Abstract

Using the block-iterative frequency domain method and the non-orthogonal FDTD method, the photonic band gap (PBG) and spectral properties are investigated for a new class of two-dimensional (2-D) trigonal structures with an approximately circular or hexagonal “atom” shape formed by holographic lithography. Calculations of band structures as a function of the intensity threshold show that the PBG of 2-D titania arrays opens only for TM polarization, and directional PBG can open for TE and TM polarization simultaneously. In addition, up to four sizeable full PBGs can open for an inverted GaAs triangular structure.

© 2003 Optical Society of America

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Appl. Phys. Lett. (2)

T. Kondo, S. Matsuo, S. Juodkazis, H. Misawa, �??Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,�?? Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

A. Shishido, Ivan B. Diviliansky, I. C. Khoo, T. S. Mayer, �??Direct Fabrication of Two-Dimensional Titania Arrays Using Interference Photolithography,�?? Appl. Phys. Lett. 79, 3332-3334 (2001).
[CrossRef]

Comput. Phys. (1)

J. P. Berenger, �??A perfectly matched layer for the absorption of electromagnetic waves,�?? J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

J. Appl. Phys. (1)

V. Berger, O. Gauthier-Lafaye, E. Costard, �??Photonic band gaps and holography,�?? J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

J. Mod. Opt. (1)

R. Padjen, J. M. Gerard, J. Y. Marzin, �??Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems,�?? J. Mod. Opt. 41, 295-310 (1994).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (1)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, A. J. Turberfield, �??Fabrication of photonic crystals for the visible spectrum by holographic lithography, �?? Nature 404, 53-56 (2000).
[CrossRef] [PubMed]

Opr. Lett. (1)

L. Z. Cai, X. L. Yang, Y. R. Wang, �??All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,�?? Opt. Lett. 27, 900-902 (2002).
[CrossRef]

Opt. Commun. (1)

M. Plihal, A. Shambrook, A. A. Maradudin, P. Sheng, �??Two-dimensional photonic band structures,�?? Opt. Commun. 80, 199-204 (1991)
[CrossRef]

Opt. Express (1)

Opt. Lett (1)

L. Z. Cai, X. L. Yang, Y. R. Wang, �??Formation of a microfiber bundle by interference of three noncoplanar beams,�?? Opt. Lett. 26, 1858-1860 (2001).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (5)

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

A. J. Ward and J. B. Pendry, �??Calculating photonic Green's functions using a nonorthogonal finite-difference time-domain method,�?? Phys. Rev. B 58, 7252-7259 (1998).
[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]

C. M. Anderson and K. P. Giapis, �??Symmetry reduction in group 4 mm photonic crystals�??, Phys. Rev. B 56, 7313-7320 (1997).
[CrossRef]

X. Zhang, Z.Q. Zhang, L. M. Li, C. Jin, D. Zhang, B. Man, B. Cheng, �??Enlarging a photonic band gap by using insertion,�?? Phys. Rev. B 61, 1892-1897 (2000).
[CrossRef]

Phys. Rev. Lett. (4)

C. M. Anderson and K. P. Giapis, �??Larger two-dimensional photonic band gaps,�?? Phys. Rev. Lett. 77, 2949-2952 (1996).
[CrossRef] [PubMed]

Z. Y. Li, B. Y. Gu, G. Z. Yang, �??Large absolute band gap in 2D anisotropic photonic crystals,�?? Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

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]

Phys. Rev. Lett. B (1)

X. H. Wang, B. Y. Gu, Z. Y. Li, G. Z. Yang, �??Large absolute photonic band gaps created by rotating noncircular rods in two-dimensional lattices,�?? Phys. Rev. B 60, 11417�??11421 (1999).
[CrossRef]

Other (1)

Richard Brent, Algorithms for minimization without derivatives (Prentice-Hall, 1973; republished by Dover in paperback, 2002).

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Figures (5)

Fig. 1.
Fig. 1.

(a) 2-D triangular photonic lattice fabricated by the interference technique of three noncoplanar beam and the first Brillouin zone with the symmetry points indicated; (b) and (c), dotted lines (I) present the relation between the intensity threshold and the FR of dielectric, and solid lines (II) present the derivative of curves (I), where (b) is for titania and (c) is for GaAs.

Fig. 2.
Fig. 2.

(a) TM gap map for the 2-D triangular titania arrays; (b) TM photonic band structure for It =3.0.

Fig. 3.
Fig. 3.

(a) Gap map of directional PBG for 2-D titania arrays; (b) Gap map of full PBG for the inverted GaAs structure, where blue area is for TM polarization, red is for TE polarization and yellow area is for both.

Fig. 4.
Fig. 4.

The directional photonic band diagrams (a and c) and calculated transmission spectra (b and d) for TE (red line) and TM (blue line) polarizations respectively, where (a) and (b) are for It =3.0, and (c) and (d) are for It =4.6.

Fig. 5.
Fig. 5.

Photonic band structures when the intensity threshold is 1.6 (a) and 2.0 (b) for TE (red line) and TM (blue line) polarizations, respectively.

Equations (1)

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I 0 = 3 + cos [ 2 π 3 a ( 2 y ) ] + cos [ 2 π 3 a ( 3 3 x + y ) ] + cos [ 2 π 3 a ( 3 3 x y ) ] ,

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