Abstract

We present a procedure for optimizing two-dimensional (2D) Photonic Band Gap (PBG) structures. The procedure discretizes the unit cell of a PBG structure into a binary cell and uses Direct Binary Search to search through a terrain of possible solutions in order to find a more optimal one. This process is designed either for improving the absolute band gap or opening a new one, for a predefined PBG structure. By applying the procedure on a honeycomb array of high dielectric objects in an air background, we increased its Maximum Absolute Gap-to-Midgap Ratio (MAGTMR) to more than twice that of the initial structure. To further prove the utility of this procedure, we also present other examples.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  30. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495 (1992).
    [CrossRef]
  31. K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152 (1990).
    [CrossRef] [PubMed]
  32. K. M. Leung and Y. F. Liu, "Full Vector Wave Calculation of Photonic Band Structures in Face-Centered-Cubic Dielectric Media," Phys. Rev. Lett. 65, 2646 (1990).
    [CrossRef] [PubMed]
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Appl. Opt.

Appl. Phy. Lett.

A. Ferrando and J. J. Miret, "Single-polarization single-mode intraband guidance in supersquare photonic crystals fibers," Appl. Phy. Lett. 78, 3184 (2001).
[CrossRef]

Appl. Phys. Lett.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495 (1992).
[CrossRef]

F. Gadot, A. Chelnokov, A. D. Lustrac, P. Crozat, J.-M. Lourtioz, D. Cassagne, and C. Jouanin, "Experimental demonstration of complete photonic band gap in graphite structure," Appl. Phys. Lett. 71, 1780 (1997).
[CrossRef]

IEICE Trans. Electro.

M. Notomi, A. Shinya, E. Kuramochi, I. Yokohama, C. Takahashi, K. Yamada, J. Takahashi, T. Kawashima, and S. Kawakami, "Si-based photonic crystals and photonic-bandgap waveguides," IEICE Trans. Electro. E85C, 1025 (2002).

International J. Optoelectronics

N. Wang, Y. Chen, Z. Nakao, S.Tamura, and H. Aritome, "Sythesis of Binary Computer-generated holograms based on a coding and frequency domain optimization algorithm," International J. Optoelectronics 12, 69 (1998).

J. Appl. Phys.

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 (2001).
[CrossRef]

B. Temelkuran, M. Bayindir, E. Ozbay, R. Biswas, M. M. Sigalas, G. Tuttle, and K. M. Ho, "Photonic Crystal-based resonant antenna with a very high directivity," J. Appl. Phys. 87, 603 (2000).
[CrossRef]

J. Lightwave Technol.

M. Imada, S. Noda, A. Chutinan, M. Mochizuk, and T. Tanaka, "Channel Drop Filter Using a Single Defect in a 2-D Photonic Crystal Slab Waveguide," J. Lightwave Technol. 20, 873 (2002).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

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

Microelectron. Eng.

J. Moosburger, M. Kamp, F. Klopf, M. Fischer, and A. Forchel, "Fabrication of semiconductor lasers with 2Dphotonic crystal mirrors using a wet oxidized Al2O3-mask," Microelectron. Eng. 57, 1017 (2001).
[CrossRef]

Opt. Commun.

V. Boutenko and R. Chevallier, "Second order direct binary search algorithm for the synthesis of computergenerated holograms," Opt. Commun. 125, 43 (1996).
[CrossRef]

Phys. Rev. A

M. Florescu and S. John, "Single-atom switching in photonic crystals," Phys. Rev. A 64, 033801 (2001).
[CrossRef]

Phys. Rev. B

Z. Li, J. Wang, and B. Gu, "Creation of partial band gaps in anisotropic photonic-band-gap structures," Phys. Rev. B 58, 3721 (1998).
[CrossRef]

A. R.McGurn, "Photonic crystal circuits: A theory for two- and three-dimensional networks," Phys. Rev. B 61, 13235 (2000).
[CrossRef]

X. Wang, B. Gu, Z. Li, and G. Yang, "Large absolute photonic band gaps created by rotating noncircular rods in two-dimensional lattices," Phys. Rev. B 60, 11417 (1999).
[CrossRef]

M. Qiu and S. He, "Large Complete band gap in two-dimensional photonic crystals with elliptic air holes," Phys. Rev. B 60, 10610 (1999).
[CrossRef]

P. R. Villeneuve and M. Piche, "Photonic band gaps in two-dimensional square lattices: Square and circular rods," Phys. Rev. B 46, 4973 (1992).
[CrossRef]

C. M. Anderson and K. P. Giapis, "Symmetry reduction in grounp 4mm Photonic crystals," Phys. Rev. B 56, 7313 (1997).
[CrossRef]

P. R. Villeneuve and M. Piche, "Photonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B 46, 4969 (1992).
[CrossRef]

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

Phys. Rev. E

C. S. Kee, J. E. Kim, and H. Y. Park, "Absolute photonic band gap in a two-dimensional square lattice of square dielectric rods in air," Phys. Rev. E 56, 6291 (1997).
[CrossRef]

Phys. Rev. Lett.

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

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

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

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, "Photonic band structure: The face-centered-cubic case employing nonspherical atoms," Phys. Rev. Lett. 67, 2295 (1991).
[CrossRef] [PubMed]

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

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

K. M. Leung and Y. F. Liu, "Full Vector Wave Calculation of Photonic Band Structures in Face-Centered-Cubic Dielectric Media," Phys. Rev. Lett. 65, 2646 (1990).
[CrossRef] [PubMed]

Phys. Stat. Sol.

W. H. R.Hillebrand, and W.Harms, "Theoretical Band Gap Studies of Two-Dimensional Photonic Crystals with Varying Column Roundness," Phys. Stat. Sol. 217, 981 (2000).
[CrossRef]

Science

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

Other

K. Nam, "Photonic Crystals," <a href="http://www.phys.ksu.edu/~namkv/photonic.html">http://www.phys.ksu.edu/~namkv/photonic.html</a>.

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

T. D. Happ, A. Markard, M. Kamp, J. L. Gentner, and A. Forchel, "Short cavity InP-lasers with 2D photonic crystal mirrors," presented at Optoelectronics, 2001.

J. S. Shirk, R. G. S. Pong, S. R. Flom, and E. A. Bolden, "Nonlinear 2-d Photonic Crystals for Optical Limiting," <a href="http://www.ee.ucla.edu/~pbmuri/1999-review/shirk/">http://www.ee.ucla.edu/~pbmuri/1999-review/shirk/</a>.

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Figures (7)

Fig. 1.
Fig. 1.

The discretized unit cell of a honeycomb lattice structure of dielectric cylinders in air with a resolution a/17

Fig. 2.
Fig. 2.

The unit cells and the numbered grids used for synthesis (a) the triangular/honeycomb lattice case (b) the rectangular lattice case

Fig. 3.
Fig. 3.

The brillouin zones and the irreducible brillouin zones for unit cell with diagonal symmetry (a) the rectangular lattice case (b) the triangular lattice case

Fig. 4.
Fig. 4.

The convergence of the maximum absolute bandgap-to-midgap ratio for optimization of a honeycomb lattice of hexagonal GaAs cylinders in air Figure 4 indicates that some

Fig. 5.
Fig. 5.

Optimization of a honeycomb lattice of hexagonal GaAs cylinders in air (a) the unit cell of the initial structure and its dispersion diagram (b) the unit cell of the optimized structure and its dispersion diagram

Fig. 6.
Fig. 6.

Optimization of a hexagonal lattice of hexagonal air holes with orientation θ = 24≊ in GaAs and the filling factor ƒ = 0.805 (a) the unit cell of the initial structure and its dispersion diagram (b) the unit cell of the optimized structure and its dispersion diagram

Fig. 7.
Fig. 7.

Optimization of a square lattice of square air holes with orientation θ = 30° in GaAs and the filling factor ƒ = 0.68 (a) the unit cell of the initial structure and its dispersion diagram (b) the unit cell of the optimized structure and its dispersion diagram

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