Abstract

Coupled-microdisk photonic molecules with high-symmetry geometries that support nondegenerate whispering gallery modes with high quality factors are numerically designed, based on a two-dimensional model. Dramatic enhancement of calculated Q factors of nondegenerate modes as compared with single-microdisk whispering gallery modes of the same radial order is achieved by tuning the intercavity coupling distances. Potential applications of this work to the design of single-mode coupled-microdisk structures with large spontaneous emission factors and low threshold lasing operation and to random laser simulations are discussed.

© 2006 Optical Society of America

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  1. K. J. Vahala, Nature 424, 839 (2003).
    [CrossRef] [PubMed]
  2. 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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    [CrossRef] [PubMed]
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    [CrossRef]
  5. J. Ripoll, C. M. Soukoulis, and E. N. Economou, J. Opt. Soc. Am. B 21, 141 (2004).
    [CrossRef]
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    [CrossRef]
  8. Ch. M. Briskina, V. M. Markushev, and N. E. Ter-Gabrielyan, Quantum Electron. 26, 923 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. J. R. Cao, W. Kuang, S.-J. Choi, P.-T. Lee, J. D. O'Brien, and P. D. Dapkus, Appl. Phys. Lett. 83, 4107 (2003).
    [CrossRef]
  15. P. J. Rodrigo, V. R. Daria, and J. Glückstad, Appl. Phys. Lett. 86, 074103 (2005).
    [CrossRef]

2005 (3)

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

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Quantum Electron. 41, 857 (2005).
[CrossRef]

P. J. Rodrigo, V. R. Daria, and J. Glückstad, Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

2004 (3)

J. Ripoll, C. M. Soukoulis, and E. N. Economou, J. Opt. Soc. Am. B 21, 141 (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]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, J. Opt. Soc. Am. A 21, 393 (2004).
[CrossRef]

2003 (3)

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Opt. Lett. 28, 2437 (2003).
[CrossRef] [PubMed]

J. R. Cao, W. Kuang, S.-J. Choi, P.-T. Lee, J. D. O'Brien, and P. D. Dapkus, Appl. Phys. Lett. 83, 4107 (2003).
[CrossRef]

1999 (1)

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[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]

1997 (2)

B. E. Little, J. P. Laine, and S. T. Chu, Opt. Lett. 22, 4 (1997).
[CrossRef] [PubMed]

T. Baba, M. Fujita, A. Sakai, M. Kihara, and R. Watanabe, IEEE Photon. Technol. Lett. 9, 878 (1997).
[CrossRef]

1996 (1)

Ch. M. Briskina, V. M. Markushev, and N. E. Ter-Gabrielyan, Quantum Electron. 26, 923 (1996).
[CrossRef]

Baba, T.

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

T. Baba, M. Fujita, A. Sakai, M. Kihara, and R. Watanabe, IEEE Photon. Technol. Lett. 9, 878 (1997).
[CrossRef]

Bayer, M.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

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.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Quantum Electron. 41, 857 (2005).
[CrossRef]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, J. Opt. Soc. Am. A 21, 393 (2004).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, "Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing," submitted to IEEE J. Sel. Topics Quantum. Electron.

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, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Quantum Electron. 41, 857 (2005).
[CrossRef]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, J. Opt. Soc. Am. A 21, 393 (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]

Briskina, Ch. M.

Ch. M. Briskina, V. M. Markushev, and N. E. Ter-Gabrielyan, Quantum Electron. 26, 923 (1996).
[CrossRef]

Cao, J. R.

J. R. Cao, W. Kuang, S.-J. Choi, P.-T. Lee, J. D. O'Brien, and P. D. Dapkus, Appl. Phys. Lett. 83, 4107 (2003).
[CrossRef]

Choi, S.-J.

J. R. Cao, W. Kuang, S.-J. Choi, P.-T. Lee, J. D. O'Brien, and P. D. Dapkus, Appl. Phys. Lett. 83, 4107 (2003).
[CrossRef]

Chu, S. T.

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]

Dapkus, P. D.

J. R. Cao, W. Kuang, S.-J. Choi, P.-T. Lee, J. D. O'Brien, and P. D. Dapkus, Appl. Phys. Lett. 83, 4107 (2003).
[CrossRef]

Daria, V. R.

P. J. Rodrigo, V. R. Daria, and J. Glückstad, Appl. Phys. Lett. 86, 074103 (2005).
[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]

Economou, E. N.

Forchel, A.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

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

Fujita, M.

T. Baba, M. Fujita, A. Sakai, M. Kihara, and R. Watanabe, IEEE Photon. Technol. Lett. 9, 878 (1997).
[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]

Glückstad, J.

P. J. Rodrigo, V. R. Daria, and J. Glückstad, Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

Gutbrod, T.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

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

Hara, Y.

Ishii, S.

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

Kihara, M.

T. Baba, M. Fujita, A. Sakai, M. Kihara, and R. Watanabe, IEEE Photon. Technol. Lett. 9, 878 (1997).
[CrossRef]

Knipp, P. A.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

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

Kuang, W.

J. R. Cao, W. Kuang, S.-J. Choi, P.-T. Lee, J. D. O'Brien, and P. D. Dapkus, Appl. Phys. Lett. 83, 4107 (2003).
[CrossRef]

Kuwata-Gonokami, M.

Laine, J. P.

Lee, P.-T.

J. R. Cao, W. Kuang, S.-J. Choi, P.-T. Lee, J. D. O'Brien, and P. D. Dapkus, Appl. Phys. Lett. 83, 4107 (2003).
[CrossRef]

Little, B. E.

Markushev, V. M.

Ch. M. Briskina, V. M. Markushev, and N. E. Ter-Gabrielyan, Quantum Electron. 26, 923 (1996).
[CrossRef]

Mukaiyama, T.

Nakagawa, A.

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

Nosich, A. I.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Quantum Electron. 41, 857 (2005).
[CrossRef]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, J. Opt. Soc. Am. A 21, 393 (2004).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, "Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing," submitted to IEEE J. Sel. Topics Quantum. Electron.

O'Brien, J. D.

J. R. Cao, W. Kuang, S.-J. Choi, P.-T. Lee, J. D. O'Brien, and P. D. Dapkus, Appl. Phys. Lett. 83, 4107 (2003).
[CrossRef]

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, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

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, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

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

Ripoll, J.

Rodrigo, P. J.

P. J. Rodrigo, V. R. Daria, and J. Glückstad, Appl. Phys. Lett. 86, 074103 (2005).
[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]

Sakai, A.

T. Baba, M. Fujita, A. Sakai, M. Kihara, and R. Watanabe, IEEE Photon. Technol. Lett. 9, 878 (1997).
[CrossRef]

Sewell, P.

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Quantum Electron. 41, 857 (2005).
[CrossRef]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, J. Opt. Soc. Am. A 21, 393 (2004).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, "Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing," submitted to IEEE J. Sel. Topics Quantum. Electron.

Smotrova, E. I.

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, "Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing," submitted to IEEE J. Sel. Topics Quantum. Electron.

Soukoulis, C. M.

Takeda, K.

Ter-Gabrielyan, N. E.

Ch. M. Briskina, V. M. Markushev, and N. E. Ter-Gabrielyan, Quantum Electron. 26, 923 (1996).
[CrossRef]

Vahala, K. J.

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Watanabe, R.

T. Baba, M. Fujita, A. Sakai, M. Kihara, and R. Watanabe, IEEE Photon. Technol. Lett. 9, 878 (1997).
[CrossRef]

Werner, R.

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

Appl. Phys. Lett. (3)

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

J. R. Cao, W. Kuang, S.-J. Choi, P.-T. Lee, J. D. O'Brien, and P. D. Dapkus, Appl. Phys. Lett. 83, 4107 (2003).
[CrossRef]

P. J. Rodrigo, V. R. Daria, and J. Glückstad, Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, IEEE J. Quantum Electron. 41, 857 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. Baba, M. Fujita, A. Sakai, M. Kihara, and R. Watanabe, IEEE Photon. Technol. Lett. 9, 878 (1997).
[CrossRef]

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

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

Nature (1)

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (1)

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. Lett. (2)

M. Bayer, T. Gutbrod, A. Forchel, T. L. Reinecke, P. A. Knipp, R. Werner, and J. P. Reithmaier, Phys. Rev. Lett. 83, 5374 (1999).
[CrossRef]

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

Quantum Electron. (1)

Ch. M. Briskina, V. M. Markushev, and N. E. Ter-Gabrielyan, Quantum Electron. 26, 923 (1996).
[CrossRef]

Other (1)

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, "Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing," submitted to IEEE J. Sel. Topics Quantum. Electron.

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Figures (5)

Fig. 1
Fig. 1

Shift and splitting of wavelengths (a) and change of Q factors (b) of the WGE 6 , 1 modes in a triangular photonic molecule as a function of the cavities’ distances to the molecule’s center. Corresponding single-cavity characteristics are plotted for comparison (straight line).

Fig. 2
Fig. 2

Magnetic near-field portraits of the (a) O and (b) E modes in the triangular molecule with d = 1.25 μ m .

Fig. 3
Fig. 3

Shift and splitting of wavelengths (a) and change of Q factors (b) of the WGE 6 , 1 modes in a square photonic molecule as a function of cavities' distances to the molecule center.

Fig. 4
Fig. 4

Magnetic near-field portraits of the (a) OE and (b) OO modes in the square molecule with d = 1.45 μ m .

Fig. 5
Fig. 5

Spectral lines with respective Q factors for the WG modes in (a) 2.3 μ m diameter single microdisk and (b) optimally tuned ( d = 1.6125 μ m ) square photonic molecule composed of 1.8 μ m diameter microdisks. The dotted curve is an approximation (a.u.) of the spontaneous emission spectrum in GaInAsP–InP quantum well microdisk lasers (Ref. [12]).

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