Abstract

Photonic crystals exhibiting a photonic band gap in both TE and TM polarizations are particularly interesting for a better control of light confinement. The simultaneous achievement of large band gaps in both polarizations requires to reduce the symmetry properties of the photonic crystal lattice. In this letter, we propose two different designs of two-dimensional photonic crystals patterned in high refractive index thin silicon slabs. These slabs are known to limit the opening of photonic band gaps for both polarizations. The proposed designs exhibit large complete photonic band gaps : the first photonic crystal structure is based on the honey-comb lattice with two different hole radii and the second structure is based on a “tri-ellipse” pattern in a triangular lattice. Photonic band gap calculations show that these structures offer large complete photonic band gaps Δωω larger than 10 % between first and second photonic bands. This figure of merit is obtained with single-mode slab waveguides and is not restricted to modes below light cone.

© 2008 Optical Society of America

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  1. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
    [CrossRef] [PubMed]
  2. S. Noda, M. Fujita, and T. Asano, "Spontaneous-emission control by photonic crystals and nanocavities," Nature Photonics 1, 449-458 (2007).
    [CrossRef]
  3. E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (2006).
    [CrossRef]
  4. T. Tanabe, M. Notomi, E. Kuramochi, and H. Taniyama, "Large pulse delay and small group velocity achieved using ultrahigh-Q photonic crystal nanocavities," Opt. Express 15, 7826-7839 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  6. Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
    [CrossRef]
  7. N. Li, M. Arita, S. Kako, M. Kitamura, S. Iwamoto, and Y. Arakawa, "Fabrication and optical characterization of III-nitride air-bridge photonic crystal with GaN quantum dots," Phys. Status Solidi C - Current TopicsIn Solid State Physics  4, 90-94 (2007).
  8. 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]
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    [CrossRef]
  10. X. Li, P. Boucaud, X. Checoury, O. Kermarrec, Y. Campidelli, and D. Bensahel, "Probing photonic crystals on silicon-on-insulator with Ge/Si self-assembled islands as an internal source," J. Appl. Phys. 99, 023103 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  15. S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
    [CrossRef]
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    [CrossRef]

2007 (3)

N. Li, M. Arita, S. Kako, M. Kitamura, S. Iwamoto, and Y. Arakawa, "Fabrication and optical characterization of III-nitride air-bridge photonic crystal with GaN quantum dots," Phys. Status Solidi C - Current TopicsIn Solid State Physics  4, 90-94 (2007).

S. Noda, M. Fujita, and T. Asano, "Spontaneous-emission control by photonic crystals and nanocavities," Nature Photonics 1, 449-458 (2007).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, and H. Taniyama, "Large pulse delay and small group velocity achieved using ultrahigh-Q photonic crystal nanocavities," Opt. Express 15, 7826-7839 (2007).
[CrossRef] [PubMed]

2006 (4)

E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (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]

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]

X. Li, P. Boucaud, X. Checoury, O. Kermarrec, Y. Campidelli, and D. Bensahel, "Probing photonic crystals on silicon-on-insulator with Ge/Si self-assembled islands as an internal source," J. Appl. Phys. 99, 023103 (2006).
[CrossRef]

2005 (2)

W. M. Kuang, Z. L. Hou, Y. Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A-Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

2003 (3)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

S. David, M. El kurdi, P. Boucaud, A. Chelnokov, V. Le Thanh, D. Bouchier, and J. M. Lourtioz, "Twodimensional photonic crystals with Ge/Si self-assembled islands," Appl. Phys. Lett. 83, 2509-2511 (2003).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

2002 (1)

C. G. Bostan and R. M. de Ridder, "Design of photonic crystal slab structures with absolute gaps in guided modes," J. Optoelectron. Adv. Mat. 4, 921-928 (2002).

2001 (1)

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

1999 (1)

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

1996 (1)

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Akahane, Y.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Andreani, L. C.

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]

Arakawa, Y.

N. Li, M. Arita, S. Kako, M. Kitamura, S. Iwamoto, and Y. Arakawa, "Fabrication and optical characterization of III-nitride air-bridge photonic crystal with GaN quantum dots," Phys. Status Solidi C - Current TopicsIn Solid State Physics  4, 90-94 (2007).

Arita, M.

N. Li, M. Arita, S. Kako, M. Kitamura, S. Iwamoto, and Y. Arakawa, "Fabrication and optical characterization of III-nitride air-bridge photonic crystal with GaN quantum dots," Phys. Status Solidi C - Current TopicsIn Solid State Physics  4, 90-94 (2007).

Asano, T.

S. Noda, M. Fujita, and T. Asano, "Spontaneous-emission control by photonic crystals and nanocavities," Nature Photonics 1, 449-458 (2007).
[CrossRef]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Benisty, H.

E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Bensahel, D.

X. Li, P. Boucaud, X. Checoury, O. Kermarrec, Y. Campidelli, and D. Bensahel, "Probing photonic crystals on silicon-on-insulator with Ge/Si self-assembled islands as an internal source," J. Appl. Phys. 99, 023103 (2006).
[CrossRef]

Bertho, D.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Bostan, C. G.

C. G. Bostan and R. M. de Ridder, "Design of photonic crystal slab structures with absolute gaps in guided modes," J. Optoelectron. Adv. Mat. 4, 921-928 (2002).

Boucaud, P.

X. Li, P. Boucaud, X. Checoury, O. Kermarrec, Y. Campidelli, and D. Bensahel, "Probing photonic crystals on silicon-on-insulator with Ge/Si self-assembled islands as an internal source," J. Appl. Phys. 99, 023103 (2006).
[CrossRef]

Campidelli, Y.

X. Li, P. Boucaud, X. Checoury, O. Kermarrec, Y. Campidelli, and D. Bensahel, "Probing photonic crystals on silicon-on-insulator with Ge/Si self-assembled islands as an internal source," J. Appl. Phys. 99, 023103 (2006).
[CrossRef]

Cassagne, D.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Cassette, S.

E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Checoury, X.

X. Li, P. Boucaud, X. Checoury, O. Kermarrec, Y. Campidelli, and D. Bensahel, "Probing photonic crystals on silicon-on-insulator with Ge/Si self-assembled islands as an internal source," J. Appl. Phys. 99, 023103 (2006).
[CrossRef]

Combrie, S.

E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

David, S.

S. David, M. El kurdi, P. Boucaud, A. Chelnokov, V. Le Thanh, D. Bouchier, and J. M. Lourtioz, "Twodimensional photonic crystals with Ge/Si self-assembled islands," Appl. Phys. Lett. 83, 2509-2511 (2003).
[CrossRef]

de Ridder, R. M.

C. G. Bostan and R. M. de Ridder, "Design of photonic crystal slab structures with absolute gaps in guided modes," J. Optoelectron. Adv. Mat. 4, 921-928 (2002).

De Rossi, A.

E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Fan, S. H.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Fujita, M.

S. Noda, M. Fujita, and T. Asano, "Spontaneous-emission control by photonic crystals and nanocavities," Nature Photonics 1, 449-458 (2007).
[CrossRef]

Gerace, D.

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]

Gu, B. Y.

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Hou, Z. L.

W. M. Kuang, Z. L. Hou, Y. Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A-Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

Iwamoto, S.

N. Li, M. Arita, S. Kako, M. Kitamura, S. Iwamoto, and Y. Arakawa, "Fabrication and optical characterization of III-nitride air-bridge photonic crystal with GaN quantum dots," Phys. Status Solidi C - Current TopicsIn Solid State Physics  4, 90-94 (2007).

Joannopoulos, J. D.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Johnson, S. G.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Jouanin, C.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Kako, S.

N. Li, M. Arita, S. Kako, M. Kitamura, S. Iwamoto, and Y. Arakawa, "Fabrication and optical characterization of III-nitride air-bridge photonic crystal with GaN quantum dots," Phys. Status Solidi C - Current TopicsIn Solid State Physics  4, 90-94 (2007).

Kermarrec, O.

X. Li, P. Boucaud, X. Checoury, O. Kermarrec, Y. Campidelli, and D. Bensahel, "Probing photonic crystals on silicon-on-insulator with Ge/Si self-assembled islands as an internal source," J. Appl. Phys. 99, 023103 (2006).
[CrossRef]

Kitagawa, H.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Kitamura, M.

N. Li, M. Arita, S. Kako, M. Kitamura, S. Iwamoto, and Y. Arakawa, "Fabrication and optical characterization of III-nitride air-bridge photonic crystal with GaN quantum dots," Phys. Status Solidi C - Current TopicsIn Solid State Physics  4, 90-94 (2007).

Kolodziejski, L. A.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Kuang, W. M.

W. M. Kuang, Z. L. Hou, Y. Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A-Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

Kuramochi, E.

Li, H.

W. M. Kuang, Z. L. Hou, Y. Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A-Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

Li, N.

N. Li, M. Arita, S. Kako, M. Kitamura, S. Iwamoto, and Y. Arakawa, "Fabrication and optical characterization of III-nitride air-bridge photonic crystal with GaN quantum dots," Phys. Status Solidi C - Current TopicsIn Solid State Physics  4, 90-94 (2007).

Li, X.

X. Li, P. Boucaud, X. Checoury, O. Kermarrec, Y. Campidelli, and D. Bensahel, "Probing photonic crystals on silicon-on-insulator with Ge/Si self-assembled islands as an internal source," J. Appl. Phys. 99, 023103 (2006).
[CrossRef]

Liu, Y. Y.

W. M. Kuang, Z. L. Hou, Y. Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A-Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

Nagle, J.

E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Noda, S.

S. Noda, M. Fujita, and T. Asano, "Spontaneous-emission control by photonic crystals and nanocavities," Nature Photonics 1, 449-458 (2007).
[CrossRef]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Notomi, M.

Scherer, A.

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]

Song, B. S.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Takayama, S.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Talneau, A.

E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Tanabe, T.

Tanaka, Y.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Taniyama, H.

Tran, N. V. Q.

E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Wang, R. Z.

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Wang, X. H.

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Weidner, E.

E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Xu, J.

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]

Yang, G. Z.

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

Yoshie, T.

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]

Zhang, Z.

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]

Zhu, X.

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]

Appl. Phys. Lett. (5)

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]

S. David, M. El kurdi, P. Boucaud, A. Chelnokov, V. Le Thanh, D. Bouchier, and J. M. Lourtioz, "Twodimensional photonic crystals with Ge/Si self-assembled islands," Appl. Phys. Lett. 83, 2509-2511 (2003).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, "Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes," Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

E. Weidner, S. Combrie, N. V. Q. Tran, A. De Rossi, J. Nagle, S. Cassette, A. Talneau, and H. Benisty, "Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity," Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

In Solid State Physics (1)

N. Li, M. Arita, S. Kako, M. Kitamura, S. Iwamoto, and Y. Arakawa, "Fabrication and optical characterization of III-nitride air-bridge photonic crystal with GaN quantum dots," Phys. Status Solidi C - Current TopicsIn Solid State Physics  4, 90-94 (2007).

J. Appl. Phys. (2)

R. Z. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001).
[CrossRef]

X. Li, P. Boucaud, X. Checoury, O. Kermarrec, Y. Campidelli, and D. Bensahel, "Probing photonic crystals on silicon-on-insulator with Ge/Si self-assembled islands as an internal source," J. Appl. Phys. 99, 023103 (2006).
[CrossRef]

J. Opt. A-Pure Appl. Opt. (1)

W. M. Kuang, Z. L. Hou, Y. Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A-Pure Appl. Opt. 7, 525-528 (2005).
[CrossRef]

J. Optoelectron. Adv. Mat. (1)

C. G. Bostan and R. M. de Ridder, "Design of photonic crystal slab structures with absolute gaps in guided modes," J. Optoelectron. Adv. Mat. 4, 921-928 (2002).

Nature (1)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Nature Photonics (1)

S. Noda, M. Fujita, and T. Asano, "Spontaneous-emission control by photonic crystals and nanocavities," Nature Photonics 1, 449-458 (2007).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (3)

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
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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).
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[CrossRef]

Other (1)

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2005).

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Figures (8)

Fig. 1.
Fig. 1.

Photonic band diagrams of photonic crystals of air holes drilled in a high refractive index silicon slab, (a) Triangular photonic crystal with radius r = 0.4a, (b) Honey-comb lattice with radius r = 0.25a.

Fig. 2.
Fig. 2.

(a) Drawing of the symmetries in the elementary cells and at the K point for a triangular lattice with different patterns: (a-1) Lattice with a C 6v symmetry possesses the symmetries associated with m1 and m2 mirrors, K point possesses C 3v symmetry with a m2 mirror; (a-2) Lattice with a C 3v symmetry possesses the m2 mirrors, K point possesses C 3v symmetry with a m2 mirror; (a-3) Lattice with a C 3v symmetry possesses the m1 mirrors, K point possesses C 3 symmetry only without m1 mirror symmetry. (b) Photonic band diagrams: in black curve, honey-comb lattice with a radius r = 0.25a band 1 and band 2 are degenerate at K point; in red curve, honey-comb lattice with two radius r1 = 0.23a and r2 = 0.27a, degeneracy at K point is lifted. (c) Real and imaginary part of the Hz component of optical modes associated with band 1 and band 2 at the K point for honey-comb lattice constituted of similar hole sizes. The m2 mirror is shown in the optical mode. Blue and red areas of the optical modes correspond to minimum and maximum magnitudes. (d) Real and imaginary part of the Hz component of optical modes associated with band 1 and band 2 at the K point for honey-comb lattice constituted of two different hole sizes. Blue and red areas of the optical modes correspond to minimum and maximum magnitudes.

Fig. 3.
Fig. 3.

(a) Honey-comb photonic crystal design with two different hole sizes. (b) Band diagram calculated (according to Γ M and K of the reciprocal space) with optimized photonic band gap for a honey-comb photonic crystal with two different holes sizes ( R1/a = 0.14, ( R2/a = 0.38, n(TE) = 2.91 and n(TM) = 2.52 ), and drawing of the Γ M and K points in the first Brillouin zone.

Fig. 4.
Fig. 4.

Gap map in both polarizations for a honey-comb photonic crystal with two different hole sizes versus R 2/a ( R1/a = 0.14). The blue and yellow areas show the opening of TE and TM photonic band gap and the green one shows the complete photonic band gap.

Fig. 5.
Fig. 5.

Gap map in both polarizations for a honey-comb photonic crystal with two different hole sizes versus ΔDmin , minimum distance between two holes. The blue and yellow areas show the opening of TE and TM photonic band gaps and the green one shows the complete photonic band gap.

Fig. 6.
Fig. 6.

(a) Triangular photonic crystal design with a “tri-ellipse” shape. (b) Band diagram of the optimized photonic band gap of a triangular photonic crystal with a “tri-ellipse” shape ( L /a = 0.17, A /a = 0.27 and B /a = 0.3) and drawing of the Γ M and K points in the first Brillouin zone.

Fig. 7.
Fig. 7.

Ez and Hz fields for TM and TE respectively between honey-comb lattice design with two different hole sizes and “tri-ellipse” triangular lattice. The figure shows both real and imaginary parts of fields and shows the similarity between the mode profiles.

Fig. 8.
Fig. 8.

Gap/midgap map of a triangular photonic crystal with “tri-ellipse” shape. (a) versus semi-axis length A/a and B/a, each colored line defines one percentage of gap/midgap. (b) versus L/a.

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