Abstract

Mode coupling between the whispering-gallery modes (WGMs) is numerically investigated for a two-dimensional microdisk resonator with an output waveguide. The equilateral-polygonal shaped mode patterns can be constructed by mode coupling in the microdisk, and the coupled modes can still keep high quality factors (Q factors). For a microdisk with a diameter of 4.5 μm and a refractive index of 3.2 connected to a 0.6-μm-wide output waveguide, the coupled mode at the wavelength of 1490 nm has a Q factor in the order of 104, which is ten times larger than those of the uncoupled WGMs, and the output efficiency defined as the ratio of the energy flux confined in the output waveguide to the total radiation energy flux is about 0.65. The mode coupling can be used to realize high efficiency directional-emission microdisk lasers.

©2009 Optical Society of America

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  1. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 ( 1992).
    [Crossref]
  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(5369), 1556–1564 ( 1998).
    [Crossref] [PubMed]
  3. G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 ( 2003).
    [Crossref]
  4. S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 ( 2004).
    [Crossref]
  5. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 ( 2006).
    [Crossref]
  6. S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photon. Technol. Lett. 15(10), 1330–1332 ( 2003).
    [Crossref]
  7. J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15(11), 6744–6749 ( 2007).
    [Crossref] [PubMed]
  8. Y. Baryshnikov, P. Heider, W. Parz, and V. Zharnitsky, “Whispering gallery modes inside asymmetric resonant cavities,” Phys. Rev. Lett. 93(13), 133902 ( 2004).
    [Crossref] [PubMed]
  9. 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(16), 164102 ( 2004).
    [Crossref] [PubMed]
  10. J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73(3), 031802 ( 2006).
    [Crossref]
  11. Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-Temperature Continuous-Wave Electrically Injected InP–GaInAsP Equilateral-Triangle-Resonator Lasers,” IEEE Photon. Technol. Lett. 19(13), 963–965 ( 2007).
    [Crossref]
  12. Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, Y. Du, and Z. C. Fan, “Directional emission InP/GaInAsP square-resonator microlasers,” Opt. Lett. 33(19), 2170–2172 ( 2008).
    [Crossref] [PubMed]
  13. M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5 Pt 2), 056207 ( 2002).
    [Crossref] [PubMed]
  14. A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method. (Boston: Artech House, 2005).
  15. W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonator frequencies and quality factors of cavities by FDTD technique and padé approximation,” IEEE Microwave. Wireless Compon. Lett. 11(5), 223–225 ( 2001).
    [Crossref]
  16. Y. Z. Huang, S. J. Wang, Y. D. Yang, J. L. Xiao, Y. H. Hu, and Y. Du, “Optical bistability in InP/GaInAsP equilateral-triangle-resonator microlasers,” Opt. Lett. 34(12), 1852–1854 ( 2009).
    [Crossref] [PubMed]
  17. M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80(12), 2051–2053 ( 2002).
    [Crossref]
  18. Y. D. Yang, Y. Z. Huang, and S. J. Wang, “Mode analysis for equilateral–triangle -resonator microlasers with metal confinement layers,” IEEE J. Quantum Electron.in press.
    [PubMed]
  19. Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 ( 2007).
    [Crossref]

2009 (1)

2008 (1)

2007 (3)

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-Temperature Continuous-Wave Electrically Injected InP–GaInAsP Equilateral-Triangle-Resonator Lasers,” IEEE Photon. Technol. Lett. 19(13), 963–965 ( 2007).
[Crossref]

Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 ( 2007).
[Crossref]

J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15(11), 6744–6749 ( 2007).
[Crossref] [PubMed]

2006 (2)

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 ( 2006).
[Crossref]

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73(3), 031802 ( 2006).
[Crossref]

2004 (3)

Y. Baryshnikov, P. Heider, W. Parz, and V. Zharnitsky, “Whispering gallery modes inside asymmetric resonant cavities,” Phys. Rev. Lett. 93(13), 133902 ( 2004).
[Crossref] [PubMed]

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(16), 164102 ( 2004).
[Crossref] [PubMed]

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 ( 2004).
[Crossref]

2003 (2)

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 ( 2003).
[Crossref]

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photon. Technol. Lett. 15(10), 1330–1332 ( 2003).
[Crossref]

2002 (2)

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5 Pt 2), 056207 ( 2002).
[Crossref] [PubMed]

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80(12), 2051–2053 ( 2002).
[Crossref]

2001 (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonator frequencies and quality factors of cavities by FDTD technique and padé approximation,” IEEE Microwave. Wireless Compon. Lett. 11(5), 223–225 ( 2001).
[Crossref]

1998 (1)

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(5369), 1556–1564 ( 1998).
[Crossref] [PubMed]

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 ( 1992).
[Crossref]

Baba, T.

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80(12), 2051–2053 ( 2002).
[Crossref]

Baets, R.

Baryshnikov, Y.

Y. Baryshnikov, P. Heider, W. Parz, and V. Zharnitsky, “Whispering gallery modes inside asymmetric resonant cavities,” Phys. Rev. Lett. 93(13), 133902 ( 2004).
[Crossref] [PubMed]

Benson, T. M.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 ( 2006).
[Crossref]

Boriskina, S. V.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 ( 2006).
[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(5369), 1556–1564 ( 1998).
[Crossref] [PubMed]

Chang, R. K.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 ( 2003).
[Crossref]

Che, K. J.

Chen, Q.

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-Temperature Continuous-Wave Electrically Injected InP–GaInAsP Equilateral-Triangle-Resonator Lasers,” IEEE Photon. Technol. Lett. 19(13), 963–965 ( 2007).
[Crossref]

Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 ( 2007).
[Crossref]

Chern, G. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 ( 2003).
[Crossref]

Cho, A. Y.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280(5369), 1556–1564 ( 1998).
[Crossref] [PubMed]

Choi, 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(16), 164102 ( 2004).
[Crossref] [PubMed]

Choi, S. J.

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photon. Technol. Lett. 15(10), 1330–1332 ( 2003).
[Crossref]

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photon. Technol. Lett. 15(10), 1330–1332 ( 2003).
[Crossref]

Dapkus, P. D.

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photon. Technol. Lett. 15(10), 1330–1332 ( 2003).
[Crossref]

Di Cioccio, L.

Djordjev, K.

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photon. Technol. Lett. 15(10), 1330–1332 ( 2003).
[Crossref]

Du, Y.

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(5369), 1556–1564 ( 1998).
[Crossref] [PubMed]

Fan, Z. C.

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, Y. Du, and Z. C. Fan, “Directional emission InP/GaInAsP square-resonator microlasers,” Opt. Lett. 33(19), 2170–2172 ( 2008).
[Crossref] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-Temperature Continuous-Wave Electrically Injected InP–GaInAsP Equilateral-Triangle-Resonator Lasers,” IEEE Photon. Technol. Lett. 19(13), 963–965 ( 2007).
[Crossref]

Fedeli, J. M.

Fujita, M.

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80(12), 2051–2053 ( 2002).
[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(5369), 1556–1564 ( 1998).
[Crossref] [PubMed]

Guo, W. H.

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonator frequencies and quality factors of cavities by FDTD technique and padé approximation,” IEEE Microwave. Wireless Compon. Lett. 11(5), 223–225 ( 2001).
[Crossref]

Heider, P.

Y. Baryshnikov, P. Heider, W. Parz, and V. Zharnitsky, “Whispering gallery modes inside asymmetric resonant cavities,” Phys. Rev. Lett. 93(13), 133902 ( 2004).
[Crossref] [PubMed]

Hentschel, M.

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73(3), 031802 ( 2006).
[Crossref]

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5 Pt 2), 056207 ( 2002).
[Crossref] [PubMed]

Hu, Y. H.

Y. Z. Huang, S. J. Wang, Y. D. Yang, J. L. Xiao, Y. H. Hu, and Y. Du, “Optical bistability in InP/GaInAsP equilateral-triangle-resonator microlasers,” Opt. Lett. 34(12), 1852–1854 ( 2009).
[Crossref] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-Temperature Continuous-Wave Electrically Injected InP–GaInAsP Equilateral-Triangle-Resonator Lasers,” IEEE Photon. Technol. Lett. 19(13), 963–965 ( 2007).
[Crossref]

Huang, Y. Z.

Y. Z. Huang, S. J. Wang, Y. D. Yang, J. L. Xiao, Y. H. Hu, and Y. Du, “Optical bistability in InP/GaInAsP equilateral-triangle-resonator microlasers,” Opt. Lett. 34(12), 1852–1854 ( 2009).
[Crossref] [PubMed]

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, Y. Du, and Z. C. Fan, “Directional emission InP/GaInAsP square-resonator microlasers,” Opt. Lett. 33(19), 2170–2172 ( 2008).
[Crossref] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-Temperature Continuous-Wave Electrically Injected InP–GaInAsP Equilateral-Triangle-Resonator Lasers,” IEEE Photon. Technol. Lett. 19(13), 963–965 ( 2007).
[Crossref]

Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 ( 2007).
[Crossref]

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonator frequencies and quality factors of cavities by FDTD technique and padé approximation,” IEEE Microwave. Wireless Compon. Lett. 11(5), 223–225 ( 2001).
[Crossref]

Y. D. Yang, Y. Z. Huang, and S. J. Wang, “Mode analysis for equilateral–triangle -resonator microlasers with metal confinement layers,” IEEE J. Quantum Electron.in press.
[PubMed]

Johnson, N. M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 ( 2003).
[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(16), 164102 ( 2004).
[Crossref] [PubMed]

Kim, G. H.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 ( 2004).
[Crossref]

Kim, S. H.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 ( 2004).
[Crossref]

Kim, S. K.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 ( 2004).
[Crossref]

Kneissl, M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 ( 2003).
[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(16), 164102 ( 2004).
[Crossref] [PubMed]

Lagahe, C.

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(16), 164102 ( 2004).
[Crossref] [PubMed]

Lee, Y. H.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 ( 2004).
[Crossref]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 ( 1992).
[Crossref]

Li, W. J.

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonator frequencies and quality factors of cavities by FDTD technique and padé approximation,” IEEE Microwave. Wireless Compon. Lett. 11(5), 223–225 ( 2001).
[Crossref]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 ( 1992).
[Crossref]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 ( 1992).
[Crossref]

Narimanov, E. E.

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(5369), 1556–1564 ( 1998).
[Crossref] [PubMed]

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(5369), 1556–1564 ( 1998).
[Crossref] [PubMed]

Nosich, A. I.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 ( 2006).
[Crossref]

Park, H. G.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 ( 2004).
[Crossref]

Parz, W.

Y. Baryshnikov, P. Heider, W. Parz, and V. Zharnitsky, “Whispering gallery modes inside asymmetric resonant cavities,” Phys. Rev. Lett. 93(13), 133902 ( 2004).
[Crossref] [PubMed]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 ( 1992).
[Crossref]

Regreny, P.

Richter, K.

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5 Pt 2), 056207 ( 2002).
[Crossref] [PubMed]

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(16), 164102 ( 2004).
[Crossref] [PubMed]

Rojo Romeo, P.

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(16), 164102 ( 2004).
[Crossref] [PubMed]

Seassal, C.

Sewell, P.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 ( 2006).
[Crossref]

Shin, D. J.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 ( 2004).
[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(5369), 1556–1564 ( 1998).
[Crossref] [PubMed]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 ( 1992).
[Crossref]

Stone, A. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 ( 2003).
[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(5369), 1556–1564 ( 1998).
[Crossref] [PubMed]

Tureci, H. E.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 ( 2003).
[Crossref]

Van Campenhout, J.

Van Thourhout, D.

Verstuyft, S.

Wang, S. J.

Y. Z. Huang, S. J. Wang, Y. D. Yang, J. L. Xiao, Y. H. Hu, and Y. Du, “Optical bistability in InP/GaInAsP equilateral-triangle-resonator microlasers,” Opt. Lett. 34(12), 1852–1854 ( 2009).
[Crossref] [PubMed]

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, Y. Du, and Z. C. Fan, “Directional emission InP/GaInAsP square-resonator microlasers,” Opt. Lett. 33(19), 2170–2172 ( 2008).
[Crossref] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-Temperature Continuous-Wave Electrically Injected InP–GaInAsP Equilateral-Triangle-Resonator Lasers,” IEEE Photon. Technol. Lett. 19(13), 963–965 ( 2007).
[Crossref]

Y. D. Yang, Y. Z. Huang, and S. J. Wang, “Mode analysis for equilateral–triangle -resonator microlasers with metal confinement layers,” IEEE J. Quantum Electron.in press.
[PubMed]

Wiersig, J.

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73(3), 031802 ( 2006).
[Crossref]

Xiao, J. L.

Yang, Y. D.

Y. Z. Huang, S. J. Wang, Y. D. Yang, J. L. Xiao, Y. H. Hu, and Y. Du, “Optical bistability in InP/GaInAsP equilateral-triangle-resonator microlasers,” Opt. Lett. 34(12), 1852–1854 ( 2009).
[Crossref] [PubMed]

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, Y. Du, and Z. C. Fan, “Directional emission InP/GaInAsP square-resonator microlasers,” Opt. Lett. 33(19), 2170–2172 ( 2008).
[Crossref] [PubMed]

Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 ( 2007).
[Crossref]

Y. D. Yang, Y. Z. Huang, and S. J. Wang, “Mode analysis for equilateral–triangle -resonator microlasers with metal confinement layers,” IEEE J. Quantum Electron.in press.
[PubMed]

Zharnitsky, V.

Y. Baryshnikov, P. Heider, W. Parz, and V. Zharnitsky, “Whispering gallery modes inside asymmetric resonant cavities,” Phys. Rev. Lett. 93(13), 133902 ( 2004).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. 83(9), 1710–1712 ( 2003).
[Crossref]

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, “Highly directional emission from few-micron-size elliptical microdisks,” Appl. Phys. Lett. 84(6), 861–863 ( 2004).
[Crossref]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 ( 1992).
[Crossref]

M. Fujita and T. Baba, “Microgear laser,” Appl. Phys. Lett. 80(12), 2051–2053 ( 2002).
[Crossref]

IEEE J. Quantum Electron. (1)

Y. D. Yang, Y. Z. Huang, and S. J. Wang, “Mode analysis for equilateral–triangle -resonator microlasers with metal confinement layers,” IEEE J. Quantum Electron.in press.
[PubMed]

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

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors of 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 ( 2006).
[Crossref]

IEEE Microwave. Wireless Compon. Lett. (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonator frequencies and quality factors of cavities by FDTD technique and padé approximation,” IEEE Microwave. Wireless Compon. Lett. 11(5), 223–225 ( 2001).
[Crossref]

IEEE Photon. Technol. Lett. (2)

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photon. Technol. Lett. 15(10), 1330–1332 ( 2003).
[Crossref]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-Temperature Continuous-Wave Electrically Injected InP–GaInAsP Equilateral-Triangle-Resonator Lasers,” IEEE Photon. Technol. Lett. 19(13), 963–965 ( 2007).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (2)

Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A 75(1), 013817 ( 2007).
[Crossref]

J. Wiersig and M. Hentschel, “Unidirectional light emission from high-Q modes in optical microcavities,” Phys. Rev. A 73(3), 031802 ( 2006).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. Hentschel and K. Richter, “Quantum chaos in optical systems: the annular billiard,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5 Pt 2), 056207 ( 2002).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

Y. Baryshnikov, P. Heider, W. Parz, and V. Zharnitsky, “Whispering gallery modes inside asymmetric resonant cavities,” Phys. Rev. Lett. 93(13), 133902 ( 2004).
[Crossref] [PubMed]

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(16), 164102 ( 2004).
[Crossref] [PubMed]

Science (1)

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(5369), 1556–1564 ( 1998).
[Crossref] [PubMed]

Other (1)

A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method. (Boston: Artech House, 2005).

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Figures (5)
Fig. 1
Fig. 1 The triangular shaped mode field patterns constructed by the superposition of TM18,3 and TM15,4 with phase difference of (a) π and (b) 0 in the perfect microdisk

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Fig. 2
Fig. 2 The intensity spectra for TM modes obtained by FDTD simulation and Padé approximation for the 4.5-μm-diameter microdisk (a) with a 0.6-μm-wide output waveguide and (b) without the output waveguide, the circles mark the modes for coupling.

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Fig. 3
Fig. 3 The field distributions of the (a) high Q and (b) low Q TM coupled modes at wavelength of 1490 nm, and the (c) high Q and (d) low Q TM coupled mode at wavelength of 1786 nm in the 4.5-μm-diameter microdisk with a 0.6-μm-wide output waveguide. The field at the right side output waveguide is magnified 5 times for high Q coupled modes in (a) and (c).

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Fig. 4
Fig. 4 Mode Q factors and output coupling efficiencies versus the width of the output waveguide for (a) symmetric and (b) antisymmetric coupling modes in the 4.5-μm-diameter microdisk, where symbols S and L mark the coupling modes with short and long wavelengths around 1490 nm.

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Fig. 5
Fig. 5 The spectra of TE modes obtained by FDTD simulation and Padé approximation for a 5 μm diameter microdisk (a) with a 0.8-μm-wide output waveguide and (b) without the output waveguide, the circles mark the modes for coupling.

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Equations (1)

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J v ( n k 0 R ) H v ( 1 ) ' ( k 0 R ) = η J v ' ( n k 0 R ) H v ( 1 ) ( k 0 R ) ,

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