillations of a spatially chaotic wave function in a microstadium laser,” Phys. Rev. Lett. 90, 063901 (2003).
[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]

Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108, 243902 (2012).
[Crossref]

R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114, 053903 (2015).
[Crossref]

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
[Crossref]

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

S. Sunada, S. Shinohara, T. Fukushima, and T. Harayama, “Signature of wave chaos in spectral characteristics of microcavity lasers,” Phys. Rev. Lett. 116, 203903 (2016).
[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]

S.-Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93, 164102 (2004).
[Crossref]

R. A. Jalabert, H. U. Baranger, and A. D. Stone, “Conductance fluctuations in the ballistic regime: a probe of quantum chaos?” Phys. Rev. Lett. 65, 2442–2445 (1990).
[Crossref]

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, “Conductance fluctuations and chaotic scattering in ballistic microstructures,” Phys. Rev. Lett. 69, 506–509 (1992).
[Crossref]

O. Bohigas, M. J. Giannoni, and C. Schmit, “Characterization of chaotic quantum spectra and universality of level fluctuation laws,” Phys. Rev. Lett. 52, 1–4 (1984).
[Crossref]

S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, “Periodic-orbit theory of universality in quantum chaos,” Phys. Rev. Lett. 93, 014103 (2004).
[Crossref]

S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, “Periodic-orbit theory of level correlations,” Phys. Rev. Lett. 98, 044103 (2007).
[Crossref]

Phys. Scr. (1)

M. Sieber and K. Richter, “Correlations between periodic orbits and their role in spectral statistics,” Phys. Scr. T90, 128–133 (2001).
[Crossref]

Proc. Natl. Acad. Sci. USA (2)

V. A. Podolskiy, E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proc. Natl. Acad. Sci. USA 101, 10498–10500 (2004).
[Crossref]

B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112, 1304–1309 (2015).
[Crossref]

Proc. R. Soc. London Ser. A (1)

M. V. Berry, “Semiclassical theory of spectral rigidity,” Proc. R. Soc. London Ser. A 400, 229–251 (1985).
[Crossref]

Rev. Mod. Phys. (2)

H. Cao and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87, 61–111 (2015).
[Crossref]

M. Fisher, “The renormalization group in the theory of critical behavior,” Rev. Mod. Phys. 46, 597–616 (1974).
[Crossref]

Science (2)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[Crossref]

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643–646 (2008).
[Crossref]

Usp. Mat. Nauk (1)

A. I. Shnirelman, “Ergodic properties of eigenfunctions,” Usp. Mat. Nauk 29, 181–182 (1974).

Other (4)

H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University, 1999).

F. Haake, Quantum Signatures of Chaos (Springer, 2000).

K. Nakamura and T. Harayama, Quantum Chaos and Quantum Dots (Oxford University, 2004).

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1974).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (42)

Equations on this page are rendered with MathJax. Learn more.

tE˜=i2(xy2+1)E˜αLE˜+2πNκϵρ˜,
nout2nin2tE˜=i2(xy2+nout2nin2)E˜,
tρ˜=γ˜ρ˜iΔ0ρ˜+κ˜WE˜,
tW=γ˜(WW)2κ˜(E˜ρ˜*+E˜*ρ˜),
E˜=iEi(t)eiΔitUi(x,y),
ρ˜=iρi(t)eiΔitVi(x,y),
dEi(t)dt+jidEj(t)dteiΔijtUij=[i(Δi+12)(αL+γ˜ii)]Ei(t)+ji{[i(Δj+12)αL]Uijγ˜ij}Ej(t)eiΔijt+2πNκεjeiΔijtρj(t)DUi*(x,y)Vj(x,y)dxdy,
γ˜iji2DdxdyUi*(x,y)2Uj(x,y).
ρj(t)Vj(x,y)=κ˜Wγ˜iΔ0jEj(t)Uj(x,y).
W=W/{1+[ij2κ˜2EiEj*UiUj*eiΔjit(γ˜+iΔ0j)(γ˜iΔji)+c.c.]}.
L(x,y)1+mam|Um|2,
C(x,y)l,jlj2κ˜2ElEj*UlUj*eiΔjlt(γ˜+iΔ0j)(γ˜iΔjl)+c.c.
dEi(t)dt+jidEj(t)dteiΔijtUij=[i(Δi+12)(αL+γ˜ii)]Ei(t)ji{[i(Δj+12)αL]Uijγ˜ij}Ej(t)eiΔijt+ξWkeiΔiktEkγ˜iΔ0k×DdxdyUi*UkL(x,y){1C(x,y)L(x,y)+[C(x,y)L(x,y)]2},
dEidt[i(Δi+12)(αL+γ˜ii)]Ei+ξWEiγ˜iΔ0iDdxdy|Ui|2L(x,y)ξWEiDdxdy|Ui|2[L(x,y)]2kki2κ˜2|Ek|2|Uk|2(γ˜iΔ0k)(γ˜iΔki)×(1γ˜+iΔ0k+1γ˜iΔ0i).
d|Ei|2dt=ddt(EiEi*)=Ei*dEidt+EidEi*dt=(2αL+γ˜ii+γ˜ii*)|Ei|2+2ξWg(Δi)Ddxdy[L(x,y)]2×|Ei|2|Ui|2{L(x,y)k,ki2κ˜2g(Δk)g(ΔiΔk)×[2γ˜+(ΔiΔ0)(ΔiΔk)/γ˜+(ΔiΔk)(Δi+Δk2Δ0)/γ˜]|Ek|2|Uk|2},
L(x,y)1+k,|ΔkΔi|γ˜4κ˜2γ˜g(Δk)|Ek|2|Uk|2.
2γ˜(ΔiΔ0)(ΔiΔk)/γ˜+(ΔiΔk)(Δi+Δk2Δ0)/γ˜.
d|Ei|2dt=(2αL+γ˜ii+γ˜ii*)|Ei|2+2ξWg(Δi)Ddxdy[L(x,y)]2|Ei|2|Ui|2×[1+k,|ΔkΔi|γ˜4κ˜2γ˜g(Δk)|Ek|2|Uk|2k,ki,|ΔkΔi|γ˜4κ˜2γ˜g(Δk)|Ek|2|Uk|2]=(2αL+γ˜ii+γ˜ii*)|Ei|2+2ξWg(Δi)Ddxdy[L(x,y)]2|Ei|2|Ui|2×[1+4κ˜2γ˜g(Δi)|Ei|2|Ui|2].
dIidtSiIi,
Si2(αL+γi)+2ξWg(Δi)Ddxdy|Ui|2Li(x,y)[L(x,y)]2,
γii4Dds(Ui*UinUiUi*n),
Mij{Sj+2ξWbj2Ddxdy|Uj|4[L(x,y)]2}δij4ξWbibjDdxdy|Ui|2|Uj|2Li(x,y)[L(x,y)]3,
M˜jj=2ξWbj2Ddxdy|Uj|4Ls,j2<0,
M˜ii=2ξWg(Δi)Ddxdy|Ui|2Ls,iLs,j2Ls,j2Ls,i,
Mii=2ξWbi2Ddxdy|Ui|4Li(x,y)[L(x,y)]3[L(x,y)Li(x,y)2],
Mij=4ξWbibjDdxdy|Ui|2|Uj|2Li(x,y)[L(x,y)]3.
Ddxdyεi(x,y)|U0(x,y)|2=0,
M˜ii=2ξWg(Δi)Sdxdy(1+εi)|U0|2×as,i(1+εi)as,j2(1+εj)2|U0|2as,j2(1+εj)2(1+εi)as,i|U0|6|U0|2=2ξWg(Δi)as,j2as,iSdxdy{[1+O(εi(x,y)|U0(x,y)|2)]as,i|U0|2[1+O(εj(x,y)|U0(x,y)|2)]as,j2}2ξWg(Δi)as,j2as,i(as,iSdxdy1|U0|2Aas,j2),
(as,jA)2>as,iASdxdy1A2|U0|2.
Li(x,y)(1+εi)ai|U0|2,
L(x,y)m=1N(1+εm)am|U0|2
Mii4ξAWbi2aiatot3(1atot2ai),
Mij4ξAWbibjaiatot3,
M(N)4ξAWatot3diag(a1,,aN)×BRBdiag(a1,,aN).
|M(k)|=(2ξAWatot2)k(1i=1k2aiatot)i=1kbi2.
Mx=diag(B1,,BN)Cdiag(A1,,AN)x=λx.
diag(B1,,BN)Cdiag(A11/2,,AN1/2)×diag(A11/2,,AN1/2)diag(B11/2,,BN1/2)×diag(B11/2,,BN1/2)x=diag(B1,,BN)Cdiag(B11/2,,BN1/2)×diag(A11/2,,AN1/2)diag(B11/2,,BN1/2)×diag(A11/2,,AN1/2)x.
λdiag(A11/2,,AN1/2)diag(A11/2,,AN1/2)×diag(B11/2,,BN1/2)diag(B11/2,,BN1/2)x=λdiag(A11/2,,AN1/2)diag(B11/2,,BN1/2)×diag(B11/2,,BN1/2)diag(A11/2,,AN1/2)x.
diag(B1,,BN)Cdiag(B11/2,,BN1/2)×diag(A11/2,,AN1/2)x=λdiag(A11/2,,AN1/2)diag(B11/2,,BN1/2)x,
diag(A11/2,,AN1/2)diag(B11/2,,BN1/2)C×diag(B11/2,,BN1/2)diag(A11/2,,AN1/2)x=λx.
Mdiag(A11/2,,AN1/2)diag(B11/2,,BN1/2)C×diag(B11/2,,BN1/2)diag(A11/2,,AN1/2)
|M|=|diag(A11/2,,AN1/2)||diag(B11/2,,BN1/2)||C|×|diag(B11/2,,BN1/2)||diag(A11/2,,AN1/2)|=(i=1NAiBi)(i=1N(Ci1))(1+i=1N(Ci1)1).

Metrics