Abstract

Mechanisms of whispering-gallery (WG)-mode coupling in microdisk photonic molecules (PMs) with slight and significant size mismatches are numerically investigated. The results reveal two different scenarios of modes interaction depending on the degree of this mismatch and offer new insight into how PM parameters can be tuned to control and modify WG-mode wavelengths and Q factors. From a practical point of view, these findings offer a way to fabricate PM microlaser structures that exhibit low thresholds and directional emission and at the same time are more tolerant to fabrication errors than previously explored coupled-cavity structures composed of identical microresonators.

© 2007 Optical Society of America

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  1. M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, and P. A. Knipp, Phys. Rev. Lett. 81, 2582 (1998).
    [CrossRef]
  2. A. Nakagawa, S. Ishii, and T. Baba, Appl. Phys. Lett. 86, 041112 (2005).
    [CrossRef]
  3. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
    [CrossRef]
  4. Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
    [CrossRef]
  5. B. Moller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113-S121 (2006).
    [CrossRef]
  6. S. V. Boriskina, Opt. Lett. 31, 338 (2006).
    [CrossRef] [PubMed]
  7. S. V. Boriskina, J. Opt. Soc. Am. B 23, 1565 (2006).
    [CrossRef]
  8. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Sel. Top. Quantum Electron. 12, 1175 (2006).
    [CrossRef]
  9. S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
    [CrossRef]
  10. A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
    [CrossRef]
  11. W. D. Heiss, Phys. Rev. E 61, 929-932 (2000).
    [CrossRef]
  12. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
    [CrossRef]
  13. S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, "Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends," submitted to J. Lightwave Technol.
  14. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, J. Lightwave Technol. 20, 1563 (2002).
    [CrossRef]
  15. X.-S. Luo, Y.-Z. Huang, and Q. Chen, Opt. Lett. 31, 1073 (2006).
    [CrossRef] [PubMed]
  16. J. Wiersig and M. Hentschel, Phys. Rev. A 73, 031802 (2006).
    [CrossRef]

2006 (9)

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

B. Moller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113-S121 (2006).
[CrossRef]

S. V. Boriskina, Opt. Lett. 31, 338 (2006).
[CrossRef] [PubMed]

S. V. Boriskina, J. Opt. Soc. Am. B 23, 1565 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Sel. Top. Quantum Electron. 12, 1175 (2006).
[CrossRef]

S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
[CrossRef]

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

X.-S. Luo, Y.-Z. Huang, and Q. Chen, Opt. Lett. 31, 1073 (2006).
[CrossRef] [PubMed]

J. Wiersig and M. Hentschel, Phys. Rev. A 73, 031802 (2006).
[CrossRef]

2005 (1)

A. Nakagawa, S. Ishii, and T. Baba, Appl. Phys. Lett. 86, 041112 (2005).
[CrossRef]

2004 (2)

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

2002 (1)

2000 (1)

W. D. Heiss, Phys. Rev. E 61, 929-932 (2000).
[CrossRef]

1998 (1)

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, and P. A. Knipp, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Artemyev, M. V.

B. Moller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113-S121 (2006).
[CrossRef]

Astratov, V. N.

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

Baba, T.

S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
[CrossRef]

A. Nakagawa, S. Ishii, and T. Baba, Appl. Phys. Lett. 86, 041112 (2005).
[CrossRef]

Bayer, M.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, and P. A. Knipp, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Benson, T. M.

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Sel. Top. Quantum Electron. 12, 1175 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, J. Lightwave Technol. 20, 1563 (2002).
[CrossRef]

S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, "Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends," submitted to J. Lightwave Technol.

Boland, J. J.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
[CrossRef]

Boriskina, S. V.

S. V. Boriskina, Opt. Lett. 31, 338 (2006).
[CrossRef] [PubMed]

S. V. Boriskina, J. Opt. Soc. Am. B 23, 1565 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Sel. Top. Quantum Electron. 12, 1175 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, J. Lightwave Technol. 20, 1563 (2002).
[CrossRef]

S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, "Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends," submitted to J. Lightwave Technol.

Boyd, R. W.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Bradley, A. L.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
[CrossRef]

Cai, W.

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

Chang, H.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Chen, Q.

Connolly, T. M.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
[CrossRef]

Donegan, J. F.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
[CrossRef]

Forchel, A.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, and P. A. Knipp, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Fuller, K. A.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Gaponik, N.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
[CrossRef]

Gerlach, M.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
[CrossRef]

Gutbrod, T.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, and P. A. Knipp, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Heiss, W. D.

W. D. Heiss, Phys. Rev. E 61, 929-932 (2000).
[CrossRef]

Hentschel, M.

J. Wiersig and M. Hentschel, Phys. Rev. A 73, 031802 (2006).
[CrossRef]

Huang, Y.-Z.

Ishii, S.

S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
[CrossRef]

A. Nakagawa, S. Ishii, and T. Baba, Appl. Phys. Lett. 86, 041112 (2005).
[CrossRef]

Kanaev, A. V.

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

Knipp, P. A.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, and P. A. Knipp, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Luo, X.-S.

Moller, B.

B. Moller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113-S121 (2006).
[CrossRef]

Nakagawa, A.

S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
[CrossRef]

A. Nakagawa, S. Ishii, and T. Baba, Appl. Phys. Lett. 86, 041112 (2005).
[CrossRef]

Nosich, A. I.

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Sel. Top. Quantum Electron. 12, 1175 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, J. Lightwave Technol. 20, 1563 (2002).
[CrossRef]

Pishko, S. V.

S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, "Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends," submitted to J. Lightwave Technol.

Rakovich, Y. P.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
[CrossRef]

Reinecke, T. L.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, and P. A. Knipp, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Reithmaier, J. P.

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, and P. A. Knipp, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Rogach, A.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
[CrossRef]

Rosenberger, A. T.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Sewell, P.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Sel. Top. Quantum Electron. 12, 1175 (2006).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, J. Lightwave Technol. 20, 1563 (2002).
[CrossRef]

S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, "Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends," submitted to J. Lightwave Technol.

Smith, D. D.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Smotrova, E. I.

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

Wiersig, J.

J. Wiersig and M. Hentschel, Phys. Rev. A 73, 031802 (2006).
[CrossRef]

Woggon, U.

B. Moller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113-S121 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

A. Nakagawa, S. Ishii, and T. Baba, Appl. Phys. Lett. 86, 041112 (2005).
[CrossRef]

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (3)

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Sel. Top. Quantum Electron. 12, 1175 (2006).
[CrossRef]

S. Ishii, A. Nakagawa, and T. Baba, IEEE J. Sel. Top. Quantum Electron. 12, 71 (2006).
[CrossRef]

J. Lightwave Technol. (2)

S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, "Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends," submitted to J. Lightwave Technol.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, J. Lightwave Technol. 20, 1563 (2002).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

B. Moller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113-S121 (2006).
[CrossRef]

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

Opt. Lett. (2)

Phys. Rev. A (3)

J. Wiersig and M. Hentschel, Phys. Rev. A 73, 031802 (2006).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, Phys. Rev. A 69, 063804 (2004).
[CrossRef]

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bradley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801(R) (2004).
[CrossRef]

Phys. Rev. E (1)

W. D. Heiss, Phys. Rev. E 61, 929-932 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, and P. A. Knipp, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Geometry of a PM composed of two microdisks of different radii; (b) wavelength migration and (c) Q factor change of PM supermodes as a function of the radius of disk B ( R A = 1.1 μ m , w = 400 nm ). The insets show the magnetic field distribution of the bonding (EE) and the antibonding (OE) WG 8 , 1 supermodes in the symmetrical ( R A = R B = 1.1 μ m ) PM. Here and hereafter, corresponding characteristics of the WG 8 , 1 mode of an isolated cavity with radius 1.1 μ m are plotted for comparison (dashed-dotted line).

Fig. 2
Fig. 2

Supermode wavelengths (left) and Q factors (right) in the vicinity of anticrossing point AC 1 ( R B = R A ) . Mode switching (see the modal near-field distributions at points A and B shown in the insets) and Q-factor enhancement of one of the supermodes can be observed.

Fig. 3
Fig. 3

Supermode wavelengths (left) and Q factors (right) in the vicinity of anti-crossing point AC 2 . Wavelength repulsion accompanied by the linewidth crossing is observed. The insets demonstrate mode switching. The modal near-field distributions shown in the upper (lower) insets correspond to the eigenfrequency values at the points labeled A and D (B and C), respectively.

Fig. 4
Fig. 4

Supermode wavelengths (left) and Q factors (right) in the vicinity of crossing point C 1 . Wavelength crossing accompanied by damping of the high-Q supermodes is observed. The insets show supermode near-field portraits at the crossing point.

Fig. 5
Fig. 5

Resonance wavelength (left) and Q-factor (right) of an antibonding WG supermode in a three-disk PM. The central disk of radius 1.065 μ m is separated from the side disks of radii 1.1 μ m by 400 nm air gaps. Inset, supermode near-field portrait and directional far-field emission pattern at point A.

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