Abstract

Two nano-resonator modes are designed in a woodpile three-dimensional photonic crystal by the modulation of unit cell size along a low-loss optical waveguide. One is a dipole mode with 2.88 cubic half-wavelengths mode volume. The other is a quadrupole mode with 8.3 cubic half-wavelengths mode volume. Light is three-dimensionally confined by a complete photonic band gap so that, in the analyzed range, the quality factor exponentially increases as the increase in the number of unit cells used for confinement of light.

© 2007 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 Certian Disordered Dielectric Superlattices," Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  3. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
    [CrossRef]
  4. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature Materials 4, 207-210 (2005).
    [CrossRef]
  5. 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]
  6. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
    [CrossRef] [PubMed]
  7. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-623 (2002).
    [CrossRef] [PubMed]
  8. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
    [CrossRef] [PubMed]
  9. T. Baba, T. Hamano, F. Koyama, and K. Iga, "Spontaneous emission factor of a microcavity DBR surface-emitting laser," IEEE J. of Quantum Electron. 27, 1347-1358 (1991).
    [CrossRef]
  10. H. Mabuchi, and A. C. Doherty, "Cavity Quantum Electrodynamics: Coherence in Context," Science 298, 1372-1377 (2002).
    [CrossRef] [PubMed]
  11. K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
    [CrossRef] [PubMed]
  12. J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
    [CrossRef] [PubMed]
  13. E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, "Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity," Phys. Rev. Lett. 95, 067401 (2005).
    [CrossRef] [PubMed]
  14. 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, 1819-1821 (1999).
    [CrossRef] [PubMed]
  15. K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical devices", Opt. Express 10, 670-684 (2002).
    [PubMed]
  16. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Optimization of the Q factor in photonic crystal microcavities", IEEE J. of Quantum Electron. 38850-856 (2002).
    [CrossRef]
  17. Z. Zhang and M. Qiu, "Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs", Opt. Express 12, 3988-3995 (2004).
    [CrossRef] [PubMed]
  18. D. Englund, I. Fushman, and J. Vuckovic, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5975 (2005).
    [CrossRef] [PubMed]
  19. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths," Science 289, 604-606 (2000).
    [CrossRef] [PubMed]
  20. M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
    [CrossRef] [PubMed]
  21. S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Ligth Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
    [CrossRef] [PubMed]
  22. M. Okano, A. Chutinan, and S. Noda, "Analysis and design of single-defect cavities in a three-dimensional photonic crystal," Phys. Rev. B 66, 165211 (2002).
    [CrossRef]
  23. M. Okano, S. Kako, and S. Noda, "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
    [CrossRef]
  24. M. Okano, and S. Noda, "Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains," Phys. Rev. B 70, 125105 (2004).
    [CrossRef]
  25. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Communications 89, 413-416 (1994).
    [CrossRef]
  26. S. Kawashima, L. H. Lee, M. Okano, M. Imada, and S. Noda, "Design of donor-type line-defect waveguides in three-dimensional photonic crystals," Opt. Express 13, 9774-9781 (2005).
    [CrossRef] [PubMed]
  27. S. Johnson, and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [CrossRef] [PubMed]
  28. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, "Improving accuracy by subpixel smoothing in FDTD," Opt. Lett. 31, 2972-2974 (2006).
    [CrossRef] [PubMed]
  29. J.-P. Berenger, "A Perfectly Matched Layer for the Absorption of Electromagnetic Waves," J. Comput. Phys. 114, 185-200 (1994).
    [CrossRef]

2006

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, "Improving accuracy by subpixel smoothing in FDTD," Opt. Lett. 31, 2972-2974 (2006).
[CrossRef] [PubMed]

2005

2004

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Ligth Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

M. Okano, and S. Noda, "Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains," Phys. Rev. B 70, 125105 (2004).
[CrossRef]

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]

Z. Zhang and M. Qiu, "Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs", Opt. Express 12, 3988-3995 (2004).
[CrossRef] [PubMed]

2003

M. Okano, S. Kako, and S. Noda, "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
[CrossRef]

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

2002

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

H. Mabuchi, and A. C. Doherty, "Cavity Quantum Electrodynamics: Coherence in Context," Science 298, 1372-1377 (2002).
[CrossRef] [PubMed]

M. Okano, A. Chutinan, and S. Noda, "Analysis and design of single-defect cavities in a three-dimensional photonic crystal," Phys. Rev. B 66, 165211 (2002).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Optimization of the Q factor in photonic crystal microcavities", IEEE J. of Quantum Electron. 38850-856 (2002).
[CrossRef]

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical devices", Opt. Express 10, 670-684 (2002).
[PubMed]

2001

2000

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

1999

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, 1819-1821 (1999).
[CrossRef] [PubMed]

1994

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Communications 89, 413-416 (1994).
[CrossRef]

J.-P. Berenger, "A Perfectly Matched Layer for the Absorption of Electromagnetic Waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

1991

T. Baba, T. Hamano, F. Koyama, and K. Iga, "Spontaneous emission factor of a microcavity DBR surface-emitting laser," IEEE J. of Quantum Electron. 27, 1347-1358 (1991).
[CrossRef]

1987

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 Certian Disordered Dielectric Superlattices," Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Akahane, Y.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature Materials 4, 207-210 (2005).
[CrossRef]

Asano, T.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature Materials 4, 207-210 (2005).
[CrossRef]

Baba, T.

T. Baba, T. Hamano, F. Koyama, and K. Iga, "Spontaneous emission factor of a microcavity DBR surface-emitting laser," IEEE J. of Quantum Electron. 27, 1347-1358 (1991).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, "A Perfectly Matched Layer for the Absorption of Electromagnetic Waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Bermel, P.

Biswas, R.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Communications 89, 413-416 (1994).
[CrossRef]

Bloch, J.

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, "Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity," Phys. Rev. Lett. 95, 067401 (2005).
[CrossRef] [PubMed]

Burr, G.

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Communications 89, 413-416 (1994).
[CrossRef]

Chutinan, A.

M. Okano, A. Chutinan, and S. Noda, "Analysis and design of single-defect cavities in a three-dimensional photonic crystal," Phys. Rev. B 66, 165211 (2002).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

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, 1819-1821 (1999).
[CrossRef] [PubMed]

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]

Doherty, A. C.

H. Mabuchi, and A. C. Doherty, "Cavity Quantum Electrodynamics: Coherence in Context," Science 298, 1372-1377 (2002).
[CrossRef] [PubMed]

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]

Englund, D.

Farjadpour, A.

Forchel, A.

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

Fushman, I.

Gerard, J. M.

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, "Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity," Phys. Rev. Lett. 95, 067401 (2005).
[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]

Hamano, T.

T. Baba, T. Hamano, F. Koyama, and K. Iga, "Spontaneous emission factor of a microcavity DBR surface-emitting laser," IEEE J. of Quantum Electron. 27, 1347-1358 (1991).
[CrossRef]

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]

Ho, K. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Communications 89, 413-416 (1994).
[CrossRef]

Hofmann, C.

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

Hours, J.

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, "Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity," Phys. Rev. Lett. 95, 067401 (2005).
[CrossRef] [PubMed]

Ibanescu, M.

Iga, K.

T. Baba, T. Hamano, F. Koyama, and K. Iga, "Spontaneous emission factor of a microcavity DBR surface-emitting laser," IEEE J. of Quantum Electron. 27, 1347-1358 (1991).
[CrossRef]

Imada, M.

Ippen, E. P.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Joannopoulos, J.

Joannopoulos, J. D.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, "Improving accuracy by subpixel smoothing in FDTD," Opt. Lett. 31, 2972-2974 (2006).
[CrossRef] [PubMed]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

John, S.

S. John, "Strong Localization of Photons in Certian Disordered Dielectric Superlattices," Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Johnson, S.

Johnson, S. G.

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, "Improving accuracy by subpixel smoothing in FDTD," Opt. Lett. 31, 2972-2974 (2006).
[CrossRef] [PubMed]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Kako, S.

M. Okano, S. Kako, and S. Noda, "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
[CrossRef]

Kawashima, S.

Keldysh, L. V.

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

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]

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, 1819-1821 (1999).
[CrossRef] [PubMed]

Kippenberg, T. J.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

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

Kira, G.

Koyama, F.

T. Baba, T. Hamano, F. Koyama, and K. Iga, "Spontaneous emission factor of a microcavity DBR surface-emitting laser," IEEE J. of Quantum Electron. 27, 1347-1358 (1991).
[CrossRef]

Kuhn, S.

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

Kulakovskii, V. D.

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

Kuramochi, E.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
[CrossRef] [PubMed]

Lee, L. H.

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, 1819-1821 (1999).
[CrossRef] [PubMed]

Lemaitre, A.

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, "Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity," Phys. Rev. Lett. 95, 067401 (2005).
[CrossRef] [PubMed]

Lidorikis, E.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Loffler, A.

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

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. 38850-856 (2002).
[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. 38850-856 (2002).
[CrossRef]

H. Mabuchi, and A. C. Doherty, "Cavity Quantum Electrodynamics: Coherence in Context," Science 298, 1372-1377 (2002).
[CrossRef] [PubMed]

Martrou, D.

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, "Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity," Phys. Rev. Lett. 95, 067401 (2005).
[CrossRef] [PubMed]

Mitsugi, S.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
[CrossRef] [PubMed]

Noda, S.

S. Kawashima, L. H. Lee, M. Okano, M. Imada, and S. Noda, "Design of donor-type line-defect waveguides in three-dimensional photonic crystals," Opt. Express 13, 9774-9781 (2005).
[CrossRef] [PubMed]

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature Materials 4, 207-210 (2005).
[CrossRef]

M. Okano, and S. Noda, "Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains," Phys. Rev. B 70, 125105 (2004).
[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Ligth Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

M. Okano, S. Kako, and S. Noda, "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
[CrossRef]

M. Okano, A. Chutinan, and S. Noda, "Analysis and design of single-defect cavities in a three-dimensional photonic crystal," Phys. Rev. B 66, 165211 (2002).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Notomi, M.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
[CrossRef] [PubMed]

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, 1819-1821 (1999).
[CrossRef] [PubMed]

Ogawa, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Ligth Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Okano, M.

S. Kawashima, L. H. Lee, M. Okano, M. Imada, and S. Noda, "Design of donor-type line-defect waveguides in three-dimensional photonic crystals," Opt. Express 13, 9774-9781 (2005).
[CrossRef] [PubMed]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Ligth Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

M. Okano, and S. Noda, "Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains," Phys. Rev. B 70, 125105 (2004).
[CrossRef]

M. Okano, S. Kako, and S. Noda, "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
[CrossRef]

M. Okano, A. Chutinan, and S. Noda, "Analysis and design of single-defect cavities in a three-dimensional photonic crystal," Phys. Rev. B 66, 165211 (2002).
[CrossRef]

Painter, O.

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical devices", Opt. Express 10, 670-684 (2002).
[PubMed]

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, 1819-1821 (1999).
[CrossRef] [PubMed]

Peter, E.

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, "Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity," Phys. Rev. Lett. 95, 067401 (2005).
[CrossRef] [PubMed]

Qi, M.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Qiu, M.

Rakich, P. T.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Reinecke, T. L.

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

Reithmaier, J. P.

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

Reitzenstein, S.

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

Rodriguez, A.

Roundy, D.

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]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Optimization of the Q factor in photonic crystal microcavities", IEEE J. of Quantum Electron. 38850-856 (2002).
[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, 1819-1821 (1999).
[CrossRef] [PubMed]

Sek, G.

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

Senellart, P.

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, "Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity," Phys. Rev. Lett. 95, 067401 (2005).
[CrossRef] [PubMed]

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]

Shinya, A.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
[CrossRef] [PubMed]

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Communications 89, 413-416 (1994).
[CrossRef]

Smith, H. I.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Song, B.-S.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature Materials 4, 207-210 (2005).
[CrossRef]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Communications 89, 413-416 (1994).
[CrossRef]

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

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

Srinivasan, K.

Tanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
[CrossRef] [PubMed]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Vahala, K. J.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

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

Vuckovic, J.

D. Englund, I. Fushman, and J. Vuckovic, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5975 (2005).
[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. 38850-856 (2002).
[CrossRef]

Watanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Yablonovitch, E.

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

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths," Science 289, 604-606 (2000).
[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, 1819-1821 (1999).
[CrossRef] [PubMed]

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]

Yoshimoto, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Ligth Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Zhang, Z.

Appl. Phys. Lett.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, "Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect," Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

IEEE J. of Quantum Electron.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Optimization of the Q factor in photonic crystal microcavities", IEEE J. of Quantum Electron. 38850-856 (2002).
[CrossRef]

T. Baba, T. Hamano, F. Koyama, and K. Iga, "Spontaneous emission factor of a microcavity DBR surface-emitting laser," IEEE J. of Quantum Electron. 27, 1347-1358 (1991).
[CrossRef]

J. Comput. Phys.

J.-P. Berenger, "A Perfectly Matched Layer for the Absorption of Electromagnetic Waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Nature

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]

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

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

J. P. Reithmaier, G. Sek, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot-semiconductor microcavity system," Nature 432, 197-200 (2004).
[CrossRef] [PubMed]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Nature Materials

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature Materials 4, 207-210 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

M. Okano, A. Chutinan, and S. Noda, "Analysis and design of single-defect cavities in a three-dimensional photonic crystal," Phys. Rev. B 66, 165211 (2002).
[CrossRef]

M. Okano, S. Kako, and S. Noda, "Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal," Phys. Rev. B 68, 235110 (2003).
[CrossRef]

M. Okano, and S. Noda, "Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains," Phys. Rev. B 70, 125105 (2004).
[CrossRef]

Phys. Rev. Lett.

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 Certian Disordered Dielectric Superlattices," Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gerard, and J. Bloch, "Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity," Phys. Rev. Lett. 95, 067401 (2005).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

Science

H. Mabuchi, and A. C. Doherty, "Cavity Quantum Electrodynamics: Coherence in Context," Science 298, 1372-1377 (2002).
[CrossRef] [PubMed]

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, 1819-1821 (1999).
[CrossRef] [PubMed]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full Three-Dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Ligth Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Solid State Communications

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Communications 89, 413-416 (1994).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Woodpile 3D photonic crystal waveguide, dispersion relations, mode gap ranges and the waveguide Q factor. (a) A waveguide formed by a wider dielectric rod along y direction. One unit cell in y direction is shown, and Block boundary condition is applied in calculation. (b) The dispersion relations for the wx/a=0.6 waveguide. Note that there are two mode gaps: the mode gap A∈(0.3576, 0.3834) and the mode gap B∈(0.4028, 0.4089) in a dimensionless frequency unit (a0). (c) The mode gap frequency ranges as a function of the line-defect waveguide width. (d) The waveguide Q factor as a function of the number of unit cells used to confine each mode. Squares and circles show the Q factor for the mode-c with WG0.7 and that for the mode-a with WG0.6, respectively.

Fig. 2.
Fig. 2.

3D photonic crystal nano-resonator geometry formed by sandwiching a waveguide II with two waveguide I structures. The waveguides I and II use the same unit cell length in xz plane.

Fig. 3.
Fig. 3.

Properties of the cavity modes constructed on a wx/a=0.7 waveguide, and the comparison of loose and tight confinement. (a) The profile of Ex component in the central xy plane of the waveguide. (b) The profile of Ex component in the central xy plane of the cavity with a =1.033a. (c) The profile of Ex component in the same plane of the cavity with a =1.067a, and wy =0.333a. The total number of unit cells of these structures is 7×11×7. (d) The development of the Q factor with the number of unit cells in the cavity with a =1.067a, and wy =0.333a.

Fig. 4.
Fig. 4.

Profiles of the magnitude of electric field in the central xy plane of waveguide or cavity. One unit cell length PML is applied to all walls except ones in the waveguide propagation direction. (a) Mode-c in WG0.7. Supercell size is 7×1×7. (b) The cavity mode formed by inducing waveguide mode-c into the mode gap of WG0.7. a =1.067a, and wy =0.333a. Nx =Nz =7, Ny =15. (c) Mode-a of WG0.6 in one unit cell in y direction. Supercell size is 7×1×7. (d) The cavity mode formed by inducing waveguide mode-a into mode gap A in WG0.6. a =1.2a, and wy =0.4a. Nx =Nz =7, Ny =11.

Fig. 5.
Fig. 5.

Vector plots of electric field on (a) xy plane and (b) xz plane for the designed quadrupole mode (based on WG0.7, a =1.067a, and wy =0.333a), and ones on (c) xy plane and (d) xz plane for the designed dipole mode (based on WG0.6, a =1.2a, and wy =0.4a).

Fig. 6.
Fig. 6.

The properties of the cavity mode based on the waveguide of wx/a=0.6. In the core region, a =1.2a, and wy =0.4a. (a) The Ex distribution in the central xy plane of the cavity. Nx =Nz =7, Ny =11. (b) The Q factor for different unit cell numbers. The Q factor increases exponentially with N, and no saturation is observed.

Fig. 7.
Fig. 7.

The resonator Q factor and mode volume for a different amount of unit cell size modulation. The waveguide has a line defect wx/a=0.5, and the parameters (a , wy ) in the core region are shown on the top axis. The unit cell size of these structures is 9×9×9.

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