Abstract

Coupling between whispering-gallery modes of concentric microcavity lasers was analyzed, and a closed-form three-dimensional vectorial solution for the coupled fields was obtained. Experiments performed with concentric gain-guided vertical cavity ring lasers resulted in regimes of resonant coupling in good agreement with the theory.

© 1998 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, Appl. Phys. Lett. 60, 289 (1992).
    [CrossRef]
  2. N. C. Frateschi and A. F. J. Levi, Appl. Phys. Lett. 66, 2932 (1995).
    [CrossRef]
  3. B. Corbett, J. Justice, L. Considine, S. Walsh, and W. M. Kelly, IEEE Photon. Technol. Lett. 8, 855 (1996).
    [CrossRef]
  4. T. D. Lee, P. H. Cheng, J. S. Pan, K. Tai, Y. Lai, and W. Lin, Opt. Quantum Electron. 28, 1335 (1996).
    [CrossRef]
  5. M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
    [CrossRef]
  6. J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.
  7. J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, IEEE Photon. Technol. Lett. 8, 968 (1996).
    [CrossRef]
  8. S. Flügge, ed., Handbuch der Physik (Springer-Verlag, Berlin, 1958), Vol. XVI, p. 358.
  9. D. Arbel, L. Djaloshinski, and M. Orenstein, in Digest of the 15th IEEE International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), p. 79.
    [CrossRef]
  10. Q. Deng, H. Deng, and D. G. Deppe, Opt. Lett. 22, 463 (1997).
    [CrossRef] [PubMed]
  11. M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
    [CrossRef]

1997 (1)

1996 (3)

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, IEEE Photon. Technol. Lett. 8, 968 (1996).
[CrossRef]

B. Corbett, J. Justice, L. Considine, S. Walsh, and W. M. Kelly, IEEE Photon. Technol. Lett. 8, 855 (1996).
[CrossRef]

T. D. Lee, P. H. Cheng, J. S. Pan, K. Tai, Y. Lai, and W. Lin, Opt. Quantum Electron. 28, 1335 (1996).
[CrossRef]

1995 (2)

M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
[CrossRef]

N. C. Frateschi and A. F. J. Levi, Appl. Phys. Lett. 66, 2932 (1995).
[CrossRef]

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

1991 (1)

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

Arbel, D.

D. Arbel, L. Djaloshinski, and M. Orenstein, in Digest of the 15th IEEE International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), p. 79.
[CrossRef]

Bi, W. G.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, IEEE Photon. Technol. Lett. 8, 968 (1996).
[CrossRef]

Cheng, P. H.

T. D. Lee, P. H. Cheng, J. S. Pan, K. Tai, Y. Lai, and W. Lin, Opt. Quantum Electron. 28, 1335 (1996).
[CrossRef]

Chu, D. Y.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, IEEE Photon. Technol. Lett. 8, 968 (1996).
[CrossRef]

Chu, S.

J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.

Considine, L.

B. Corbett, J. Justice, L. Considine, S. Walsh, and W. M. Kelly, IEEE Photon. Technol. Lett. 8, 855 (1996).
[CrossRef]

Corbett, B.

B. Corbett, J. Justice, L. Considine, S. Walsh, and W. M. Kelly, IEEE Photon. Technol. Lett. 8, 855 (1996).
[CrossRef]

Deng, H.

Deng, Q.

Deppe, D. G.

Djaloshinski, L.

D. Arbel, L. Djaloshinski, and M. Orenstein, in Digest of the 15th IEEE International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), p. 79.
[CrossRef]

Florez, L. T.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

Foresi, J. S.

J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.

Frateschi, N. C.

N. C. Frateschi and A. F. J. Levi, Appl. Phys. Lett. 66, 2932 (1995).
[CrossRef]

Freiler, M. B.

M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
[CrossRef]

Greene, W.

J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.

Harbison, J. P.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

Haus, H.

J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.

Ho, S. T.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, IEEE Photon. Technol. Lett. 8, 968 (1996).
[CrossRef]

Hu, M. H.

M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
[CrossRef]

Ippen, E.

J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.

Justice, J.

B. Corbett, J. Justice, L. Considine, S. Walsh, and W. M. Kelly, IEEE Photon. Technol. Lett. 8, 855 (1996).
[CrossRef]

Kapon, E.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

Kelly, W. M.

B. Corbett, J. Justice, L. Considine, S. Walsh, and W. M. Kelly, IEEE Photon. Technol. Lett. 8, 855 (1996).
[CrossRef]

Kimerling, L.

J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.

Lai, Y.

T. D. Lee, P. H. Cheng, J. S. Pan, K. Tai, Y. Lai, and W. Lin, Opt. Quantum Electron. 28, 1335 (1996).
[CrossRef]

Lee, T. D.

T. D. Lee, P. H. Cheng, J. S. Pan, K. Tai, Y. Lai, and W. Lin, Opt. Quantum Electron. 28, 1335 (1996).
[CrossRef]

Levi, A. F. J.

N. C. Frateschi and A. F. J. Levi, Appl. Phys. Lett. 66, 2932 (1995).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Levy, M.

M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
[CrossRef]

Lin, W.

T. D. Lee, P. H. Cheng, J. S. Pan, K. Tai, Y. Lai, and W. Lin, Opt. Quantum Electron. 28, 1335 (1996).
[CrossRef]

Little, B.

J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Orenstein, M.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

D. Arbel, L. Djaloshinski, and M. Orenstein, in Digest of the 15th IEEE International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), p. 79.
[CrossRef]

Osgood, R. M.

M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
[CrossRef]

Pan, J. S.

T. D. Lee, P. H. Cheng, J. S. Pan, K. Tai, Y. Lai, and W. Lin, Opt. Quantum Electron. 28, 1335 (1996).
[CrossRef]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Scarmozzino, R.

M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
[CrossRef]

Shih, M. C.

M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
[CrossRef]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Steinmeyer, G.

J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.

Stoffel, N. G.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

Tai, K.

T. D. Lee, P. H. Cheng, J. S. Pan, K. Tai, Y. Lai, and W. Lin, Opt. Quantum Electron. 28, 1335 (1996).
[CrossRef]

Tao, I. W.

M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
[CrossRef]

Thoen, E.

J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.

Tiberio, R. C.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, IEEE Photon. Technol. Lett. 8, 968 (1996).
[CrossRef]

Tu, C. W.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, IEEE Photon. Technol. Lett. 8, 968 (1996).
[CrossRef]

Walsh, S.

B. Corbett, J. Justice, L. Considine, S. Walsh, and W. M. Kelly, IEEE Photon. Technol. Lett. 8, 855 (1996).
[CrossRef]

Wang, W. I.

M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
[CrossRef]

Wu, S. L.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, IEEE Photon. Technol. Lett. 8, 968 (1996).
[CrossRef]

Wullert, J.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

Zhang, J. P.

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, IEEE Photon. Technol. Lett. 8, 968 (1996).
[CrossRef]

Appl. Phys. Lett. (4)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

N. C. Frateschi and A. F. J. Levi, Appl. Phys. Lett. 66, 2932 (1995).
[CrossRef]

M. C. Shih, M. H. Hu, M. B. Freiler, M. Levy, R. Scarmozzino, R. M. Osgood, I. W. Tao, and W. I. Wang, Appl. Phys. Lett. 66, 2608 (1995).
[CrossRef]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, Appl. Phys. Lett. 58, 804 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J. P. Zhang, D. Y. Chu, S. L. Wu, W. G. Bi, R. C. Tiberio, C. W. Tu, and S. T. Ho, IEEE Photon. Technol. Lett. 8, 968 (1996).
[CrossRef]

B. Corbett, J. Justice, L. Considine, S. Walsh, and W. M. Kelly, IEEE Photon. Technol. Lett. 8, 855 (1996).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

T. D. Lee, P. H. Cheng, J. S. Pan, K. Tai, Y. Lai, and W. Lin, Opt. Quantum Electron. 28, 1335 (1996).
[CrossRef]

Other (3)

S. Flügge, ed., Handbuch der Physik (Springer-Verlag, Berlin, 1958), Vol. XVI, p. 358.

D. Arbel, L. Djaloshinski, and M. Orenstein, in Digest of the 15th IEEE International Semiconductor Laser Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), p. 79.
[CrossRef]

J. S. Foresi, B. Little, G. Steinmeyer, E. Thoen, S. Chu, H. Haus, E. Ippen, L. Kimerling, and W. Greene, in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1997), paper CPD22.

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Figures (4)

Fig. 1
Fig. 1

Experimental near-field intensity patterns at various injection currents. Current and pulse-width values are SE, 30  mA, 0.9 µs; l=6, 55  mA, 2.0 µs; l=7, 50  mA, 3.5 µs; l=11, 75  mA, 3.5 µs; l=12, 78  mA, 3.5 µs; l=30, 240  mA, 6.0 µs. For the l=30 mode the inner ring disappears.

Fig. 2
Fig. 2

Coupled l=6 mode. (a) Experimental near-field intensity, I=55 mA, tp=2.0 µs. (b) Calculated intensity pattern. (c) Refractive-index profile in the transform plane.

Fig. 3
Fig. 3

Coupled l=13 mode. (a) Experimental near-field intensity, I=100 mA, tp=3.5 µs. (b) Calculated intensity pattern. (c) Refractive-index profile in the transform plane.

Fig. 4
Fig. 4

Coupled l=30 mode. (a) Experimental near-field intensity, I=240 mA, tp=6.0 µs. (b) Calculated intensity pattern. (c) Refractive-index profile in the transform plane.

Equations (6)

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

u+iv=R lnr/R+iRϕ,
2u2+2v2+exp2uR2z2+k2UuVvZz=0,
Ezjlu, v, z=UlEξjucoslRv+αcoskzz+γ,
ξjk0nuvjRkj2-kz2 expu/RR,
Eujlu, v, z=1kj2-kz2×-kzUlEξj-iη0k0lξjUlHξj×coslRv+αsinkzz+γ,
Evjlu, v, z=1kj2-kz2×kzlξjUlEξj+iη0k0UlHξj×sinlRv+αsinkzz+γ,

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