Abstract

We examine spontaneous emission and photon dynamics in a microcavity coupled to a coupled-resonator optical waveguide (CROW) in a photonic crystal. We present an efficient tight-binding approach to obtain the Green tensor in large, arbitrary systems of coupled microcavities. We use this approach to examine spontaneous emission when the microcavity is strongly coupled to the CROW at the band center and band edge. We confirm the validity of weak-coupling theories for microcavities resonant at band center and obtain strong peak splitting in the previously inaccessible case of band-edge coupled structures.

© 2007 Optical Society of America

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  1. M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
    [CrossRef] [PubMed]
  2. Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
    [CrossRef] [PubMed]
  3. S. Hughes, Opt. Lett. 29, 2659 (2004).
    [CrossRef] [PubMed]
  4. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
    [CrossRef]
  5. S. Noda, A. Chutinan, and M. Imada, Nature 407, 608 (2000).
    [CrossRef] [PubMed]
  6. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Hahn, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
    [CrossRef]
  7. H. A. Haus, Wave and Fields in Optoelectronics (Prentice-Hall, 1984).
  8. N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
    [CrossRef]
  9. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
    [CrossRef]
  10. H. Ryu, S. Kim, H. Park, J. Hwang, Y. Lee, and J. Kim, Appl. Phys. Lett. 80, 3883 (2002).
    [CrossRef]
  11. D. P. Fussell, M. M. Dignam, M. J. Steel, C. Martijn de Sterke, and R. C. McPhedran, Phys. Rev. A 74, 043806 (2006).
    [CrossRef]
  12. T. Kamalakis and T. Sphicopoulos, IEEE J. Quantum Electron. 41, 1419 (2005).
    [CrossRef]
  13. S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
    [CrossRef] [PubMed]

2006

D. P. Fussell, M. M. Dignam, M. J. Steel, C. Martijn de Sterke, and R. C. McPhedran, Phys. Rev. A 74, 043806 (2006).
[CrossRef]

2005

T. Kamalakis and T. Sphicopoulos, IEEE J. Quantum Electron. 41, 1419 (2005).
[CrossRef]

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

2004

2002

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

H. Ryu, S. Kim, H. Park, J. Hwang, Y. Lee, and J. Kim, Appl. Phys. Lett. 80, 3883 (2002).
[CrossRef]

2000

S. Noda, A. Chutinan, and M. Imada, Nature 407, 608 (2000).
[CrossRef] [PubMed]

1999

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Hahn, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

1998

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

1995

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

1994

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

Akahane, Y.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

Asano, T.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, Nature 407, 608 (2000).
[CrossRef] [PubMed]

de Sterke, C. Martijn

D. P. Fussell, M. M. Dignam, M. J. Steel, C. Martijn de Sterke, and R. C. McPhedran, Phys. Rev. A 74, 043806 (2006).
[CrossRef]

Dignam, M. M.

D. P. Fussell, M. M. Dignam, M. J. Steel, C. Martijn de Sterke, and R. C. McPhedran, Phys. Rev. A 74, 043806 (2006).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Hahn, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

Fussell, D. P.

D. P. Fussell, M. M. Dignam, M. J. Steel, C. Martijn de Sterke, and R. C. McPhedran, Phys. Rev. A 74, 043806 (2006).
[CrossRef]

Hahn, M. J.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Hahn, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

Haus, H. A.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Hahn, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

H. A. Haus, Wave and Fields in Optoelectronics (Prentice-Hall, 1984).

Hood, C. J.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Hughes, S.

Hwang, J.

H. Ryu, S. Kim, H. Park, J. Hwang, Y. Lee, and J. Kim, Appl. Phys. Lett. 80, 3883 (2002).
[CrossRef]

Imada, M.

S. Noda, A. Chutinan, and M. Imada, Nature 407, 608 (2000).
[CrossRef] [PubMed]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Hahn, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

John, S.

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

Kamalakis, T.

T. Kamalakis and T. Sphicopoulos, IEEE J. Quantum Electron. 41, 1419 (2005).
[CrossRef]

Kim, J.

H. Ryu, S. Kim, H. Park, J. Hwang, Y. Lee, and J. Kim, Appl. Phys. Lett. 80, 3883 (2002).
[CrossRef]

Kim, S.

H. Ryu, S. Kim, H. Park, J. Hwang, Y. Lee, and J. Kim, Appl. Phys. Lett. 80, 3883 (2002).
[CrossRef]

Kimble, H. J.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Lange, W.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Lee, R. K.

Lee, Y.

H. Ryu, S. Kim, H. Park, J. Hwang, Y. Lee, and J. Kim, Appl. Phys. Lett. 80, 3883 (2002).
[CrossRef]

Mabuchi, H.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Manolatou, C.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Hahn, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

McPhedran, R. C.

D. P. Fussell, M. M. Dignam, M. J. Steel, C. Martijn de Sterke, and R. C. McPhedran, Phys. Rev. A 74, 043806 (2006).
[CrossRef]

Modinos, A.

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

Noda, S.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

S. Noda, A. Chutinan, and M. Imada, Nature 407, 608 (2000).
[CrossRef] [PubMed]

Park, H.

H. Ryu, S. Kim, H. Park, J. Hwang, Y. Lee, and J. Kim, Appl. Phys. Lett. 80, 3883 (2002).
[CrossRef]

Pelton, M.

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

Plant, J.

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

Quang, T.

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

Ryu, H.

H. Ryu, S. Kim, H. Park, J. Hwang, Y. Lee, and J. Kim, Appl. Phys. Lett. 80, 3883 (2002).
[CrossRef]

Santori, C.

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

Scherer, A.

Solomon, G. S.

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

Song, B.-S.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

Sphicopoulos, T.

T. Kamalakis and T. Sphicopoulos, IEEE J. Quantum Electron. 41, 1419 (2005).
[CrossRef]

Steel, M. J.

D. P. Fussell, M. M. Dignam, M. J. Steel, C. Martijn de Sterke, and R. C. McPhedran, Phys. Rev. A 74, 043806 (2006).
[CrossRef]

Stefanou, N.

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

Turchette, Q. A.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Hahn, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

Vuckovic, J.

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

Xu, Y.

Yamamoto, Y.

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

Yariv, A.

Zhang, B.

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett.

H. Ryu, S. Kim, H. Park, J. Hwang, Y. Lee, and J. Kim, Appl. Phys. Lett. 80, 3883 (2002).
[CrossRef]

IEEE J. Quantum Electron.

T. Kamalakis and T. Sphicopoulos, IEEE J. Quantum Electron. 41, 1419 (2005).
[CrossRef]

Nat. Mater.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, Nat. Mater. 4, 207 (2005).
[CrossRef]

Nature

S. Noda, A. Chutinan, and M. Imada, Nature 407, 608 (2000).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

S. John and T. Quang, Phys. Rev. A 50, 1764 (1994).
[CrossRef] [PubMed]

D. P. Fussell, M. M. Dignam, M. J. Steel, C. Martijn de Sterke, and R. C. McPhedran, Phys. Rev. A 74, 043806 (2006).
[CrossRef]

Phys. Rev. B

N. Stefanou and A. Modinos, Phys. Rev. B 57, 12127 (1998).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Hahn, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

Phys. Rev. Lett.

M. Pelton, C. Santori, J. Vuckovic, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
[CrossRef] [PubMed]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, Phys. Rev. Lett. 75, 4710 (1995).
[CrossRef] [PubMed]

Other

H. A. Haus, Wave and Fields in Optoelectronics (Prentice-Hall, 1984).

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Figures (3)

Fig. 1
Fig. 1

Microcavity-CROW structure in a 2D PhC slab composed of a square array of air voids in silicon. The quadrupole mode in the microcavity is shown by using a gray scale. The CROW consists of 201 resonators, of which only the central 7 are shown.

Fig. 2
Fig. 2

Microcavity coupled to the CROW at band center. (a) SE ratio for the full structure obtained by using the full calculation (bold) and by using the weak-coupling approximation (solid). Also shown is the SE ratio for the CROW uncoupled to the microcavity (gray). (b) Photon dynamics for a photon initially in the microcavity: B c and B w are the probability amplitudes of finding the photon in the microcavity and in the CROW, respectively. Also shown are B c found by using the weak-coupling expression for the decay rate, γ t , and B c for the uncoupled microcavity.

Fig. 3
Fig. 3

Microcavity coupled to the CROW at the upper band edge. (a) SE ratio for the full structure (bold), for the CROW uncoupled to the microcavity (gray), and for the microcavity uncoupled to the CROW (dashed). (b) Photon dynamics for a photon initially in the microcavity: B c and B w are the probability amplitudes of finding the photon in the microcavity and in the CROW, respectively. Also shown is B c for the uncoupled microcavity.

Equations (4)

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

× × M ( r ) ω 2 c 2 ϵ m ( r ) M ( r ) = 0 ,
A c = Λ c ,
G ( N ) ( ω ; r , r ) = π c 2 2 ω m , ν , n = 1 N M m * ( r ) c m ν ρ ν c ( ω ) c ν n M n ( r ) ,
γ w = ω c 2 κ c 2 2 v g ( ω c ) ,

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