Abstract

We have observed the emission spectra of three-dimensional Rayleigh-Fabry-Perot cavity whispering-gallery modes from photonic quantum ring lasers that give rise to uniform angular mode spacing in space. The observed angular distribution (0° ∼ 30°) of the emission modes is linear with respect to the mode number. For example, the average angular mode spacing is 0.95° with a standard deviation of 0.098° for a 20-µm-diameter laser, whose potential angle-resolving power is promising for angle-sensing applications in the future.

© 2003 Optical Society of America

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  1. J. C. Ahn, K. S. Kwak, B. H. Park, H. Y. Kang, J. Y. Kim, O’Dae Kwon, “Photonic quantum ring,” Phys. Rev. Lett. 82, 536–539 (1999).
    [CrossRef]
  2. B. H. Park, J. Bae, M. J. Kim, O’Dae Kwon, “Chiral wave propagation manifold of the photonic quantum ring laser,” Appl. Phys. Lett. 81, 580–582 (2002).
    [CrossRef]
  3. J. C. Ahn, H. Y. Kang, O’Dae Kwon, “Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser,” in Physics and Simulation of Optoelectronic Devices VI, M. Osinski, P. Blood, A. Ishibashi, eds., Proc. SPIE3283, 241–251 (1998).
    [CrossRef]
  4. J. Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, 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]
  5. J. Bae, J. Lee, O’Dae Kwon, V. G. Minogin, “Spectrum of three-dimensional photonic quantum ring microdisk cavities: comparison between theory and experiment,” Opt. Lett. (to be published).
  6. Although a 3-D ray optics view, based on a knot theory, was tentatively adopted in Ref. 2, a detailed analysis based on a 3-D Bragg diffraction law is reported in Ref. 5.
  7. E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
    [CrossRef]
  8. B. H. Park, S. D. Baek, J. Y. Kim, J. Bae, H. Han, O’Dae Kwon, “Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors,” Opt. Eng. 41, 1339–1345 (2002).
    [CrossRef]

2002

B. H. Park, J. Bae, M. J. Kim, 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, O’Dae Kwon, “Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors,” Opt. Eng. 41, 1339–1345 (2002).
[CrossRef]

2001

J. Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, 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]

1999

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

1992

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

Ahn, J. C.

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

J. C. Ahn, H. Y. Kang, O’Dae Kwon, “Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser,” in Physics and Simulation of Optoelectronic Devices VI, M. Osinski, P. Blood, A. Ishibashi, eds., Proc. SPIE3283, 241–251 (1998).
[CrossRef]

Bae, J.

B. H. Park, J. Bae, M. J. Kim, 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, O’Dae Kwon, “Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors,” Opt. Eng. 41, 1339–1345 (2002).
[CrossRef]

J. Bae, J. Lee, O’Dae Kwon, V. G. Minogin, “Spectrum of three-dimensional photonic quantum ring microdisk cavities: comparison between theory and experiment,” Opt. Lett. (to be published).

Baek, S. D.

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

Becker, P. C.

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

Feldman, L. C.

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

Han, H.

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

Hunt, N. E. J.

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

Jacobson, D. C.

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

Kang, B.

J. Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, 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, H. Y.

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

J. C. Ahn, H. Y. Kang, O’Dae Kwon, “Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser,” in Physics and Simulation of Optoelectronic Devices VI, M. Osinski, P. Blood, A. Ishibashi, eds., Proc. SPIE3283, 241–251 (1998).
[CrossRef]

Kim, J. S.

J. Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, 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.

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

J. Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, 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, O’Dae Kwon, “Photonic quantum ring,” Phys. Rev. Lett. 82, 536–539 (1999).
[CrossRef]

Kim, M. J.

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

Kwak, K. S.

J. Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, 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, O’Dae Kwon, “Photonic quantum ring,” Phys. Rev. Lett. 82, 536–539 (1999).
[CrossRef]

Kwon, O’Dae

B. H. Park, J. Bae, M. J. Kim, 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, O’Dae Kwon, “Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors,” Opt. Eng. 41, 1339–1345 (2002).
[CrossRef]

J. Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, 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, O’Dae Kwon, “Photonic quantum ring,” Phys. Rev. Lett. 82, 536–539 (1999).
[CrossRef]

J. C. Ahn, H. Y. Kang, O’Dae Kwon, “Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser,” in Physics and Simulation of Optoelectronic Devices VI, M. Osinski, P. Blood, A. Ishibashi, eds., Proc. SPIE3283, 241–251 (1998).
[CrossRef]

J. Bae, J. Lee, O’Dae Kwon, V. G. Minogin, “Spectrum of three-dimensional photonic quantum ring microdisk cavities: comparison between theory and experiment,” Opt. Lett. (to be published).

Lee, J.

J. Bae, J. Lee, O’Dae Kwon, V. G. Minogin, “Spectrum of three-dimensional photonic quantum ring microdisk cavities: comparison between theory and experiment,” Opt. Lett. (to be published).

Minogin, V. G.

J. Bae, J. Lee, O’Dae Kwon, V. G. Minogin, “Spectrum of three-dimensional photonic quantum ring microdisk cavities: comparison between theory and experiment,” Opt. Lett. (to be published).

Park, B. H.

B. H. Park, J. Bae, M. J. Kim, 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, O’Dae Kwon, “Optical sensing by using photonic quantum ring lasers and resonance enhanced photodetectors,” Opt. Eng. 41, 1339–1345 (2002).
[CrossRef]

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

Poate, J. M.

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

Schubert, E. F.

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

Vredenberg, A. M.

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

Wong, Y. H.

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

Zydzik, G. J.

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

Appl. Phys. Lett.

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

E. F. Schubert, A. M. Vredenberg, N. E. J. Hunt, Y. H. Wong, P. C. Becker, J. M. Poate, D. C. Jacobson, L. C. Feldman, G. J. Zydzik, “Giant enhancement of luminescence intensity in Er-doped Si/SiO2 resonant cavities,” Appl. Phys. Lett. 61, 1381–1383 (1992).
[CrossRef]

J. Vac. Sci. Technol. B

J. Y. Kim, K. S. Kwak, J. S. Kim, B. Kang, 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.

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

Phys. Rev. Lett.

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

Other

J. Bae, J. Lee, O’Dae Kwon, V. G. Minogin, “Spectrum of three-dimensional photonic quantum ring microdisk cavities: comparison between theory and experiment,” Opt. Lett. (to be published).

Although a 3-D ray optics view, based on a knot theory, was tentatively adopted in Ref. 2, a detailed analysis based on a 3-D Bragg diffraction law is reported in Ref. 5.

J. C. Ahn, H. Y. Kang, O’Dae Kwon, “Angle-dependent multiple-wavelength radial emissions in a toroidal microcavity: a photonic quantum ring laser,” in Physics and Simulation of Optoelectronic Devices VI, M. Osinski, P. Blood, A. Ishibashi, eds., Proc. SPIE3283, 241–251 (1998).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a cylindrical PQR laser and its angle-dependent spectrum measurement setup. A tapered multimode optical fiber probe having a 1.5-µm-diameter tip is directed to the PQR emission. DBR, distributed Bragg reflector.

Fig. 2
Fig. 2

(a) Near-field CCD micrograph of a PQR laser of 15 µm in diameter (I th = 7 µA) with the injection current I = 10 µA. (b) Spectral linewidth (FWHM) behavior of a 10-µm-diameter PQR laser against the injection currents showing a continuous line narrowing from 10 through 800 µA that is approximately 2 orders of magnitude above threshold. The inset is a spectrum measured in the near-surface normal direction (θv ≈ 0°) at 800 µA.

Fig. 3
Fig. 3

Multichromatic spectra of ϕ = 20 µm from a PQR laser at view angles of θv = 10° (solid curve) and θv = 15° (dotted curve) with an injection current of 2.5 mA.

Fig. 4
Fig. 4

Relationships between the view angle and the emission wavelength calculated by the off-normal Fabry-Perot condition (solid curve) and the measured spectral points of the envelope maxima at various view angles (filled squares).

Fig. 5
Fig. 5

(a) Wavelengths of the PQR lasing modes collected from the angle-dependent emission spectra of ϕ = 20 and ϕ = 45 µm measured from the PQR lasers. (b) Angular distribution of the emission modes (open symbols) and its linear fittings (solid lines). (c) Fluctuating angular mode spacings measured from the angular modes (filled symbols) and their average values (solid lines).

Equations (2)

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λθ=λ01-sinθ/n21/2,
θλ=sin-1n1-λ/λ021/2.

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