Abstract

We investigate the optical modes in a coupled pair of semiconductor microdisks in symmetric and asymmetric configurations both experimentally and theoretically. While the quality factors of coupled first- and second-order whispering gallery modes (WGMs) show a conventional crossing, the quality factors of the same-order WGMs reveal an interesting splitting behavior, leading to the formation of high- and low-quality supermodes. Our results are reproduced by numerical simulations, and an explanation based on optical interference is suggested. Quality-factor splitting is a subtle phenomenon that might help to design microarchitectures for efficient optical coupling in cavity quantum electrodynamic experiments.

© 2011 Optical Society of America

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Q. H. Song and H. Cao, Phys. Rev. Lett. 105, 053902 (2010).
[CrossRef] [PubMed]

J. Pan, S. Sandhu, Y. Huo, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, Phys. Rev. B 81, 041101(2010).
[CrossRef]

2009 (2)

A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Express 17, 15210 (2009).
[CrossRef] [PubMed]

C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, T. Pertsch, V. Shuvayev, and L. I. Deych, Phys. Rev. A 80, 043841 (2009).
[CrossRef]

2008 (1)

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, Phys. Rev. B 77, 035108 (2008).
[CrossRef]

2007 (3)

2006 (7)

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[CrossRef]

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

E. I. Smotrova and T. M. Benson, IEEE J. Sel. Top. Quant. Electron. 12, 78 (2006).
[CrossRef]

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, Phys. Rev. A 74, 013804 (2006).
[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

J. Wiersig, Phys. Rev. Lett. 97, 253901 (2006).
[CrossRef]

2005 (2)

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

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

2004 (3)

2003 (1)

J. Wiersig, J. Opt. A 5, 53 (2003).
[CrossRef]

2002 (1)

J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

2000 (2)

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

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

1999 (2)

J. M. Gérard and B. Gayral, J. Lightwave Technol. 17, 2089 (1999).
[CrossRef]

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (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]

Absil, P. P.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Astratov, V. N.

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

Awschalom, D. D.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[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, and P. A. Knipp, Phys. Rev. Lett. 81, 2582 (1998).
[CrossRef]

Benson, T. M.

E. I. Smotrova and T. M. Benson, IEEE J. Sel. Top. Quant. Electron. 12, 78 (2006).
[CrossRef]

Benyoucef, M.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Boriskina, S.

Boyd, R. W.

J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

Burkard, G.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Cai, W.

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

S. Deng, W. Cai, and A. V. Kanaev, Opt. Express 12, 6468(2004).
[CrossRef] [PubMed]

Cao, H.

Q. H. Song and H. Cao, Phys. Rev. Lett. 105, 053902 (2010).
[CrossRef] [PubMed]

Chipouline, A.

C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, T. Pertsch, V. Shuvayev, and L. I. Deych, Phys. Rev. A 80, 043841 (2009).
[CrossRef]

Cole, J. H.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[CrossRef]

Deng, S.

Deych, L. I.

C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, T. Pertsch, V. Shuvayev, and L. I. Deych, Phys. Rev. A 80, 043841 (2009).
[CrossRef]

DiVincenzo, D. P.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Dong, P.

Q. Xu, P. Dong, and M. Lipson, Nat. Phys. 3, 406 (2007).
[CrossRef]

Economou, E. N.

Fan, S.

J. Pan, S. Sandhu, Y. Huo, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, Phys. Rev. B 81, 041101(2010).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Fejer, M. M.

J. Pan, S. Sandhu, Y. Huo, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, Phys. Rev. B 81, 041101(2010).
[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]

Gayral, B.

Gérard, J. M.

Greentree, A. D.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[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]

Hara, Y.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

Harris, J. S.

J. Pan, S. Sandhu, Y. Huo, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, Phys. Rev. B 81, 041101(2010).
[CrossRef]

Heebner, J. E.

J. E. Heebner and R. W. Boyd, J. Mod. Opt. 49, 2629 (2002).
[CrossRef]

Heiss, W. D.

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

Ho, P.-T.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Hollenberg, L. C. L.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[CrossRef]

Hryniewicz, J. V.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Huang, Y.-Z.

Huo, Y.

J. Pan, S. Sandhu, Y. Huo, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, Phys. Rev. B 81, 041101(2010).
[CrossRef]

Ilchenko, V. S.

A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Express 17, 15210 (2009).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, J. Mod. Opt. 51, 2515 (2004).
[CrossRef]

Imamoglu, A.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Ishii, S.

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]

S. Deng, W. Cai, and A. V. Kanaev, Opt. Express 12, 6468(2004).
[CrossRef] [PubMed]

Käsebier, T.

C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, T. Pertsch, V. Shuvayev, and L. I. Deych, Phys. Rev. A 80, 043841 (2009).
[CrossRef]

Kim, C.-M.

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, Phys. Rev. A 74, 013804 (2006).
[CrossRef]

Kiravittaya, S.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Kley, E.-B.

C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, T. Pertsch, V. Shuvayev, and L. I. Deych, Phys. Rev. A 80, 043841 (2009).
[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]

Kuwata-Gonokami, M.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

Lee, S.-Y.

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, Phys. Rev. A 74, 013804 (2006).
[CrossRef]

Li, J.-J.

Liang, W.

Lipson, M.

Q. Xu, P. Dong, and M. Lipson, Nat. Phys. 3, 406 (2007).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Little, B. E.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Loss, D.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Maleki, L.

A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Express 17, 15210 (2009).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, J. Mod. Opt. 51, 2515 (2004).
[CrossRef]

Matsko, A. B.

A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Express 17, 15210 (2009).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, J. Mod. Opt. 51, 2515 (2004).
[CrossRef]

Mei, Y. F.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Mukaiyama, T.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

Nakagawa, A.

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

Pan, J.

J. Pan, S. Sandhu, Y. Huo, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, Phys. Rev. B 81, 041101(2010).
[CrossRef]

Park, Y.-J.

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, Phys. Rev. A 74, 013804 (2006).
[CrossRef]

Pertsch, T.

C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, T. Pertsch, V. Shuvayev, and L. I. Deych, Phys. Rev. A 80, 043841 (2009).
[CrossRef]

Povinelli, M. L.

J. Pan, S. Sandhu, Y. Huo, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, Phys. Rev. B 81, 041101(2010).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Rastelli, A.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, Phys. Rev. B 77, 035108 (2008).
[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]

Ripoll, J.

Ryu, J.-W.

J.-W. Ryu, S.-Y. Lee, C.-M. Kim, and Y.-J. Park, Phys. Rev. A 74, 013804 (2006).
[CrossRef]

Sandhu, S.

J. Pan, S. Sandhu, Y. Huo, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, Phys. Rev. B 81, 041101(2010).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Savchenkov, A. A.

A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Express 17, 15210 (2009).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, J. Mod. Opt. 51, 2515 (2004).
[CrossRef]

Schmidt, C.

C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, T. Pertsch, V. Shuvayev, and L. I. Deych, Phys. Rev. A 80, 043841 (2009).
[CrossRef]

Schmidt, O. G.

M. Benyoucef, S. Kiravittaya, Y. F. Mei, A. Rastelli, and O. G. Schmidt, Phys. Rev. B 77, 035108 (2008).
[CrossRef]

Seidel, D.

Shakya, J.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

Sherwin, M.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Shuvayev, V.

C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, T. Pertsch, V. Shuvayev, and L. I. Deych, Phys. Rev. A 80, 043841 (2009).
[CrossRef]

Small, A.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, Phys. Rev. Lett. 83, 4204 (1999).
[CrossRef]

Smotrova, E. I.

E. I. Smotrova and T. M. Benson, IEEE J. Sel. Top. Quant. Electron. 12, 78 (2006).
[CrossRef]

Song, Q. H.

Q. H. Song and H. Cao, Phys. Rev. Lett. 105, 053902 (2010).
[CrossRef] [PubMed]

Soukoulis, C. M.

Strekalov, D.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, J. Mod. Opt. 51, 2515 (2004).
[CrossRef]

Stuhrmann, N.

J. Pan, S. Sandhu, Y. Huo, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, Phys. Rev. B 81, 041101(2010).
[CrossRef]

Tahan, C.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, Nat. Phys. 2, 856 (2006).
[CrossRef]

Takeda, K.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

Tünnermann, A.

C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, T. Pertsch, V. Shuvayev, and L. I. Deych, Phys. Rev. A 80, 043841 (2009).
[CrossRef]

Wang, J.-X.

Wiersig, J.

J. Wiersig, Phys. Rev. Lett. 97, 253901 (2006).
[CrossRef]

J. Wiersig, J. Opt. A 5, 53 (2003).
[CrossRef]

Wilson, R. A.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, IEEE Photon. Technol. Lett. 12, 320 (2000).
[CrossRef]

Xu, Q.

Q. Xu, P. Dong, and M. Lipson, Nat. Phys. 3, 406 (2007).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef] [PubMed]

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).
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IEEE J. Sel. Top. Quant. Electron. (1)

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Figures (4)

Fig. 1
Fig. 1

(a) Measured mode energies of coupled TE(2,20) WGMs as a function of laser power. Inset, optical microscopy image of the PM with a disk diameter of about 2.8 μm (see also [19]). (b)–(d) PL spectra of the higher energy TE(2,20) WGMs recorded before, at, and after resonance, respectively. The PL spectrum in (b) and (c) were shifted to higher energy for comparison.

Fig. 2
Fig. 2

(a) Measured Q factors of coupled TE(2,20) WGMs versus laser power. (b) Simulated Q factors of the same WGMs versus detuning [ n s ( n l ) refractive index of small (large) disk] in the presence of absorption.

Fig. 3
Fig. 3

(a) Measured energies of coupled TE(1,25) and TE(2,21) WGMs as a function of laser power from the larger and smaller microdisks, respectively. (b), (c) Measured and simulated Q factors of TE(1,25) and TE(2,21) WGMs, respectively.

Fig. 4
Fig. 4

Computed (a) odd and (b) even parity supermode in the symmetric case of two coupled TE(2,20) modes in log scale. Inset, in the odd (even) parity case, light emission along the vertical symmetry line is reduced (enhanced). (c), (d) Supermodes in the asymmetric case of coupled TE(1,25) and (2,21) modes.

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