Abstract

The electromagnetic field of a high-quality photonic crystal nanocavity is computed using the finite difference time domain method. It is shown that a separatrix occurs in the local energy flux discriminating between predominantly near and far field components. Placing a two-level atom into the cavity leads to characteristic field modifications and normal-mode splitting in the transmission spectra.

© 2005 Optical Society of America

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References

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  1. J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995)
  2. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
    [Crossref] [PubMed]
  3. T. Yoshie, J. Vuckovic, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
    [Crossref]
  4. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608-1–11 (2001).
    [Crossref]
  5. H. Haug and S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors4th ed., (World Scientific, Singapore, 2004).
  6. L. Allen and J.H. Eberly, Optical Resonance and Two-Level Atoms. (Dover, 1975)
  7. A. Taflove and S.C. Hagness, Computational Electrodynamics: the FDTD method2nd ed. (Artech House, Boston, London, 2000)
  8. N. Kaneda, B. Houshmand, and T. Itoh, “FDTD Analysis of Dielectric Resonators with Curved Surfaces,” IEEE Trans. on Microwave Theory and Techniques  45, 1645–1649 (1997).
  9. L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge Univ. Press, 1995)
  10. P.R. Berman (Editor), Cavity Quantum Electrodynamics (Academic Press, San Diego, 1994)
  11. Full versions of animations are available at: http://acms.arizona.edu/oe/

2004 (1)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

2001 (2)

T. Yoshie, J. Vuckovic, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[Crossref]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608-1–11 (2001).
[Crossref]

1997 (1)

N. Kaneda, B. Houshmand, and T. Itoh, “FDTD Analysis of Dielectric Resonators with Curved Surfaces,” IEEE Trans. on Microwave Theory and Techniques  45, 1645–1649 (1997).

Allen, L.

L. Allen and J.H. Eberly, Optical Resonance and Two-Level Atoms. (Dover, 1975)

Chen, H.

T. Yoshie, J. Vuckovic, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[Crossref]

Deppe, D.

T. Yoshie, J. Vuckovic, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[Crossref]

Deppe, D.G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

Eberly, J.H.

L. Allen and J.H. Eberly, Optical Resonance and Two-Level Atoms. (Dover, 1975)

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

Gibbs, H.M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

Hagness, S.C.

A. Taflove and S.C. Hagness, Computational Electrodynamics: the FDTD method2nd ed. (Artech House, Boston, London, 2000)

Haug, H.

H. Haug and S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors4th ed., (World Scientific, Singapore, 2004).

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

Houshmand, B.

N. Kaneda, B. Houshmand, and T. Itoh, “FDTD Analysis of Dielectric Resonators with Curved Surfaces,” IEEE Trans. on Microwave Theory and Techniques  45, 1645–1649 (1997).

Itoh, T.

N. Kaneda, B. Houshmand, and T. Itoh, “FDTD Analysis of Dielectric Resonators with Curved Surfaces,” IEEE Trans. on Microwave Theory and Techniques  45, 1645–1649 (1997).

Joannopoulos, J.D.

J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995)

Kaneda, N.

N. Kaneda, B. Houshmand, and T. Itoh, “FDTD Analysis of Dielectric Resonators with Curved Surfaces,” IEEE Trans. on Microwave Theory and Techniques  45, 1645–1649 (1997).

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

Koch, S.W.

H. Haug and S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors4th ed., (World Scientific, Singapore, 2004).

Loncar, M.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608-1–11 (2001).
[Crossref]

Mabuchi, H.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608-1–11 (2001).
[Crossref]

Mandel, L.

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge Univ. Press, 1995)

Meade, R.D.

J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995)

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

T. Yoshie, J. Vuckovic, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[Crossref]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608-1–11 (2001).
[Crossref]

Shchekin, O.B.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

Taflove, A.

A. Taflove and S.C. Hagness, Computational Electrodynamics: the FDTD method2nd ed. (Artech House, Boston, London, 2000)

Vuckovic, J.

T. Yoshie, J. Vuckovic, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[Crossref]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608-1–11 (2001).
[Crossref]

Winn, J.N.

J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995)

Wolf, E.

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge Univ. Press, 1995)

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

T. Yoshie, J. Vuckovic, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[Crossref]

Appl. Phys. Lett. (1)

T. Yoshie, J. Vuckovic, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[Crossref]

IEEE Trans. (1)

N. Kaneda, B. Houshmand, and T. Itoh, “FDTD Analysis of Dielectric Resonators with Curved Surfaces,” IEEE Trans. on Microwave Theory and Techniques  45, 1645–1649 (1997).

Nature (1)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H.M. Gibbs, G. Rupper, C. Ell, O.B. Shchekin, and D.G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004)
[Crossref] [PubMed]

Phys. Rev. E (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65, 016608-1–11 (2001).
[Crossref]

Other (7)

H. Haug and S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors4th ed., (World Scientific, Singapore, 2004).

L. Allen and J.H. Eberly, Optical Resonance and Two-Level Atoms. (Dover, 1975)

A. Taflove and S.C. Hagness, Computational Electrodynamics: the FDTD method2nd ed. (Artech House, Boston, London, 2000)

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge Univ. Press, 1995)

P.R. Berman (Editor), Cavity Quantum Electrodynamics (Academic Press, San Diego, 1994)

Full versions of animations are available at: http://acms.arizona.edu/oe/

J.D. Joannopoulos, R.D. Meade, and J.N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995)

Supplementary Material (3)

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Figures (5)

Fig. 1.
Fig. 1.

Averaged (left) and time instantaneous (right) energy density W 0 of the electro-magnetic field (1ps after excitation). Note the hexagonal symmetry of the evanescent field extending around the cavity and the radiation pattern above the structure. See also animation[11]. (mpeg, 1.2mb)

Fig. 2.
Fig. 2.

Poynting vector in the x-z plane (1ps after excitation). Around the cavity a separatrix between near and far field can be seen. See also animation[11]. (mpeg, 2.4mb)

Fig. 3.
Fig. 3.

Energy density of the propagating, evanescent and total parts of the electromagnetic field (1ps after excitation) in the z-direction above the photonic crystal structure with an empty cavity (left) and with atom (right). Around 1µm above the structure the propagating part (dominating the far-field) equals the evanescent part (dominating the near-field). Differences introduced due to the atom are most pronounced in the far-field (about 2µm above the structure).

Fig. 4.
Fig. 4.

Normalized difference (Watom -W 0)/W 0 of the energy densities for simulations with (Wqd ) and without (W 0) an atom in the defect in the x-z plane (left) and the y-z plane (right). The largest normalized differences occur about 2µm above the structure. See also animation[11]. (mpeg, 1.6mb)

Fig. 5.
Fig. 5.

Left: Spectrum of the structure’s emission with and without atom. A normal mode splitting of 873GHz can be observed. Right: Temporal intensity envelope with and without atom normalized to input pulse maximum. With the atom a beating which corresponds to the normal mode splitting occurs.

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