Abstract

A new type of two-dimensional photonic-crystal (PC) structure called annular PC composed of a dielectric-rod and a circular-air-hole array in a square or triangular lattice such that a dielectric rod is centered within each air hole is studied. The dielectric rods within the air holes greatly modify the dispersion diagram of the photonic crystal despite the fact that the percentage of volume occupied by the dielectric rods may be small (<12%). Increasing the radius of the inner-dielectric rod, starting from zero to a critical value, reduces the band gap and closes it completely as expected, because of the addition of more dielectric material inside the unit cell. Continuing to increase the radius of the rod above the critical value surprisingly creates another photonic band gap. Comparison of the dispersion diagrams of the new structure and the original lattice (circular air hole square/triangular array in dielectric background) reveals that the photonic band gap is considerably enhanced in size for both square and triangular lattice with the new structure. This approach preserves the symmetry of the structure and provides a complete photonic band gap away from the close-packed condition and at low normalized frequencies.

© 2005 Optical Society of America

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  1. E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, NJ, 1995).
  4. C. M. Soukoulis (Ed.) Photonic Crystals and Light Localization in the 21st Century (Kluwer Academic Publishers, The Netherlands, 2001).
  5. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
    [CrossRef]
  6. H. Y. Ryu, M. Notomi, and Y. H. Lee, "Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab," Phys. Rev. B 68, 045209 (8 pages) (2003).
    [CrossRef]
  7. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
    [CrossRef]
  8. T. Yoshie, J. Vuckovic, A, Scherer, H. Chen, and D. Deppe, "High quality two-dimensional photonic crystal slab cavities," Appl. Phys. Lett. 79, 4289-4291 (2001).
    [CrossRef]
  9. 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]
  10. K. Srinivasan, P. E. Barclay, and O. Painter, "Fabrication-tolerant high quality factor photonic crystal microcavities," Opt. Express 12, 1458-1463 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1458">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1458</a>.
    [CrossRef] [PubMed]
  11. B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature Materials 4, 207-210 (2005).
    [CrossRef]
  12. 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]
  13. S. Noda, M. Yokoyoma, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
    [CrossRef] [PubMed]
  14. M. Notomi, H. Suzuki, and T. Tamamura, "Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps," Appl. Phys. Lett. 78, 1325-1327 (2001).
    [CrossRef]
  15. M. F. Yanik, S. Fan, and M. Soljačić, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
    [CrossRef]
  16. S. John and M. Florescu, "Photonic bandgap materials: towards an all-optical micro-transistor," J. Opt. A: Pure Appl. Opt. 3, S103-S120 (2001).
    [CrossRef]
  17. H. Y. D. Yang, N. G. Alexopoulos, and E. Yablonovitch, "Photonic band-gap materials for high-gain printed circuit antennas," IEEE Trans. Antennas Propag. 45, 185-187 (1997).
    [CrossRef]
  18. R. Coccioli, W. R. Deal, and T. Itoh, "Radiation characteristics of a patch antenna on a thin PBGsubstrate," IEEE Antennas and Propag. Society International Symposium, 2, 656-659 (1998).
  19. R. Gonzalo, P. De Maagt, and M. Sorolla, "Enhanced patch-antenna performance by suppressing surface waves using photonic-bandgap substrates," IEEE Trans. Microwave Theory Tech. 47, 2131-2138 (1999).
    [CrossRef]
  20. E. R. Brown, C. D. Parker, and E. Yablonovitch, "Radiation properties of a planar antenna on a photonic-crystal substrate," J. Opt. Soc. Am. B 10, 404-407 (1993).
    [CrossRef]
  21. Y. Fei-Ran, M. Kuang-Ping, Q. Yongxi, and T. Itoh, "A uniplanar compact photonic-bandgap (UC-PBG) structure and its applications for microwave circuit," IEEE Trans. Microwave Theory Tech. 47, 1509-1514 (1999).
    [CrossRef]
  22. Hamza Kurt and D. S. Citrin, "Photonic crystals for biochemical sensing in the terahertz region," Appl. Phys. Lett. 87, 041108 (3 pages) (2005).
    [CrossRef]
  23. Hamza Kurt and D. S. Citrin, "Coupled-resonator optical waveguides for biochemical sensing of nanoliter volumes of analyte in the terahertz region," Appl. Phys. Lett. (accepted).
  24. Z-Y. Li, B-Y Gu, and G-Z Yang, "Large Absolute Band Gap in 2D Anisotropic Photonic Crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
    [CrossRef]
  25. C. M. Anderson and K. P. Giapis, "Larger Two-Dimensional Photonic Band Gaps," Phys. Rev. Lett. 77, 2949-2952 (1996).
    [CrossRef] [PubMed]
  26. X. Zhang and Z-Q Zhang, "Creating a gap without symmetry breaking in two-dimensional photonic crystals," Phys. Rev. B 61, 9847-9850 (2000).
    [CrossRef]
  27. N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. Lett. 91, 3501-3510 (2002).
  28. M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519-15522 (2000).
    [CrossRef]
  29. 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 (3 pages) (2005).
    [CrossRef]
  30. M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).
    [CrossRef]
  31. S. Guo and S. Albin, "Simple plane wave implementation for photonic crystal calculations," Opt. Express 11, 167-175 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-167">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-167</a>.
    [CrossRef] [PubMed]
  32. R. Zoli, M. Gnan, D. Castaldini, G. Bellanca, P. Bassi, "Reformulation of the plane wave method to model photonic crystals," Opt. Express 11, 2905-2910 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2905">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2905</a>.
    [CrossRef] [PubMed]
  33. R. 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]
  34. H. Benistry, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-536 (2000).
    [CrossRef]
  35. W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. D. Zutter, "Out-of-plane scattering in Photonic Crystal Slabs," IEEE Photon. Technol. Lett. 13, 565-567 (2001).
    [CrossRef]

Appl. Phys. Lett. (7)

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

M. Notomi, H. Suzuki, and T. Tamamura, "Directional lasing oscillation of two-dimensional organic photonic crystal lasers at several photonic band gaps," Appl. Phys. Lett. 78, 1325-1327 (2001).
[CrossRef]

M. F. Yanik, S. Fan, and M. Soljačić, "High-contrast all-optical bistable switching in photonic crystal microcavities," Appl. Phys. Lett. 83, 2739-2741 (2003).
[CrossRef]

Hamza Kurt and D. S. Citrin, "Photonic crystals for biochemical sensing in the terahertz region," Appl. Phys. Lett. 87, 041108 (3 pages) (2005).
[CrossRef]

Hamza Kurt and D. S. Citrin, "Coupled-resonator optical waveguides for biochemical sensing of nanoliter volumes of analyte in the terahertz region," Appl. Phys. Lett. (accepted).

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 (3 pages) (2005).
[CrossRef]

H. Benistry, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the substrate," Appl. Phys. Lett. 76, 532-536 (2000).
[CrossRef]

IEEE Antennas and Propag. Society Intern (1)

R. Coccioli, W. R. Deal, and T. Itoh, "Radiation characteristics of a patch antenna on a thin PBGsubstrate," IEEE Antennas and Propag. Society International Symposium, 2, 656-659 (1998).

IEEE Photon. Technol. Lett. (1)

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, and D. D. Zutter, "Out-of-plane scattering in Photonic Crystal Slabs," IEEE Photon. Technol. Lett. 13, 565-567 (2001).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

H. Y. D. Yang, N. G. Alexopoulos, and E. Yablonovitch, "Photonic band-gap materials for high-gain printed circuit antennas," IEEE Trans. Antennas Propag. 45, 185-187 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

R. Gonzalo, P. De Maagt, and M. Sorolla, "Enhanced patch-antenna performance by suppressing surface waves using photonic-bandgap substrates," IEEE Trans. Microwave Theory Tech. 47, 2131-2138 (1999).
[CrossRef]

Y. Fei-Ran, M. Kuang-Ping, Q. Yongxi, and T. Itoh, "A uniplanar compact photonic-bandgap (UC-PBG) structure and its applications for microwave circuit," IEEE Trans. Microwave Theory Tech. 47, 1509-1514 (1999).
[CrossRef]

J. Appl. Phys. (1)

R. 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]

J. Appl. Phys. Lett. (1)

N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. Lett. 91, 3501-3510 (2002).

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

S. John and M. Florescu, "Photonic bandgap materials: towards an all-optical micro-transistor," J. Opt. A: Pure Appl. Opt. 3, S103-S120 (2001).
[CrossRef]

J. Opt. Soc. Am. B (1)

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 Materials (1)

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 (3)

Phys. Rev. B (6)

M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519-15522 (2000).
[CrossRef]

M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).
[CrossRef]

X. Zhang and Z-Q Zhang, "Creating a gap without symmetry breaking in two-dimensional photonic crystals," Phys. Rev. B 61, 9847-9850 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

H. Y. Ryu, M. Notomi, and Y. H. Lee, "Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab," Phys. Rev. B 68, 045209 (8 pages) (2003).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996).
[CrossRef]

Phys. Rev. Lett. (4)

Z-Y. Li, B-Y Gu, and G-Z Yang, "Large Absolute Band Gap in 2D Anisotropic Photonic Crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

C. M. Anderson and K. P. Giapis, "Larger Two-Dimensional Photonic Band Gaps," Phys. Rev. Lett. 77, 2949-2952 (1996).
[CrossRef] [PubMed]

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Science (2)

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, M. Yokoyoma, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

Other (2)

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

C. M. Soukoulis (Ed.) Photonic Crystals and Light Localization in the 21st Century (Kluwer Academic Publishers, The Netherlands, 2001).

Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram of the PC lattice. (a) Square lattice with cylindrical dielectric rods of radius r 2 and permittivity ε r 2 are inserted in the middle of the holes with radius r 1 in dielectric background ε r 1 and r 1 > r 2. The unit cell is a combination of the dielectric rod in the air and hole in dielectric background. (b) Triangular lattice with cylindrical dielectric rods of radius r 2 and permittivity ε r 2 are inserted in the middle of the holes with radius r 1 in dielectric background ε r 1 and r 1 > r 2. The unit cell is a combination of the dielectric rod in the air and hole in dielectric background.

Fig. 2.
Fig. 2.

Complete PBG variation, Δω/ω0 with respect to the changes of inner dielectric rod radius. (a) Square lattice with r 1 from 0.49a to 0.47a and r 2 from zero to 0.20a. (b) Triangular lattice with r 1 from 0.49a to 0.43a and r 2 from zero to 0.20a. After the closure of the first PBG, the second one appears as r 2 increases.

Fig. 3.
Fig. 3.

Dispersion diagram of triangular-array PBG lattice: (a) r 1/r 2 =0.47/0.02 and εr =13 (b) r 1/r 2 =0.47/0.14 and εr =13 . Solid lines represent TM modes and dashed lines represent TE modes. The shaded frequency region corresponds to the PBG.

Fig. 4.
Fig. 4.

Dispersion diagram of square-array photonic-crystal lattice: (a) r 1/r 2 =0.49/0.02 and εr = 13 (b) r 1/r 2 =0.49/0.11 and εr = 13. Solid lines represent TM modes and dashed lines represent TE modes. The shaded frequency region corresponds to the PBG.

Fig. 5.
Fig. 5.

Electric field of TM modes for square array of annular photonic crystal (Movie, 877 KB). The inner rod radius is 0.02a (left) and 0.12a (right).

Fig. 6.
Fig. 6.

(a) PBG to midgap ratio, Δω/ω 0, for square lattice with low dielectric value (εr = 4) for the TE modes with respect to the rod radius r 2 and hole radius r 1. (b) PBG to midgap ratio, Δω/ω 0, of triangular lattice with low dielectric value (εr = 4) for the TM modes with respect to the rod radius r 2 and hole radius r 1.

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