Abstract

Lasing modes in cyclic photonic molecules (CPMs) composed of several identical thin semiconductor microdisks in free space are studied in a linear approximation. Maxwell’s equations with exact boundary conditions and the radiation condition at infinity are considered as a specific eigenvalue problem that enables one to find natural frequencies and threshold gains. It is demonstrated that careful tuning of the distance between the disks in CPMs is able to drastically reduce the lasing thresholds of the whispering-gallery modes having small azimuth indices.

© 2006 Optical Society of America

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  1. P. W. Evans and N. Holonyak, Appl. Phys. Lett. 69, 2391 (1996).
    [CrossRef]
  2. M. Bayer, T. Gutbrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, Phys. Rev. Lett. 81, 2582 (1998).
    [CrossRef]
  3. Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. E. I. Smotrova and A. I. Nosich, Opt. Quantum Electron. 36, 213 (2004).
    [CrossRef]
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    [CrossRef]
  8. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 12, 78 (2006).
    [CrossRef]
  9. E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, in Proceedings of International Conference on Transparent Optical Networks, M.Marciniak, ed. (National Institute of Telecommunications, 2005), p. 139.
    [CrossRef]

2006

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

2005

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

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

2004

E. I. Smotrova and A. I. Nosich, Opt. Quantum Electron. 36, 213 (2004).
[CrossRef]

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemache, Phys. Rev. B 70, 115323 (2004).
[CrossRef]

1998

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

1996

P. W. Evans and N. Holonyak, Appl. Phys. Lett. 69, 2391 (1996).
[CrossRef]

Artemyev, M. V.

B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemache, Phys. Rev. B 70, 115323 (2004).
[CrossRef]

Baba, T.

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, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, 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]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, in Proceedings of International Conference on Transparent Optical Networks, M.Marciniak, ed. (National Institute of Telecommunications, 2005), p. 139.
[CrossRef]

Boland, J. J.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Bradley, A. L.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Connolly, T. M.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Donegan, J. F.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Dremin, A. A.

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

Evans, P. W.

P. W. Evans and N. Holonyak, Appl. Phys. Lett. 69, 2391 (1996).
[CrossRef]

Forchel, A.

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

Gaponik, N.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Gerlach, M.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Gutbrod, T.

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

Holonyak, N.

P. W. Evans and N. Holonyak, Appl. Phys. Lett. 69, 2391 (1996).
[CrossRef]

Ishii, S.

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

Knipp, P. A.

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

Kulakovskii, V. D.

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

Möller, B. M.

B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemache, Phys. Rev. B 70, 115323 (2004).
[CrossRef]

Nakagawa, A.

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]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

E. I. Smotrova and A. I. Nosich, Opt. Quantum Electron. 36, 213 (2004).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, in Proceedings of International Conference on Transparent Optical Networks, M.Marciniak, ed. (National Institute of Telecommunications, 2005), p. 139.
[CrossRef]

Przyjalgowski, M. A.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Rakovich, Yu. P.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Reinecke, T. L.

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

Reithmaier, J. P.

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

Rogach, A. L.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Ryder, A.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Sewell, P.

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

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, in Proceedings of International Conference on Transparent Optical Networks, M.Marciniak, ed. (National Institute of Telecommunications, 2005), p. 139.
[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]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

E. I. Smotrova and A. I. Nosich, Opt. Quantum Electron. 36, 213 (2004).
[CrossRef]

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, in Proceedings of International Conference on Transparent Optical Networks, M.Marciniak, ed. (National Institute of Telecommunications, 2005), p. 139.
[CrossRef]

Wannemache, R.

B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemache, Phys. Rev. B 70, 115323 (2004).
[CrossRef]

Woggon, U.

B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemache, Phys. Rev. B 70, 115323 (2004).
[CrossRef]

Appl. Phys. Lett.

P. W. Evans and N. Holonyak, Appl. Phys. Lett. 69, 2391 (1996).
[CrossRef]

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

IEEE J. Sel. Top. Quantum Electron.

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, IEEE J. Sel. Top. Quantum Electron. 11, 1135 (2005).
[CrossRef]

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

J. Appl. Phys.

Yu. P. Rakovich, M. Gerlach, A. L. Bradley, J. F. Donegan, T. M. Connolly, J. J. Boland, M. A. Przyjalgowski, A. Ryder, N. Gaponik, and A. L. Rogach, J. Appl. Phys. 96, 6761 (2004).
[CrossRef]

Opt. Quantum Electron.

E. I. Smotrova and A. I. Nosich, Opt. Quantum Electron. 36, 213 (2004).
[CrossRef]

Phys. Rev. B

B. M. Möller, U. Woggon, M. V. Artemyev, and R. Wannemache, Phys. Rev. B 70, 115323 (2004).
[CrossRef]

Phys. Rev. Lett.

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

Other

E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, in Proceedings of International Conference on Transparent Optical Networks, M.Marciniak, ed. (National Institute of Telecommunications, 2005), p. 139.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Threshold gains versus the relative rim-to-rim distance for the H z -polarized lasing supermodes in PMs of the ( H z ) 3 , 1 type of the maximally antisymmetric field class. M is a number of microdisks in the PM. The straight line is the threshold of the corresponding mode in a single cavity. The inset shows the near-field pattern at the distance providing the minimum threshold of the supermode in the PMs of six disk cavities.

Fig. 2
Fig. 2

Same as in Fig. 1 for the lasing supermodes of the ( H z ) 5 , 1 type.

Fig. 3
Fig. 3

Same as in Figs. 1, 2 for the lasing supermodes of the ( H z ) 7 , 1 type.

Fig. 4
Fig. 4

Same as in Figs. 1, 2, 3 for the lasing supermodes of the ( H z ) 10 , 1 type.

Fig. 5
Fig. 5

Same as in Fig. 3 for the lasing supermodes of the ( H z ) 7 , 1 type of the maximally symmetric field class.

Fig. 6
Fig. 6

Lasing frequencies versus the relative rim-to-rim distance for the supermodes of the ( H z ) 7 , 1 type of the maximally antisymmetric (blueshifted) and maximally symmetric (redshifted) field classes.

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