Abstract

A theoretical formalism is presented to investigate enhanced radiative decay of excited dipoles in photonic crystal waveguides and nanocavities with a view to achieving efficient single-photon emission from embedded quantum dots. Surprisingly, large enhancement effects are achievable in both waveguides and nanocavities, and enhanced emission in the waveguide is shown to scale proportionally (inversely) with the photon group index (velocity). Further, a way to include radiative coupling of the quantum dot is shown, and the importance of its inclusion is subsequently demonstrated.

© 2004 Optical Society of America

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  1. M. Pelton, C. Santori, J. Vukovi, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, Phys. Rev. Lett. 89, 233602 (2002).
    [CrossRef]
  2. G. S. Solomon, M. Pelton, and Y. Yamamoto, Phys. Rev. Lett. 86, 3903 (2001).
    [CrossRef] [PubMed]
  3. L. C. Andreani, G. Panzarini, and J.-M. Gerard, Phys. Rev. B 60, 13276 (1999).
    [CrossRef]
  4. For a textbook discussion, see, for example, P. Meystre and M. Sargent, Elements of Quantum Optics, 3rd. ed. (Springer, New York, 1997).
  5. See, for example, J. Vuckovic and Y. Yamamoto, Appl. Phys. Lett. 82, 2374 (2003).
    [CrossRef]
  6. See, for example, T. D. Happ, I. I. Tartakovskii, V. D. Kulakovskii, J.-P. Reithmaier, M. Kemp, and A. Forchel, Phys. Rev. B 66, 41303 (2002).
    [CrossRef]
  7. T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), postdeadline paper CPDB3.
  8. A. R. Cowan and J. F. Young, Phys. Rev. E 68, 46605 (2003).
    [CrossRef]
  9. S. Hughes and H. Kamada, have prepared a manuscript called “Single quantum dot strong coupling in a photonic crystal nanocavity site coupled to a waveguide,” Phys. Rev. B (to be published).
  10. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, have submitted a manuscript called “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” for submission to Phys. Rev. Lett.
  11. See, for example, B. H. Huttner and S. M. Burnett, Phys. Rev. A 46, 4306 (1992).
    [CrossRef] [PubMed]
  12. See, for example, D. Sullivan, Electromagnetic Simulation Using the FDTD Method, IEEE Press Series on RF and Microwave Technology (Institute for Electrical and Electronics Engineering, New York., New York, 2000).
    [CrossRef]
  13. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef]
  14. Y. Akahane, T. Asano, B. S. Song, and S. Noda, Nature 425, 944 (2003).
    [CrossRef] [PubMed]
  15. H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, Phys. Rev. Lett. 87, 246401 (2001).
    [CrossRef]
  16. See, for example, H. Y. Ryu and M. Notomi, Opt. Lett. 28, 2390 (2003), and references therein.
    [CrossRef] [PubMed]

2003 (4)

See, for example, J. Vuckovic and Y. Yamamoto, Appl. Phys. Lett. 82, 2374 (2003).
[CrossRef]

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 46605 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

See, for example, H. Y. Ryu and M. Notomi, Opt. Lett. 28, 2390 (2003), and references therein.
[CrossRef] [PubMed]

2002 (2)

See, for example, T. D. Happ, I. I. Tartakovskii, V. D. Kulakovskii, J.-P. Reithmaier, M. Kemp, and A. Forchel, Phys. Rev. B 66, 41303 (2002).
[CrossRef]

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

2001 (3)

G. S. Solomon, M. Pelton, and Y. Yamamoto, Phys. Rev. Lett. 86, 3903 (2001).
[CrossRef] [PubMed]

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

1999 (1)

L. C. Andreani, G. Panzarini, and J.-M. Gerard, Phys. Rev. B 60, 13276 (1999).
[CrossRef]

1992 (1)

See, for example, B. H. Huttner and S. M. Burnett, Phys. Rev. A 46, 4306 (1992).
[CrossRef] [PubMed]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

Ando, H.

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef]

Andreani, L. C.

L. C. Andreani, G. Panzarini, and J.-M. Gerard, Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

Baba, T.

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), postdeadline paper CPDB3.

Burnett, S. M.

See, for example, B. H. Huttner and S. M. Burnett, Phys. Rev. A 46, 4306 (1992).
[CrossRef] [PubMed]

Cowan, A. R.

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 46605 (2003).
[CrossRef]

Forchel, A.

See, for example, T. D. Happ, I. I. Tartakovskii, V. D. Kulakovskii, J.-P. Reithmaier, M. Kemp, and A. Forchel, Phys. Rev. B 66, 41303 (2002).
[CrossRef]

Gerard, J.-M.

L. C. Andreani, G. Panzarini, and J.-M. Gerard, Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Gotoh, H.

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef]

Happ, T. D.

See, for example, T. D. Happ, I. I. Tartakovskii, V. D. Kulakovskii, J.-P. Reithmaier, M. Kemp, and A. Forchel, Phys. Rev. B 66, 41303 (2002).
[CrossRef]

Hughes, S.

S. Hughes and H. Kamada, have prepared a manuscript called “Single quantum dot strong coupling in a photonic crystal nanocavity site coupled to a waveguide,” Phys. Rev. B (to be published).

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, have submitted a manuscript called “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” for submission to Phys. Rev. Lett.

Huttner, B. H.

See, for example, B. H. Huttner and S. M. Burnett, Phys. Rev. A 46, 4306 (1992).
[CrossRef] [PubMed]

Inoshita, K.

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), postdeadline paper CPDB3.

Kamada, H.

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef]

S. Hughes and H. Kamada, have prepared a manuscript called “Single quantum dot strong coupling in a photonic crystal nanocavity site coupled to a waveguide,” Phys. Rev. B (to be published).

Kemp, M.

See, for example, T. D. Happ, I. I. Tartakovskii, V. D. Kulakovskii, J.-P. Reithmaier, M. Kemp, and A. Forchel, Phys. Rev. B 66, 41303 (2002).
[CrossRef]

Koyama, F.

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), postdeadline paper CPDB3.

Kulakovskii, V. D.

See, for example, T. D. Happ, I. I. Tartakovskii, V. D. Kulakovskii, J.-P. Reithmaier, M. Kemp, and A. Forchel, Phys. Rev. B 66, 41303 (2002).
[CrossRef]

Kuroki, Y.

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), postdeadline paper CPDB3.

Meystre, P.

For a textbook discussion, see, for example, P. Meystre and M. Sargent, Elements of Quantum Optics, 3rd. ed. (Springer, New York, 1997).

Noda, S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

Notomi, M.

See, for example, H. Y. Ryu and M. Notomi, Opt. Lett. 28, 2390 (2003), and references therein.
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Nozaki, K.

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), postdeadline paper CPDB3.

Panzarini, G.

L. C. Andreani, G. Panzarini, and J.-M. Gerard, Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Pelton, M.

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

G. S. Solomon, M. Pelton, and Y. Yamamoto, Phys. Rev. Lett. 86, 3903 (2001).
[CrossRef] [PubMed]

Plant, J.

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

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, have submitted a manuscript called “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” for submission to Phys. Rev. Lett.

Reithmaier, J.-P.

See, for example, T. D. Happ, I. I. Tartakovskii, V. D. Kulakovskii, J.-P. Reithmaier, M. Kemp, and A. Forchel, Phys. Rev. B 66, 41303 (2002).
[CrossRef]

Ryu, H. Y.

Sano, D.

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), postdeadline paper CPDB3.

Santori, C.

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

Sargent, M.

For a textbook discussion, see, for example, P. Meystre and M. Sargent, Elements of Quantum Optics, 3rd. ed. (Springer, New York, 1997).

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Sipe, J. E.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, have submitted a manuscript called “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” for submission to Phys. Rev. Lett.

Solomon, G. S.

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

G. S. Solomon, M. Pelton, and Y. Yamamoto, Phys. Rev. Lett. 86, 3903 (2001).
[CrossRef] [PubMed]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

Sullivan, D.

See, for example, D. Sullivan, Electromagnetic Simulation Using the FDTD Method, IEEE Press Series on RF and Microwave Technology (Institute for Electrical and Electronics Engineering, New York., New York, 2000).
[CrossRef]

Takagahara, T.

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Tartakovskii, I. I.

See, for example, T. D. Happ, I. I. Tartakovskii, V. D. Kulakovskii, J.-P. Reithmaier, M. Kemp, and A. Forchel, Phys. Rev. B 66, 41303 (2002).
[CrossRef]

Temmyo, J.

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef]

Vuckovic, J.

See, for example, J. Vuckovic and Y. Yamamoto, Appl. Phys. Lett. 82, 2374 (2003).
[CrossRef]

Vukovi, J.

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

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Yamamoto, Y.

See, for example, J. Vuckovic and Y. Yamamoto, Appl. Phys. Lett. 82, 2374 (2003).
[CrossRef]

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

G. S. Solomon, M. Pelton, and Y. Yamamoto, Phys. Rev. Lett. 86, 3903 (2001).
[CrossRef] [PubMed]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Young, J. F.

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 46605 (2003).
[CrossRef]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, have submitted a manuscript called “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” for submission to Phys. Rev. Lett.

Zhang, B.

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

Appl. Phys. Lett. (1)

See, for example, J. Vuckovic and Y. Yamamoto, Appl. Phys. Lett. 82, 2374 (2003).
[CrossRef]

Nature (1)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, Nature 425, 944 (2003).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (1)

See, for example, B. H. Huttner and S. M. Burnett, Phys. Rev. A 46, 4306 (1992).
[CrossRef] [PubMed]

Phys. Rev. B (2)

See, for example, T. D. Happ, I. I. Tartakovskii, V. D. Kulakovskii, J.-P. Reithmaier, M. Kemp, and A. Forchel, Phys. Rev. B 66, 41303 (2002).
[CrossRef]

L. C. Andreani, G. Panzarini, and J.-M. Gerard, Phys. Rev. B 60, 13276 (1999).
[CrossRef]

Phys. Rev. E (1)

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 46605 (2003).
[CrossRef]

Phys. Rev. Lett. (4)

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

G. S. Solomon, M. Pelton, and Y. Yamamoto, Phys. Rev. Lett. 86, 3903 (2001).
[CrossRef] [PubMed]

H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, Phys. Rev. Lett. 87, 246401 (2001).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

Other (5)

See, for example, D. Sullivan, Electromagnetic Simulation Using the FDTD Method, IEEE Press Series on RF and Microwave Technology (Institute for Electrical and Electronics Engineering, New York., New York, 2000).
[CrossRef]

For a textbook discussion, see, for example, P. Meystre and M. Sargent, Elements of Quantum Optics, 3rd. ed. (Springer, New York, 1997).

S. Hughes and H. Kamada, have prepared a manuscript called “Single quantum dot strong coupling in a photonic crystal nanocavity site coupled to a waveguide,” Phys. Rev. B (to be published).

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, have submitted a manuscript called “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” for submission to Phys. Rev. Lett.

T. Baba, D. Sano, K. Nozaki, K. Inoshita, Y. Kuroki, and F. Koyama, in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2004), postdeadline paper CPDB3.

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Figures (2)

Fig. 1
Fig. 1

(a) Schematic diagram of the propagating mode ek inside a PPC. The QD is placed near the field antinode location. The modes are shown by the dark shaded concentric circles, and the filled circles represent the airholes in a semiconductor. (b) Schematic of the proposed PPC waveguide–nanocavity coupling scheme. The QD is located within the nanocavity, which has an exciton resonance close to the cavity resonance. The propagating field excites the defect cavity ec, which couples to the propagating Bloch mode ek and to the embedded QD.

Fig. 2
Fig. 2

(a) Top and (b) side views of the slab defect photonic crystal waveguide. Example contour plots of the calculated y-polarized Bloch vector ek are also shown in both views. The position of the QD is indicated schematically by D. White circles and rectangles highlight the airhole boundaries within the high-index (semiconductor) slab. Material parameters are given in the text.

Equations (3)

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

Fwrd,ω=3πc2angωϵdω2ehrd·nˆy2,
Fcrd,ωc=6πc3VmΓcϵd3/2ωc2.
Fcrd,ωc=6πc3VmΓc+Ω2/Γdϵd3/2ωc2.

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