Abstract

We have fabricated three-dimensional (3D) photonic quantum ring lasers with an equilateral triangle microcavity. Their spectra were well explained by combining the off-normal resonance and hexagonally bounced in-plane whispering-gallery-mode condition. The angular distribution of the emission modes and their discrete wavelengths were shown to be in excellent agreement with a 3D Rayleigh Fabry–Perot model. We confirmed that the allowed modes in the equilateral triangle microcavity decrease by decreasing the length of equilateral triangle side, L, and the spectral mode spacing linearly increases with the mode index m and is inversely proportional to L2.

© 2007 Optical Society of America

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  1. Y. Yamamoto and R. E. Slusher, "Optical processes in microcavities," Phys. Today 46(6), 66-73 (1993).
    [CrossRef]
  2. M. Cai, G. Hunziker, and K. Vahala, "Fiber-optic add-drop device based on a silica microsphere-whispering gallery mode system," IEEE Photon. Technol. Lett. 11, 686-687 (1999).
    [CrossRef]
  3. H. Taniguchi, H. Tomisawa, and J. Kido, "Ultra-low-threshold europium chelate laser in morphology-dependent resonances," Appl. Phys. Lett. 66, 1578-1580 (1995).
    [CrossRef]
  4. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
    [CrossRef]
  5. A. F. J. Levi, R. E. Slusher, S. L. McCall, T. S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
    [CrossRef]
  6. D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, and S. T. Ho, "Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range," Opt. Lett. 22, 1244-1246 (1997).
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  7. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
    [CrossRef]
  8. A. W. Poon, F. Courvoisier, and R. K. Chang, "Multimode resonances in square-shaped optical microcavities," Opt. Lett. 26, 632-634 (2001).
    [CrossRef]
  9. H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
    [CrossRef]
  10. J. Bae, J. Lee, O'Dae Kwon, and V. G. Minogin, "Spectrum of three-dimensional photonic quantum-ring microdisk cavities: comparison between theory and experiment," Opt. Lett. 26, 632-635 (2003).
  11. J. Bae, B. H. Park, J. Y. Kim, and O'Dae Kwon, "Photonic quantum corral, carrier ordering, and photonic quantum dot/ring device," Inst. Phys. Conf. Ser. 170, 183-188 (2002).
  12. B. H. Park, J. Bae, M. J. Kim, and O'Dae Kwon, "Chiral wave propagation manifold of the photonic quantum ring laser," Appl. Phys. Lett. 81, 580-582 (2002).
    [CrossRef]
  13. J. C. Ahn, K. S. Kwak, B. H. Park, H. Y. Kang, J. Y. Kim, and O'Dae Kwon, "Photonic quantum ring," Phys. Rev. Lett. 82, 536-539 (1999).
    [CrossRef]
  14. B. H. Park, S. D. Baek, J. Y. Kim, J. Bae, H. Han, and O'Dae Kwon, "Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors," Opt. Eng. 41, 1339-1345 (2002).
    [CrossRef]
  15. B. H. Park, J. C. Ahn, J. Bae, J. Y. Kim, M. S. Kim, S. D. Baek, and O'Dae Kwon, "Evanescent and propagating wave characteristics of the photonic quantum ring laser," Appl. Phys. Lett. 79, 1593-1595 (2001).
    [CrossRef]
  16. J.-Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, and O'Dae Kwon, "Fabrication of photonic quantum ring laser using chemically assisted ion beam etching," J. Vac. Sci. Technol. B 19, 1334-1338 (2001).
    [CrossRef]
  17. J.-Y. Kim, J. Lee, J. Kim, B. K. Kang, and O'Dae Kwon, "Effect of surface treatment on leakage current of GaAs/AlGaAs laser microcavities," Appl. Phys. Lett. 82, 4504-4506 (2003).
    [CrossRef]
  18. J. C. Ahn, H. Y. Kang, and O'Dae Kwon, "Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser," Proc. SPIE 3283, 241-251 (1998).
    [CrossRef]
  19. J. Piprek, Semiconductor Optoelectronic Devices (Academic, 2003).
  20. O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
    [CrossRef]
  21. G. R. Hadley, "Effective index model for vertical-cavity surface-emitting lasers," Opt. Lett. 20, 1483-1485 (1995).
    [CrossRef] [PubMed]
  22. G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, "Comprehensive numerical modeling of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 32, 607-616 (1996).
    [CrossRef]
  23. Y. F. Chen, K. F. Huang, and Y. P. Lan, "Localization of wave patterns on classical periodic orbits in a square billiard," Phys. Rev. E 66, 046215 (2002).
    [CrossRef]

2006 (1)

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

2003 (2)

J. Bae, J. Lee, O'Dae Kwon, and V. G. Minogin, "Spectrum of three-dimensional photonic quantum-ring microdisk cavities: comparison between theory and experiment," Opt. Lett. 26, 632-635 (2003).

J.-Y. Kim, J. Lee, J. Kim, B. K. Kang, and O'Dae Kwon, "Effect of surface treatment on leakage current of GaAs/AlGaAs laser microcavities," Appl. Phys. Lett. 82, 4504-4506 (2003).
[CrossRef]

2002 (4)

B. H. Park, S. D. Baek, J. Y. Kim, J. Bae, H. Han, and O'Dae Kwon, "Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors," Opt. Eng. 41, 1339-1345 (2002).
[CrossRef]

J. Bae, B. H. Park, J. Y. Kim, and O'Dae Kwon, "Photonic quantum corral, carrier ordering, and photonic quantum dot/ring device," Inst. Phys. Conf. Ser. 170, 183-188 (2002).

B. H. Park, J. Bae, M. J. Kim, and O'Dae Kwon, "Chiral wave propagation manifold of the photonic quantum ring laser," Appl. Phys. Lett. 81, 580-582 (2002).
[CrossRef]

Y. F. Chen, K. F. Huang, and Y. P. Lan, "Localization of wave patterns on classical periodic orbits in a square billiard," Phys. Rev. E 66, 046215 (2002).
[CrossRef]

2001 (3)

B. H. Park, J. C. Ahn, J. Bae, J. Y. Kim, M. S. Kim, S. D. Baek, and O'Dae Kwon, "Evanescent and propagating wave characteristics of the photonic quantum ring laser," Appl. Phys. Lett. 79, 1593-1595 (2001).
[CrossRef]

J.-Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, and O'Dae Kwon, "Fabrication of photonic quantum ring laser using chemically assisted ion beam etching," J. Vac. Sci. Technol. B 19, 1334-1338 (2001).
[CrossRef]

A. W. Poon, F. Courvoisier, and R. K. Chang, "Multimode resonances in square-shaped optical microcavities," Opt. Lett. 26, 632-634 (2001).
[CrossRef]

2000 (2)

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

1999 (2)

M. Cai, G. Hunziker, and K. Vahala, "Fiber-optic add-drop device based on a silica microsphere-whispering gallery mode system," IEEE Photon. Technol. Lett. 11, 686-687 (1999).
[CrossRef]

J. C. Ahn, K. S. Kwak, B. H. Park, H. Y. Kang, J. Y. Kim, and O'Dae Kwon, "Photonic quantum ring," Phys. Rev. Lett. 82, 536-539 (1999).
[CrossRef]

1998 (1)

J. C. Ahn, H. Y. Kang, and O'Dae Kwon, "Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser," Proc. SPIE 3283, 241-251 (1998).
[CrossRef]

1997 (1)

1996 (1)

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, "Comprehensive numerical modeling of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

1995 (2)

G. R. Hadley, "Effective index model for vertical-cavity surface-emitting lasers," Opt. Lett. 20, 1483-1485 (1995).
[CrossRef] [PubMed]

H. Taniguchi, H. Tomisawa, and J. Kido, "Ultra-low-threshold europium chelate laser in morphology-dependent resonances," Appl. Phys. Lett. 66, 1578-1580 (1995).
[CrossRef]

1993 (2)

Y. Yamamoto and R. E. Slusher, "Optical processes in microcavities," Phys. Today 46(6), 66-73 (1993).
[CrossRef]

A. F. J. Levi, R. E. Slusher, S. L. McCall, T. S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

1992 (1)

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

Absil, P. P.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

Ahn, J.

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

Ahn, J. C.

B. H. Park, J. C. Ahn, J. Bae, J. Y. Kim, M. S. Kim, S. D. Baek, and O'Dae Kwon, "Evanescent and propagating wave characteristics of the photonic quantum ring laser," Appl. Phys. Lett. 79, 1593-1595 (2001).
[CrossRef]

J. C. Ahn, K. S. Kwak, B. H. Park, H. Y. Kang, J. Y. Kim, and O'Dae Kwon, "Photonic quantum ring," Phys. Rev. Lett. 82, 536-539 (1999).
[CrossRef]

J. C. Ahn, H. Y. Kang, and O'Dae Kwon, "Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser," Proc. SPIE 3283, 241-251 (1998).
[CrossRef]

An, S.-J.

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

Bae, J.

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

J. Bae, J. Lee, O'Dae Kwon, and V. G. Minogin, "Spectrum of three-dimensional photonic quantum-ring microdisk cavities: comparison between theory and experiment," Opt. Lett. 26, 632-635 (2003).

J. Bae, B. H. Park, J. Y. Kim, and O'Dae Kwon, "Photonic quantum corral, carrier ordering, and photonic quantum dot/ring device," Inst. Phys. Conf. Ser. 170, 183-188 (2002).

B. H. Park, J. Bae, M. J. Kim, and O'Dae Kwon, "Chiral wave propagation manifold of the photonic quantum ring laser," Appl. Phys. Lett. 81, 580-582 (2002).
[CrossRef]

B. H. Park, S. D. Baek, J. Y. Kim, J. Bae, H. Han, and O'Dae Kwon, "Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors," Opt. Eng. 41, 1339-1345 (2002).
[CrossRef]

B. H. Park, J. C. Ahn, J. Bae, J. Y. Kim, M. S. Kim, S. D. Baek, and O'Dae Kwon, "Evanescent and propagating wave characteristics of the photonic quantum ring laser," Appl. Phys. Lett. 79, 1593-1595 (2001).
[CrossRef]

Baek, S. D.

B. H. Park, S. D. Baek, J. Y. Kim, J. Bae, H. Han, and O'Dae Kwon, "Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors," Opt. Eng. 41, 1339-1345 (2002).
[CrossRef]

B. H. Park, J. C. Ahn, J. Bae, J. Y. Kim, M. S. Kim, S. D. Baek, and O'Dae Kwon, "Evanescent and propagating wave characteristics of the photonic quantum ring laser," Appl. Phys. Lett. 79, 1593-1595 (2001).
[CrossRef]

Cai, M.

M. Cai, G. Hunziker, and K. Vahala, "Fiber-optic add-drop device based on a silica microsphere-whispering gallery mode system," IEEE Photon. Technol. Lett. 11, 686-687 (1999).
[CrossRef]

Chang, H. C.

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
[CrossRef]

Chang, R. K.

Chen, Y. F.

Y. F. Chen, K. F. Huang, and Y. P. Lan, "Localization of wave patterns on classical periodic orbits in a square billiard," Phys. Rev. E 66, 046215 (2002).
[CrossRef]

Choquette, K. D.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, "Comprehensive numerical modeling of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

Corzine, S. W.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, "Comprehensive numerical modeling of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

Courvoisier, F.

Hadley, G. R.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, "Comprehensive numerical modeling of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

G. R. Hadley, "Effective index model for vertical-cavity surface-emitting lasers," Opt. Lett. 20, 1483-1485 (1995).
[CrossRef] [PubMed]

Hagness, S. C.

Han, H.

B. H. Park, S. D. Baek, J. Y. Kim, J. Bae, H. Han, and O'Dae Kwon, "Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors," Opt. Eng. 41, 1339-1345 (2002).
[CrossRef]

Heatty, J.

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
[CrossRef]

Ho, P.-T.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

Ho, S. T.

Hobson, W. S.

A. F. J. Levi, R. E. Slusher, S. L. McCall, T. S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

Hryniewicz, J. V.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

Huang, K. F.

Y. F. Chen, K. F. Huang, and Y. P. Lan, "Localization of wave patterns on classical periodic orbits in a square billiard," Phys. Rev. E 66, 046215 (2002).
[CrossRef]

Hunziker, G.

M. Cai, G. Hunziker, and K. Vahala, "Fiber-optic add-drop device based on a silica microsphere-whispering gallery mode system," IEEE Photon. Technol. Lett. 11, 686-687 (1999).
[CrossRef]

Kang, B.

J.-Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, and O'Dae Kwon, "Fabrication of photonic quantum ring laser using chemically assisted ion beam etching," J. Vac. Sci. Technol. B 19, 1334-1338 (2001).
[CrossRef]

Kang, B. K.

J.-Y. Kim, J. Lee, J. Kim, B. K. Kang, and O'Dae Kwon, "Effect of surface treatment on leakage current of GaAs/AlGaAs laser microcavities," Appl. Phys. Lett. 82, 4504-4506 (2003).
[CrossRef]

Kang, H. Y.

J. C. Ahn, K. S. Kwak, B. H. Park, H. Y. Kang, J. Y. Kim, and O'Dae Kwon, "Photonic quantum ring," Phys. Rev. Lett. 82, 536-539 (1999).
[CrossRef]

J. C. Ahn, H. Y. Kang, and O'Dae Kwon, "Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser," Proc. SPIE 3283, 241-251 (1998).
[CrossRef]

Kido, J.

H. Taniguchi, H. Tomisawa, and J. Kido, "Ultra-low-threshold europium chelate laser in morphology-dependent resonances," Appl. Phys. Lett. 66, 1578-1580 (1995).
[CrossRef]

Kim, D. K.

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

Kim, J.

J.-Y. Kim, J. Lee, J. Kim, B. K. Kang, and O'Dae Kwon, "Effect of surface treatment on leakage current of GaAs/AlGaAs laser microcavities," Appl. Phys. Lett. 82, 4504-4506 (2003).
[CrossRef]

Kim, J. S.

J.-Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, and O'Dae Kwon, "Fabrication of photonic quantum ring laser using chemically assisted ion beam etching," J. Vac. Sci. Technol. B 19, 1334-1338 (2001).
[CrossRef]

Kim, J. Y.

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

J. Bae, B. H. Park, J. Y. Kim, and O'Dae Kwon, "Photonic quantum corral, carrier ordering, and photonic quantum dot/ring device," Inst. Phys. Conf. Ser. 170, 183-188 (2002).

B. H. Park, S. D. Baek, J. Y. Kim, J. Bae, H. Han, and O'Dae Kwon, "Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors," Opt. Eng. 41, 1339-1345 (2002).
[CrossRef]

B. H. Park, J. C. Ahn, J. Bae, J. Y. Kim, M. S. Kim, S. D. Baek, and O'Dae Kwon, "Evanescent and propagating wave characteristics of the photonic quantum ring laser," Appl. Phys. Lett. 79, 1593-1595 (2001).
[CrossRef]

J. C. Ahn, K. S. Kwak, B. H. Park, H. Y. Kang, J. Y. Kim, and O'Dae Kwon, "Photonic quantum ring," Phys. Rev. Lett. 82, 536-539 (1999).
[CrossRef]

Kim, J.-Y.

J.-Y. Kim, J. Lee, J. Kim, B. K. Kang, and O'Dae Kwon, "Effect of surface treatment on leakage current of GaAs/AlGaAs laser microcavities," Appl. Phys. Lett. 82, 4504-4506 (2003).
[CrossRef]

J.-Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, and O'Dae Kwon, "Fabrication of photonic quantum ring laser using chemically assisted ion beam etching," J. Vac. Sci. Technol. B 19, 1334-1338 (2001).
[CrossRef]

Kim, M. J.

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

B. H. Park, J. Bae, M. J. Kim, and O'Dae Kwon, "Chiral wave propagation manifold of the photonic quantum ring laser," Appl. Phys. Lett. 81, 580-582 (2002).
[CrossRef]

Kim, M. S.

B. H. Park, J. C. Ahn, J. Bae, J. Y. Kim, M. S. Kim, S. D. Baek, and O'Dae Kwon, "Evanescent and propagating wave characteristics of the photonic quantum ring laser," Appl. Phys. Lett. 79, 1593-1595 (2001).
[CrossRef]

Kioseoglou, G.

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
[CrossRef]

Kwak, K. S.

J.-Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, and O'Dae Kwon, "Fabrication of photonic quantum ring laser using chemically assisted ion beam etching," J. Vac. Sci. Technol. B 19, 1334-1338 (2001).
[CrossRef]

J. C. Ahn, K. S. Kwak, B. H. Park, H. Y. Kang, J. Y. Kim, and O'Dae Kwon, "Photonic quantum ring," Phys. Rev. Lett. 82, 536-539 (1999).
[CrossRef]

Kwon, O'Dae

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

J.-Y. Kim, J. Lee, J. Kim, B. K. Kang, and O'Dae Kwon, "Effect of surface treatment on leakage current of GaAs/AlGaAs laser microcavities," Appl. Phys. Lett. 82, 4504-4506 (2003).
[CrossRef]

J. Bae, J. Lee, O'Dae Kwon, and V. G. Minogin, "Spectrum of three-dimensional photonic quantum-ring microdisk cavities: comparison between theory and experiment," Opt. Lett. 26, 632-635 (2003).

B. H. Park, J. Bae, M. J. Kim, and O'Dae Kwon, "Chiral wave propagation manifold of the photonic quantum ring laser," Appl. Phys. Lett. 81, 580-582 (2002).
[CrossRef]

J. Bae, B. H. Park, J. Y. Kim, and O'Dae Kwon, "Photonic quantum corral, carrier ordering, and photonic quantum dot/ring device," Inst. Phys. Conf. Ser. 170, 183-188 (2002).

B. H. Park, S. D. Baek, J. Y. Kim, J. Bae, H. Han, and O'Dae Kwon, "Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors," Opt. Eng. 41, 1339-1345 (2002).
[CrossRef]

B. H. Park, J. C. Ahn, J. Bae, J. Y. Kim, M. S. Kim, S. D. Baek, and O'Dae Kwon, "Evanescent and propagating wave characteristics of the photonic quantum ring laser," Appl. Phys. Lett. 79, 1593-1595 (2001).
[CrossRef]

J.-Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, and O'Dae Kwon, "Fabrication of photonic quantum ring laser using chemically assisted ion beam etching," J. Vac. Sci. Technol. B 19, 1334-1338 (2001).
[CrossRef]

J. C. Ahn, K. S. Kwak, B. H. Park, H. Y. Kang, J. Y. Kim, and O'Dae Kwon, "Photonic quantum ring," Phys. Rev. Lett. 82, 536-539 (1999).
[CrossRef]

J. C. Ahn, H. Y. Kang, and O'Dae Kwon, "Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser," Proc. SPIE 3283, 241-251 (1998).
[CrossRef]

Lan, Y. P.

Y. F. Chen, K. F. Huang, and Y. P. Lan, "Localization of wave patterns on classical periodic orbits in a square billiard," Phys. Rev. E 66, 046215 (2002).
[CrossRef]

Lear, K. L.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, "Comprehensive numerical modeling of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

Lee, E. H.

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
[CrossRef]

Lee, J.

J. Bae, J. Lee, O'Dae Kwon, and V. G. Minogin, "Spectrum of three-dimensional photonic quantum-ring microdisk cavities: comparison between theory and experiment," Opt. Lett. 26, 632-635 (2003).

J.-Y. Kim, J. Lee, J. Kim, B. K. Kang, and O'Dae Kwon, "Effect of surface treatment on leakage current of GaAs/AlGaAs laser microcavities," Appl. Phys. Lett. 82, 4504-4506 (2003).
[CrossRef]

Lee, S. E.

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

Levi, A. F. J.

A. F. J. Levi, R. E. Slusher, S. L. McCall, T. S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

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

Little, B. E.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[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, 289-291 (1992).
[CrossRef]

Luo, H.

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
[CrossRef]

McCall, S. L.

A. F. J. Levi, R. E. Slusher, S. L. McCall, T. S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

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

Minogin, V. G.

Na, M. H.

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
[CrossRef]

Park, B. H.

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

J. Bae, B. H. Park, J. Y. Kim, and O'Dae Kwon, "Photonic quantum corral, carrier ordering, and photonic quantum dot/ring device," Inst. Phys. Conf. Ser. 170, 183-188 (2002).

B. H. Park, S. D. Baek, J. Y. Kim, J. Bae, H. Han, and O'Dae Kwon, "Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors," Opt. Eng. 41, 1339-1345 (2002).
[CrossRef]

B. H. Park, J. Bae, M. J. Kim, and O'Dae Kwon, "Chiral wave propagation manifold of the photonic quantum ring laser," Appl. Phys. Lett. 81, 580-582 (2002).
[CrossRef]

B. H. Park, J. C. Ahn, J. Bae, J. Y. Kim, M. S. Kim, S. D. Baek, and O'Dae Kwon, "Evanescent and propagating wave characteristics of the photonic quantum ring laser," Appl. Phys. Lett. 79, 1593-1595 (2001).
[CrossRef]

J. C. Ahn, K. S. Kwak, B. H. Park, H. Y. Kang, J. Y. Kim, and O'Dae Kwon, "Photonic quantum ring," Phys. Rev. Lett. 82, 536-539 (1999).
[CrossRef]

Pearton, S. J.

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

Pearton, T. S. J.

A. F. J. Levi, R. E. Slusher, S. L. McCall, T. S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

Petrou, A.

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
[CrossRef]

Piprek, J.

J. Piprek, Semiconductor Optoelectronic Devices (Academic, 2003).

Poon, A. W.

Rafizadeh, D.

Scott, J. W.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, "Comprehensive numerical modeling of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

Slusher, R. E.

A. F. J. Levi, R. E. Slusher, S. L. McCall, T. S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

Y. Yamamoto and R. E. Slusher, "Optical processes in microcavities," Phys. Today 46(6), 66-73 (1993).
[CrossRef]

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

Stair, K. A.

Taflove, A.

Taniguchi, H.

H. Taniguchi, H. Tomisawa, and J. Kido, "Ultra-low-threshold europium chelate laser in morphology-dependent resonances," Appl. Phys. Lett. 66, 1578-1580 (1995).
[CrossRef]

Tomisawa, H.

H. Taniguchi, H. Tomisawa, and J. Kido, "Ultra-low-threshold europium chelate laser in morphology-dependent resonances," Appl. Phys. Lett. 66, 1578-1580 (1995).
[CrossRef]

Vahala, K.

M. Cai, G. Hunziker, and K. Vahala, "Fiber-optic add-drop device based on a silica microsphere-whispering gallery mode system," IEEE Photon. Technol. Lett. 11, 686-687 (1999).
[CrossRef]

Warren, M. E.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, "Comprehensive numerical modeling of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

Wilson, R. A.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

Xuan, Y.

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
[CrossRef]

Yamamoto, Y.

Y. Yamamoto and R. E. Slusher, "Optical processes in microcavities," Phys. Today 46(6), 66-73 (1993).
[CrossRef]

Yoon, J. H.

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

Zhang, J. P.

Appl. Phys. Lett. (7)

H. Taniguchi, H. Tomisawa, and J. Kido, "Ultra-low-threshold europium chelate laser in morphology-dependent resonances," Appl. Phys. Lett. 66, 1578-1580 (1995).
[CrossRef]

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

A. F. J. Levi, R. E. Slusher, S. L. McCall, T. S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

B. H. Park, J. Bae, M. J. Kim, and O'Dae Kwon, "Chiral wave propagation manifold of the photonic quantum ring laser," Appl. Phys. Lett. 81, 580-582 (2002).
[CrossRef]

B. H. Park, J. C. Ahn, J. Bae, J. Y. Kim, M. S. Kim, S. D. Baek, and O'Dae Kwon, "Evanescent and propagating wave characteristics of the photonic quantum ring laser," Appl. Phys. Lett. 79, 1593-1595 (2001).
[CrossRef]

J.-Y. Kim, J. Lee, J. Kim, B. K. Kang, and O'Dae Kwon, "Effect of surface treatment on leakage current of GaAs/AlGaAs laser microcavities," Appl. Phys. Lett. 82, 4504-4506 (2003).
[CrossRef]

O'Dae Kwon, M. J. Kim, S.-J. An, D. K. Kim, S. E. Lee, J. Bae, J. H. Yoon, B. H. Park, J. Y. Kim, and J. Ahn, "Hole emitter of photonic quantum ring," Appl. Phys. Lett. 89, 11108 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, "Comprehensive numerical modeling of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

M. Cai, G. Hunziker, and K. Vahala, "Fiber-optic add-drop device based on a silica microsphere-whispering gallery mode system," IEEE Photon. Technol. Lett. 11, 686-687 (1999).
[CrossRef]

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, "Higher order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

Inst. Phys. Conf. Ser. (1)

J. Bae, B. H. Park, J. Y. Kim, and O'Dae Kwon, "Photonic quantum corral, carrier ordering, and photonic quantum dot/ring device," Inst. Phys. Conf. Ser. 170, 183-188 (2002).

J. Vac. Sci. Technol. B (1)

J.-Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, and O'Dae Kwon, "Fabrication of photonic quantum ring laser using chemically assisted ion beam etching," J. Vac. Sci. Technol. B 19, 1334-1338 (2001).
[CrossRef]

Opt. Eng. (1)

B. H. Park, S. D. Baek, J. Y. Kim, J. Bae, H. Han, and O'Dae Kwon, "Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors," Opt. Eng. 41, 1339-1345 (2002).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

H. C. Chang, G. Kioseoglou, E. H. Lee, J. Heatty, M. H. Na, Y. Xuan, H. Luo, and A. Petrou, "Lasing modes in equilateral-triangular laser cavities," Phys. Rev. A 62, 013816 (2000).
[CrossRef]

Phys. Rev. E (1)

Y. F. Chen, K. F. Huang, and Y. P. Lan, "Localization of wave patterns on classical periodic orbits in a square billiard," Phys. Rev. E 66, 046215 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

J. C. Ahn, K. S. Kwak, B. H. Park, H. Y. Kang, J. Y. Kim, and O'Dae Kwon, "Photonic quantum ring," Phys. Rev. Lett. 82, 536-539 (1999).
[CrossRef]

Phys. Today (1)

Y. Yamamoto and R. E. Slusher, "Optical processes in microcavities," Phys. Today 46(6), 66-73 (1993).
[CrossRef]

Proc. SPIE (1)

J. C. Ahn, H. Y. Kang, and O'Dae Kwon, "Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser," Proc. SPIE 3283, 241-251 (1998).
[CrossRef]

Other (1)

J. Piprek, Semiconductor Optoelectronic Devices (Academic, 2003).

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Figures (8)

Fig. 1
Fig. 1

(a) SEM image of the sidewall profile of the etched structure (side length L = 15   μm ) and (b) a schematic diagram of the PQR laser with the ETM and the experimental setup used to measure its angle-dependent spectrum.

Fig. 2
Fig. 2

(a) Side view of light bouncing between the DBRs with an incident angle θ in in the ETM of thickness 1 λ ; (b) top view showing the lateral propagation of the light wave in the ETM with side length L. The solid and dashed lines show closed ray trajectories with ϕ = 30 ° .

Fig. 3
Fig. 3

L–I curves of the PQR with the ETM [ L = 15 (triangles), 20 (circles), and 25   μm (squares)]. Inserts are the emission CCD images at threshold current.

Fig. 4
Fig. 4

Spectra of the PQR laser with the ETM ( L = 25   μm ) at the off-normal view angles α v 15 ° (left envelope) and α v 10 ° (right envelope) with an injection current of 2.3   mA . The dashed lines are the spectra's envelopes and vertical stems show the positions of the emission modes.

Fig. 5
Fig. 5

Spectral mode spacing Δ λ m measured from the spectra of the PQR lasers with the ETMs L = 25 (circles) and 40   μm (squares) and their linear extrapolations (solid lines).

Fig. 6
Fig. 6

(a) Emission mode wavelengths, λ m , measured from the spectra (circles and squares), and calculated using Eq. (5) (solid lines); (b) the emission angles, β m , evaluated from the measured wavelengths and Eq. (6) (circles and squares), and from the calculated wavelengths and Eq. (6) (solid curves).

Fig. 7
Fig. 7

Slopes of the spectral mode spacing, Δ λ m , for seven different side lengths L = 10 , 15, 20, 25, 30, 35, and 40   μm .

Fig. 8
Fig. 8

(Color online) See Appendix A.

Equations (11)

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

k z = k cos θ in , k t = k sin θ in ,
λ m = λ 0 n m n 0 [ 1 + ( λ 0 m 3 L n 0 ) 2 ] 1 / 2 .
β m = sin 1 { m λ 0 3 L n m n 0 [ 1 + ( λ 0 m 3 L n 0 ) 2 ] 1 / 2 } .
n m = n 0 + γ ( λ m λ 0 ) ,
λ m = λ 0 ( 1 γ λ 0 / n 0 ) [ 1 + ( λ 0 m 3 L n 0 ) 2 ] 1 / 2 γ λ 0 n 0 ,
β m = sin 1 ( m λ m 3 L ) ,
Δ λ m λ 0 3 9 L 2 n 0 2 m .
B C ¯ 2 = A B ¯ 2 + A C ¯ 2 = l 2 ( tan 2 ϕ + 1 tan 2 θ ) ,
B C ¯ 2 = l 2 ( 1 cos 2 ϕ + 1 sin 2 θ 2 cos ϕ sin θ cos ε ) .
cos ε = cos ϕ sin θ .
tan θ in = tan θ sin ϕ ,

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