Abstract

A series of microcavities in 2D hexagonal lattice photonic crystal slabs are studied in this paper. The microcavities are small sections of a photonic crystal waveguide. Finite difference time domain simulations show that these cavities preserve high Q modes with similar geometrical parameters and field profile. Effective modal volume is reduced gradually in this series of microcavity modes while maintaining high quality factor. Vertical Q value larger than 106 is obtained for one of these cavity modes with effective modal volume around 5.40 cubic half wavelengths [(λ/2nslab)3]. Another cavity mode provides even smaller modal volume around 2.30 cubic half wavelengths, with vertical Q value exceeding105.

©2004 Optical Society of America

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  1. E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059 (1987)
    [Crossref] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987)
    [Crossref] [PubMed]
  3. H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 75, 4753 (1994)
  4. A. Mekis, S. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends”, Phys. Rev. B 58, 4809 (1998)
    [Crossref]
  5. T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths”, Nature 383, 699 (1996)
    [Crossref]
  6. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B,  60, 5751 (1999)
    [Crossref]
  7. S. Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, “Channel Drop Tunneling through Localized States,” Phys. Rev. Lett. 80, 960 (1998)
    [Crossref]
  8. M. Qiu, “Ultra-compact optical filter in two-dimensional photonic crystal,” Electron. Lett. 40, 539 (2004)
    [Crossref]
  9. M. Qiu and B. Jaskorzynska, “A design of a channel drop filter in a two-dimensional triangular photonic crystal”, Appl. Phys. Lett. 83, 1074 (2003).
    [Crossref]
  10. S. Fan, Proceedings of the SPIE,  v 3002, 1997, p 67–73
    [Crossref]
  11. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” S. M. , Nature 415, 621–623 (2002)
    [Crossref]
  12. P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, “Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282 (2000)
    [Crossref] [PubMed]
  13. C. Santori, D. Fattal, J. Vučković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594 (2002)
    [Crossref] [PubMed]
  14. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670
    [Crossref] [PubMed]
  15. J. Vuckovic, M. loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. of Quantum Electron. 38, 850 (2002)
    [Crossref]
  16. K. Srinivasan and O. Painter, “Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,” Opt. Express 11, 579 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-579
    [Crossref] [PubMed]
  17. V. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944 (2003)
    [Crossref] [PubMed]
  18. H. Y. Ryu, M. Notomi, and Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294 (2003)
    [Crossref]
  19. E. Yablonovitch and T. J. Gmitter, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991)
    [Crossref] [PubMed]
  20. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas and Propagation,”  14, 302 (1966)
  21. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185 (1994)
    [Crossref]
  22. M. Qiu, “High Q cavities in photonic crystal slabs: determining resonant frequency and quality factor accurately,” submitted for publication (2004)
  23. W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of Resonant Frequencies and Quality Factors of Cavities by FDTD Technique and Padé Approximation,” IEEE Microwave Wireless Components Lett. 11, 223 (2001)
    [Crossref]
  24. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819(1999)
    [Crossref] [PubMed]
  25. J. Vuckovic, M. loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E. 65, 016608 (2001)
    [Crossref]

2004 (1)

M. Qiu, “Ultra-compact optical filter in two-dimensional photonic crystal,” Electron. Lett. 40, 539 (2004)
[Crossref]

2003 (4)

M. Qiu and B. Jaskorzynska, “A design of a channel drop filter in a two-dimensional triangular photonic crystal”, Appl. Phys. Lett. 83, 1074 (2003).
[Crossref]

V. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944 (2003)
[Crossref] [PubMed]

H. Y. Ryu, M. Notomi, and Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294 (2003)
[Crossref]

K. Srinivasan and O. Painter, “Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,” Opt. Express 11, 579 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-6-579
[Crossref] [PubMed]

2002 (4)

J. Vuckovic, M. loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. of Quantum Electron. 38, 850 (2002)
[Crossref]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-670
[Crossref] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” S. M. , Nature 415, 621–623 (2002)
[Crossref]

C. Santori, D. Fattal, J. Vučković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594 (2002)
[Crossref] [PubMed]

2001 (2)

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of Resonant Frequencies and Quality Factors of Cavities by FDTD Technique and Padé Approximation,” IEEE Microwave Wireless Components Lett. 11, 223 (2001)
[Crossref]

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

2000 (1)

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, “Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282 (2000)
[Crossref] [PubMed]

1999 (2)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B,  60, 5751 (1999)
[Crossref]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819(1999)
[Crossref] [PubMed]

1998 (2)

S. Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, “Channel Drop Tunneling through Localized States,” Phys. Rev. Lett. 80, 960 (1998)
[Crossref]

A. Mekis, S. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends”, Phys. Rev. B 58, 4809 (1998)
[Crossref]

1997 (1)

S. Fan, Proceedings of the SPIE,  v 3002, 1997, p 67–73
[Crossref]

1996 (1)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths”, Nature 383, 699 (1996)
[Crossref]

1994 (2)

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 75, 4753 (1994)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185 (1994)
[Crossref]

1991 (1)

E. Yablonovitch and T. J. Gmitter, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991)
[Crossref] [PubMed]

1987 (2)

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059 (1987)
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987)
[Crossref] [PubMed]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas and Propagation,”  14, 302 (1966)

Akahane, V.

V. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944 (2003)
[Crossref] [PubMed]

Asano, T.

V. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944 (2003)
[Crossref] [PubMed]

Becher, C.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, “Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282 (2000)
[Crossref] [PubMed]

Benisty, H.

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 75, 4753 (1994)

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185 (1994)
[Crossref]

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths”, Nature 383, 699 (1996)
[Crossref]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819(1999)
[Crossref] [PubMed]

De La Rue, R. M.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths”, Nature 383, 699 (1996)
[Crossref]

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B,  60, 5751 (1999)
[Crossref]

A. Mekis, S. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends”, Phys. Rev. B 58, 4809 (1998)
[Crossref]

S. Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, “Channel Drop Tunneling through Localized States,” Phys. Rev. Lett. 80, 960 (1998)
[Crossref]

S. Fan, Proceedings of the SPIE,  v 3002, 1997, p 67–73
[Crossref]

Fattal, D.

C. Santori, D. Fattal, J. Vučković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594 (2002)
[Crossref] [PubMed]

Gmitter, T. J.

E. Yablonovitch and T. J. Gmitter, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991)
[Crossref] [PubMed]

Guo, W. H.

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of Resonant Frequencies and Quality Factors of Cavities by FDTD Technique and Padé Approximation,” IEEE Microwave Wireless Components Lett. 11, 223 (2001)
[Crossref]

Hu, E.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, “Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282 (2000)
[Crossref] [PubMed]

Huang, Y. Z.

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of Resonant Frequencies and Quality Factors of Cavities by FDTD Technique and Padé Approximation,” IEEE Microwave Wireless Components Lett. 11, 223 (2001)
[Crossref]

Imamoglu, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, “Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282 (2000)
[Crossref] [PubMed]

Jaskorzynska, B.

M. Qiu and B. Jaskorzynska, “A design of a channel drop filter in a two-dimensional triangular photonic crystal”, Appl. Phys. Lett. 83, 1074 (2003).
[Crossref]

Joannopoulos, J. D.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B,  60, 5751 (1999)
[Crossref]

A. Mekis, S. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends”, Phys. Rev. B 58, 4809 (1998)
[Crossref]

S. Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, “Channel Drop Tunneling through Localized States,” Phys. Rev. Lett. 80, 960 (1998)
[Crossref]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987)
[Crossref] [PubMed]

Johnson, S. G.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B,  60, 5751 (1999)
[Crossref]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819(1999)
[Crossref] [PubMed]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” S. M. , Nature 415, 621–623 (2002)
[Crossref]

Kiraz, A.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, “Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282 (2000)
[Crossref] [PubMed]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B,  60, 5751 (1999)
[Crossref]

Krauss, T. F.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths”, Nature 383, 699 (1996)
[Crossref]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819(1999)
[Crossref] [PubMed]

Lee, Y. H.

H. Y. Ryu, M. Notomi, and Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294 (2003)
[Crossref]

Li, W. J.

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of Resonant Frequencies and Quality Factors of Cavities by FDTD Technique and Padé Approximation,” IEEE Microwave Wireless Components Lett. 11, 223 (2001)
[Crossref]

loncar, M.

J. Vuckovic, M. loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. of Quantum Electron. 38, 850 (2002)
[Crossref]

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

Mabuchi, H.

J. Vuckovic, M. loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. of Quantum Electron. 38, 850 (2002)
[Crossref]

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

Mekis, A.

A. Mekis, S. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends”, Phys. Rev. B 58, 4809 (1998)
[Crossref]

Michler, P.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, “Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282 (2000)
[Crossref] [PubMed]

Noda, S.

V. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944 (2003)
[Crossref] [PubMed]

Notomi, M.

H. Y. Ryu, M. Notomi, and Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294 (2003)
[Crossref]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819(1999)
[Crossref] [PubMed]

Painter, O.

Petroff, P. M.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, “Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282 (2000)
[Crossref] [PubMed]

Qiu, M.

M. Qiu, “Ultra-compact optical filter in two-dimensional photonic crystal,” Electron. Lett. 40, 539 (2004)
[Crossref]

M. Qiu and B. Jaskorzynska, “A design of a channel drop filter in a two-dimensional triangular photonic crystal”, Appl. Phys. Lett. 83, 1074 (2003).
[Crossref]

M. Qiu, “High Q cavities in photonic crystal slabs: determining resonant frequency and quality factor accurately,” submitted for publication (2004)

Ryu, H. Y.

H. Y. Ryu, M. Notomi, and Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294 (2003)
[Crossref]

Santori, C.

C. Santori, D. Fattal, J. Vučković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594 (2002)
[Crossref] [PubMed]

Scherer, A.

J. Vuckovic, M. loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. of Quantum Electron. 38, 850 (2002)
[Crossref]

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

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819(1999)
[Crossref] [PubMed]

Schoenfeld, W. V.

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, “Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282 (2000)
[Crossref] [PubMed]

Solomon, G. S.

C. Santori, D. Fattal, J. Vučković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594 (2002)
[Crossref] [PubMed]

Song, B. S.

V. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944 (2003)
[Crossref] [PubMed]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” S. M. , Nature 415, 621–623 (2002)
[Crossref]

Srinivasan, K.

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” S. M. , Nature 415, 621–623 (2002)
[Crossref]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B,  60, 5751 (1999)
[Crossref]

Villeneuve, Pierre R.

S. Fan, Pierre R. Villeneuve, and J. D. Joannopoulos, “Channel Drop Tunneling through Localized States,” Phys. Rev. Lett. 80, 960 (1998)
[Crossref]

Vuckovic, J.

C. Santori, D. Fattal, J. Vučković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594 (2002)
[Crossref] [PubMed]

J. Vuckovic, M. loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. of Quantum Electron. 38, 850 (2002)
[Crossref]

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

Yablonovitch, E.

E. Yablonovitch and T. J. Gmitter, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380 (1991)
[Crossref] [PubMed]

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059 (1987)
[Crossref] [PubMed]

Yamamoto, Y.

C. Santori, D. Fattal, J. Vučković, G. S. Solomon, and Y. Yamamoto, “Indistinguishable photons from a single-photon device,” Nature 419, 594 (2002)
[Crossref] [PubMed]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-Dimensional Photonic Band-Gap Defect Mode Laser,” Science 284, 1819(1999)
[Crossref] [PubMed]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas and Propagation,”  14, 302 (1966)

Zhang, Lidong

P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, Lidong Zhang, E. Hu, and A. Imamoglu, “Quantum Dot Single-Photon Turnstile Device,” Science 290, 2282 (2000)
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

M. Qiu and B. Jaskorzynska, “A design of a channel drop filter in a two-dimensional triangular photonic crystal”, Appl. Phys. Lett. 83, 1074 (2003).
[Crossref]

H. Y. Ryu, M. Notomi, and Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83, 4294 (2003)
[Crossref]

Electron. Lett. (1)

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Figures (7)

Fig. 1.
Fig. 1. Schematic diagram of 2D PCS microcavities with three central holes missing in a row. The refractive index of the slab is 3.4 and the thickness t is 0.7a. d and R1 are varied to find the largest Q of the M3 mode.

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Fig. 2.
Fig. 2. (a) H �� field distribution of the M3 mode. (b) k space intensity profile I. The region inside the blue dashed circle (the light line) is the leaky region.

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Fig. 3.
Fig. 3. (a) M2 cavity, with d=0.23a and R1 =0.2a . (b) H z field distribution of the M2 mode. (c) k space intensity profile I. Components inside the leaky region are reduced compared to the M3 mode in Fig. 2(b)

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Fig. 4.
Fig. 4. (a) M1 cavity, with d=0.21a, R1 =0.22a and R2 =0.25a (b) H z field distribution of the M1 mode. (c) k space intensity profile I. Components inside the leaky region are greatly reduced compared to the M2 mode in Fig. 3(c)

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Fig. 5.
Fig. 5. (a) M0 cavity, with d=0.14a and R1 =0.27a. (b) H z field distribution of the M0 mode. (c) k space intensity profile I.

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Fig. 6.
Fig. 6. Electric intensity distribution of (a) M3 mode, (b) M2 mode, (c) M1 mode, and (d) M0 mode.

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Fig. 7.
Fig. 7. (a) Q value (the blue line with diamond marker) and modal volume (the green line with circle marker) comparison of the four modes. (b) Q⊥ (the blue line with diamond marker) and radiation factor RF (the green line with circle marker) comparison of the four modes. RF is normalized to the M1 mode.

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Equations (4)

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V = ∭ ε ( x , y , z ) · ∣ E ( x , y , z ) ∣ 2 dxdydz max [ ε ( x , y , z ) · ∣ E ( x , y , z ) ∣ 2 ] ,
∣ E ( x , y , z ) ∣ 2 = ∣ E x ( x , y , z ) ∣ 2 + ∣ E y ( x , y , z ) ∣ 2 + ∣ E z ( x , y , z ) ∣ 2 .
P = η 8 λ 2 k 2 ∬ k ∥ ≤ k I · d k x · d k y ,
I = ∣ F T 2 ( H y ) + 1 η F T 2 ( E x ) ∣ 2 + ∣ F T 2 ( H x ) − 1 η F T 2 ( E y ) ∣ 2

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