Abstract

We model the optical properties of L3 photonic crystal nano-cavities as a function of the photonic crystal membrane refractive index n using a guided mode expansion method. Band structure calculations revealed that a TE-like full band-gap exists for materials of refractive index as low as 1.6. The Q-factor of such cavities showed a super-linear increase with refractive index. By adjusting the relative position of the cavity side holes, the Q-factor was optimised as a function of the photonic crystal membrane refractive index n over the range 1.6 to 3.4. Q-factors in the range 3000-8000 were predicted from absorption free materials in the visible range with refractive index between 2.45 and 2.8.

© 2007 Optical Society of America

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References

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  1. J. D. Joannopoulos, R. D. Meade and J. N. Win, Photonic crystals (Princeton University press, 1995)
  2. K. Sakada, Optical Properties of Photonic Crystals, Second edition (Springer, 2004)
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    [CrossRef] [PubMed]
  4. K. J. Vahala, ‘‘Optical microcavities,’’Nature 424, 839 (2003).
    [CrossRef] [PubMed]
  5. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, D. G. Deppe, ‘‘Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,’’Nature 432, 200 (2004).
    [CrossRef] [PubMed]
  6. S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, "Self-tuned quantum dot gain in photonic crystal lasers,’’Phys. Rev. Lett. 96, 127104 (2006).
    [CrossRef]
  7. W-H. Chang, W-Y. Chen, H-S. Chang, T-P. Hsieh, J-I. Chyi, and T-M. Hsu, ‘‘Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,’’Phys. Rev. Lett. 96, 117401 (2006).
    [CrossRef] [PubMed]
  8. 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 (2005).
    [CrossRef] [PubMed]
  9. E. M. Purcell, ‘‘Spontaneous emission probabilities at radio frequencies,’’Phys. Rev. 69,681 (1946).
  10. D. Englund, I. Fushman and J. Vuckovic, ‘‘General recipe for designing photonic crystal cavities,’’Opt. Express 13, 5961 (2005).
    [CrossRef] [PubMed]
  11. S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, S. Noda, ‘‘Control of Light Emission by 3D Photonic Crystals,’’Science 305, 227 (2004).
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  12. T. F. Krauss, R. M. De La Rue, S. Brand, ‘‘Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,’’Nature 383, 699 (1996).
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  13. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 83, 1512 (2003), and S. Noda, A. Chutinan, M. Imada, ‘‘Trapping and emission of photons by a single defect in a photonic bandgap structure,’’Nature 407, 608 (2000),
    [CrossRef]
  14. H-Y. Ryu, M. Notomi, Y-H. Lee, ‘‘High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,’’Appl. Phys. Lett. 83, 4294 (2003).
    [CrossRef]
  15. Y. Akahane, T. Asano, B-S. Song, and S. Noda, ‘‘Fine-tuned high-Q photonic-crystal nanocavity,’’Opt. Express 13, 1202 (2005).
    [CrossRef] [PubMed]
  16. Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, ‘‘Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab,’’Appl. Phys. Lett. 82, 1341 (2003).
    [CrossRef]
  17. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 016608 (2001).
    [CrossRef]
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    [CrossRef]
  19. M. Kitamura, S. Iwamoto, and Y. Arakawa, ‘‘Enhanced light emission from an organic photonic crystal with a nanocavity,’’Appl. Phys. Lett. 87, 151119 (2005).
    [CrossRef]
  20. Z. Zhang, T. Yoshie, X. Zhu, J. Xu, and A. Scherer, ‘‘Visible two-dimensional photonic crystal slab laser,’’Appl. Phys. Lett. 89, 071102 (2006).
    [CrossRef]
  21. M. Makarova, J. Vuckovic, H. Sanda, and Y. Nishi, ‘‘Silicon-based photonic crystal nanocavity light emitters,’’Appl. Phys. Lett. 89, 221101(2006).
    [CrossRef]
  22. T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, ‘‘Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,’’Appl. Phys. Lett. 91, 021110 (2007).
    [CrossRef]
  23. G. Böttger, M. Schmidt, M. Eich, R. Boucher and U. Hubner, "Photonic crystal all-polymer slab resonators," J. Appl. Phys. 98, 103101 (2005).
    [CrossRef]
  24. D. M. Whittaker, I. S. Culshaw, V. N. Astratov, and M. S. Skolnick, ‘‘Photonic band structure of patterned waveguides with dielectric and metallic cladding,’’Phys. Rev. B 65, 073102 (2002).
    [CrossRef]
  25. L. C. Andreani and D. Gerace, ‘‘Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,’’Phys. Rev. B 73, 235114 (2006).
    [CrossRef]
  26. The 3D FDTD code (CrystalWave) used in this work is a product of Photon design Ltd, http://www.photond.com
  27. J. Vuckovic, Y. Xu, A. Yariv, A. Scherer, ‘‘Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,’’IEEE J. Quantum Electron. 35, 1168 (1999).
    [CrossRef]
  28. A. M. Adawi, A. Cadby, L. G. Connolly, W-C. Hung, R. Dean, A. Tahraoui, A. M. Fox, A. G. Cullis, D. Sanvitto, M. S. Skolnick, and D. G. Lidzey ‘‘Spontaneous emission control in micropillar cavities containing a fluorescent molecular dye,’’Adv. Mater. 18, 742 (2006).
    [CrossRef]
  29. D. C. Cronemeyer, "Electrical and optical properties of rutile single crystals,’’Phys. Rev. 87, 876 (1952).
    [CrossRef]
  30. C-S. Kee, S-P. Han, K. B. Yoon, C-G. Choi, H. K. Sung, S. S. Oh, H. Y. Park, S. Park and H. Schift, ‘‘Photonic band gaps and defect modes of polymer photonic crystal slabs,’’Appl. Phys. Lett. 86, 051101 (2005).
    [CrossRef]
  31. M. Gilo, N. Croitoru, ‘‘Properties of TiO2 films prepared by ion-assisted deposition using a gridless end-Hall ion source,’’Thin Solid Films 283, 84 (1996).
    [CrossRef]
  32. S. Tomljenovic-Hanic, M. J. Steel, C. Martijin de Sterke and J. Salzman, "Diamond based photonic crystal microcavities," Opt. Express 14, 3556 (2006).
    [CrossRef] [PubMed]

2007 (2)

Y. Ruan, M-K. Kim, Y-H. Lee, B. Luther-Davies and A. Rode, ‘‘Fabrication of high-Q chalcogenide photonic crystal resonators by e-beam lithography,’’Appl. Phys. Lett. 90, 071102 (2007).
[CrossRef]

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, ‘‘Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,’’Appl. Phys. Lett. 91, 021110 (2007).
[CrossRef]

2006 (7)

Z. Zhang, T. Yoshie, X. Zhu, J. Xu, and A. Scherer, ‘‘Visible two-dimensional photonic crystal slab laser,’’Appl. Phys. Lett. 89, 071102 (2006).
[CrossRef]

M. Makarova, J. Vuckovic, H. Sanda, and Y. Nishi, ‘‘Silicon-based photonic crystal nanocavity light emitters,’’Appl. Phys. Lett. 89, 221101(2006).
[CrossRef]

L. C. Andreani and D. Gerace, ‘‘Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,’’Phys. Rev. B 73, 235114 (2006).
[CrossRef]

A. M. Adawi, A. Cadby, L. G. Connolly, W-C. Hung, R. Dean, A. Tahraoui, A. M. Fox, A. G. Cullis, D. Sanvitto, M. S. Skolnick, and D. G. Lidzey ‘‘Spontaneous emission control in micropillar cavities containing a fluorescent molecular dye,’’Adv. Mater. 18, 742 (2006).
[CrossRef]

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, "Self-tuned quantum dot gain in photonic crystal lasers,’’Phys. Rev. Lett. 96, 127104 (2006).
[CrossRef]

W-H. Chang, W-Y. Chen, H-S. Chang, T-P. Hsieh, J-I. Chyi, and T-M. Hsu, ‘‘Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,’’Phys. Rev. Lett. 96, 117401 (2006).
[CrossRef] [PubMed]

S. Tomljenovic-Hanic, M. J. Steel, C. Martijin de Sterke and J. Salzman, "Diamond based photonic crystal microcavities," Opt. Express 14, 3556 (2006).
[CrossRef] [PubMed]

2005 (6)

Y. Akahane, T. Asano, B-S. Song, and S. Noda, ‘‘Fine-tuned high-Q photonic-crystal nanocavity,’’Opt. Express 13, 1202 (2005).
[CrossRef] [PubMed]

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 (2005).
[CrossRef] [PubMed]

D. Englund, I. Fushman and J. Vuckovic, ‘‘General recipe for designing photonic crystal cavities,’’Opt. Express 13, 5961 (2005).
[CrossRef] [PubMed]

C-S. Kee, S-P. Han, K. B. Yoon, C-G. Choi, H. K. Sung, S. S. Oh, H. Y. Park, S. Park and H. Schift, ‘‘Photonic band gaps and defect modes of polymer photonic crystal slabs,’’Appl. Phys. Lett. 86, 051101 (2005).
[CrossRef]

G. Böttger, M. Schmidt, M. Eich, R. Boucher and U. Hubner, "Photonic crystal all-polymer slab resonators," J. Appl. Phys. 98, 103101 (2005).
[CrossRef]

M. Kitamura, S. Iwamoto, and Y. Arakawa, ‘‘Enhanced light emission from an organic photonic crystal with a nanocavity,’’Appl. Phys. Lett. 87, 151119 (2005).
[CrossRef]

2004 (2)

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, S. Noda, ‘‘Control of Light Emission by 3D Photonic Crystals,’’Science 305, 227 (2004).
[CrossRef] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, D. G. Deppe, ‘‘Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,’’Nature 432, 200 (2004).
[CrossRef] [PubMed]

2003 (4)

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

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, ‘‘Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab,’’Appl. Phys. Lett. 82, 1341 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, S. Noda, ‘‘High-Q photonic nanocavity in two-dimensional photonic crystal,’’Nature 425, 944 (2003).
[CrossRef] [PubMed]

K. J. Vahala, ‘‘Optical microcavities,’’Nature 424, 839 (2003).
[CrossRef] [PubMed]

2002 (1)

D. M. Whittaker, I. S. Culshaw, V. N. Astratov, and M. S. Skolnick, ‘‘Photonic band structure of patterned waveguides with dielectric and metallic cladding,’’Phys. Rev. B 65, 073102 (2002).
[CrossRef]

2001 (1)

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)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 83, 1512 (2003), and S. Noda, A. Chutinan, M. Imada, ‘‘Trapping and emission of photons by a single defect in a photonic bandgap structure,’’Nature 407, 608 (2000),
[CrossRef]

1999 (1)

J. Vuckovic, Y. Xu, A. Yariv, A. Scherer, ‘‘Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,’’IEEE J. Quantum Electron. 35, 1168 (1999).
[CrossRef]

1996 (2)

M. Gilo, N. Croitoru, ‘‘Properties of TiO2 films prepared by ion-assisted deposition using a gridless end-Hall ion source,’’Thin Solid Films 283, 84 (1996).
[CrossRef]

T. F. Krauss, R. M. De La Rue, S. Brand, ‘‘Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,’’Nature 383, 699 (1996).
[CrossRef]

1952 (1)

D. C. Cronemeyer, "Electrical and optical properties of rutile single crystals,’’Phys. Rev. 87, 876 (1952).
[CrossRef]

1946 (1)

E. M. Purcell, ‘‘Spontaneous emission probabilities at radio frequencies,’’Phys. Rev. 69,681 (1946).

Adv. Mater. (1)

A. M. Adawi, A. Cadby, L. G. Connolly, W-C. Hung, R. Dean, A. Tahraoui, A. M. Fox, A. G. Cullis, D. Sanvitto, M. S. Skolnick, and D. G. Lidzey ‘‘Spontaneous emission control in micropillar cavities containing a fluorescent molecular dye,’’Adv. Mater. 18, 742 (2006).
[CrossRef]

Appl. Phys. Lett. (8)

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, ‘‘Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab,’’Appl. Phys. Lett. 82, 1341 (2003).
[CrossRef]

C-S. Kee, S-P. Han, K. B. Yoon, C-G. Choi, H. K. Sung, S. S. Oh, H. Y. Park, S. Park and H. Schift, ‘‘Photonic band gaps and defect modes of polymer photonic crystal slabs,’’Appl. Phys. Lett. 86, 051101 (2005).
[CrossRef]

Y. Ruan, M-K. Kim, Y-H. Lee, B. Luther-Davies and A. Rode, ‘‘Fabrication of high-Q chalcogenide photonic crystal resonators by e-beam lithography,’’Appl. Phys. Lett. 90, 071102 (2007).
[CrossRef]

M. Kitamura, S. Iwamoto, and Y. Arakawa, ‘‘Enhanced light emission from an organic photonic crystal with a nanocavity,’’Appl. Phys. Lett. 87, 151119 (2005).
[CrossRef]

Z. Zhang, T. Yoshie, X. Zhu, J. Xu, and A. Scherer, ‘‘Visible two-dimensional photonic crystal slab laser,’’Appl. Phys. Lett. 89, 071102 (2006).
[CrossRef]

M. Makarova, J. Vuckovic, H. Sanda, and Y. Nishi, ‘‘Silicon-based photonic crystal nanocavity light emitters,’’Appl. Phys. Lett. 89, 221101(2006).
[CrossRef]

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, ‘‘Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,’’Appl. Phys. Lett. 91, 021110 (2007).
[CrossRef]

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

IEEE J. Quantum Electron. (1)

J. Vuckovic, Y. Xu, A. Yariv, A. Scherer, ‘‘Finite-difference time-domain calculation of the spontaneous emission coupling factor in optical microcavities,’’IEEE J. Quantum Electron. 35, 1168 (1999).
[CrossRef]

J. Appl. Phys. (1)

G. Böttger, M. Schmidt, M. Eich, R. Boucher and U. Hubner, "Photonic crystal all-polymer slab resonators," J. Appl. Phys. 98, 103101 (2005).
[CrossRef]

Nature (5)

T. F. Krauss, R. M. De La Rue, S. Brand, ‘‘Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,’’Nature 383, 699 (1996).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 83, 1512 (2003), and S. Noda, A. Chutinan, M. Imada, ‘‘Trapping and emission of photons by a single defect in a photonic bandgap structure,’’Nature 407, 608 (2000),
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, S. Noda, ‘‘High-Q photonic nanocavity in two-dimensional photonic crystal,’’Nature 425, 944 (2003).
[CrossRef] [PubMed]

K. J. Vahala, ‘‘Optical microcavities,’’Nature 424, 839 (2003).
[CrossRef] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, D. G. Deppe, ‘‘Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,’’Nature 432, 200 (2004).
[CrossRef] [PubMed]

Opt. Express (4)

Phys. Rev. (2)

E. M. Purcell, ‘‘Spontaneous emission probabilities at radio frequencies,’’Phys. Rev. 69,681 (1946).

D. C. Cronemeyer, "Electrical and optical properties of rutile single crystals,’’Phys. Rev. 87, 876 (1952).
[CrossRef]

Phys. Rev. B (2)

D. M. Whittaker, I. S. Culshaw, V. N. Astratov, and M. S. Skolnick, ‘‘Photonic band structure of patterned waveguides with dielectric and metallic cladding,’’Phys. Rev. B 65, 073102 (2002).
[CrossRef]

L. C. Andreani and D. Gerace, ‘‘Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,’’Phys. Rev. B 73, 235114 (2006).
[CrossRef]

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 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

S. Strauf, K. Hennessy, M. T. Rakher, Y. S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, "Self-tuned quantum dot gain in photonic crystal lasers,’’Phys. Rev. Lett. 96, 127104 (2006).
[CrossRef]

W-H. Chang, W-Y. Chen, H-S. Chang, T-P. Hsieh, J-I. Chyi, and T-M. Hsu, ‘‘Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities,’’Phys. Rev. Lett. 96, 117401 (2006).
[CrossRef] [PubMed]

Science (1)

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, S. Noda, ‘‘Control of Light Emission by 3D Photonic Crystals,’’Science 305, 227 (2004).
[CrossRef] [PubMed]

Thin Solid Films (1)

M. Gilo, N. Croitoru, ‘‘Properties of TiO2 films prepared by ion-assisted deposition using a gridless end-Hall ion source,’’Thin Solid Films 283, 84 (1996).
[CrossRef]

Other (3)

J. D. Joannopoulos, R. D. Meade and J. N. Win, Photonic crystals (Princeton University press, 1995)

K. Sakada, Optical Properties of Photonic Crystals, Second edition (Springer, 2004)

The 3D FDTD code (CrystalWave) used in this work is a product of Photon design Ltd, http://www.photond.com

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Figures (5)

Fig. 1.
Fig. 1.

A schematic drawing of the L3 two dimensional nano-cavities investigated in this work.

Fig. 2.
Fig. 2.

Refractive index dependence of the band-gap width and band gap centre energy for a two dimensional photonic crystal slab with a = 240 nm, d = 0.6a and r = 0.29a.

Fig. 3.
Fig. 3.

(a). Q-factor of an L3 nano-cavity versus the photonic crystal slab refractive index n for S = 0. (b) Mode volume V and Purcell factor Fp of an L3 nano-cavity as a function of the photonic crystal slab refractive index n for S = 0.

Fig. 4.
Fig. 4.

The Q-factor of an L3 nano-cavity as a function of the outside hole displacement S, and refractive index n.

Fig. 5(a)
Fig. 5(a)

shows Qmax and Fpmax as a function of the slab refractive index n. Figure 5(b) shows the energy of the cavity mode at maximum Q also as a function of refractive index.

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