Abstract

Our numerical simulation results demonstrate that 2D lattices compounding can create either a broad single complete photonic band gap or both first and second order complete band gaps. The results also show that photonic band gap properties are dependent on both the parameters of the single lattices and the relative position of the two compound lattices. Furthermore, if a compound structure is composed of two sets of lattices, the one with a larger periodic constant (a2) will serve as defects. While the defect modes are direction independent as a2 > 5 a, they are direction dependent as a2 < 5 a. Moreover, by optimizing of the rod size of the lattice with a2, many kinds of defect modes can be obtained to satisfy the different applications. The transmitted spectra and reflected spectra of this kind of structures demonstrate that the transmittances of the defect modes are dependent a2.

© 2005 Optical Society of America

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References

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Chinese Phys.Lett. (1)

Y.C. Zhong, S.A.Zhu, and H.Z.Wang, �??Fabrication of compound lattice by holographic lithography,�?? Chinese Phys. Lett. 22(2), 369-372 (2005).
[CrossRef]

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

Chelnokov, S. Rowson, J. M. Lourtioz, V. Berger, and J. Y. Courtois, "An optical drill for the fabrication of photonic crystals," J. Opt. A Pure Appl. Opt. 1, L3�?? L6 (1999).
[CrossRef]

Nature (1)

S. Noda, A. Chutinan and M. Imada, �??High-Q photonic nanocavity in a two-dimensional photonic crystal,�?? Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Nature (London) (1)

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Blur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature (London) 394, 251-253 (1998).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (2)

C.T. Chan, Q.L. Yu and K.M. Ho, "Order-N spectral method for electromagnetic waves," Phys. Rev. B 51, 16635 (1995).
[CrossRef]

T. Trifonov, L. F. Marsal, A. Rodriguez, J. Pallares, and R. Alcubilla, �??Effects of symmetry reduction in two-dimensional square and triangular lattices,�?? Phys. Rev. B 69, 235112 (2004).
[CrossRef]

Phys. Rev. Lett. (3)

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]

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)

S.Y. Lin, E. Chow, V. Hietala, P. Villeneuve and J. Joannopoulos, �??Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,�?? Science 282, 274-276 (1998).
[CrossRef] [PubMed]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1.
Fig. 1.

Two structures as examples: (a) compound square lattice formed by a square lattice of cylinder rods and a square lattice of thin sheets; (b) compound triangular lattice formed by a triangular lattice of cylinder rods and a triangular lattice of thin sheets;

Fig. 2.
Fig. 2.

(a) Photonic band structure of compound square lattice for r = 0.32 a and d = 0.05 a . Solid lines denote TM mode and dash lines denote TE mode; the purple shadow part shows the complete band gap. (b) Transmittance spectrum and reflectance spectrum (Γ direction) of this structure calculated by FDTD, the black, red, green and blue lines are reflectance spectrum (TE), transmittance spectrum (TE), reflectance spectrum (TM) and transmittance spectrum (TM) respectively. (c) The dependence of complete band gap on the parameter r for the compound square lattice for d = 0.05 a , (d) The dependence of complete band gap on the parameter d for the compound square lattice for r = 0.32 a .

Fig. 3.
Fig. 3.

(a) Dependence of complete photonic band gap width of the compound triangular lattice on the radius of rod r for d = 0.02 a . (b) Dependence of the complete band gap width of the compound triangular lattice on the parameter d for r = 0.32 a .

Fig. 4.
Fig. 4.

Band structures of the compound triangular lattice (a) for d = 0.02 a and r = 0.28 a , (b) for d = 0.02 a and r = 0.32 a . Solid lines denote the TM modes and dash lines denote the TE modes. The purple shaded areas denote the complete band gaps.

Fig. 5.
Fig. 5.

Compound structures which are composed of a lattice with a periodic constant of a and a lattice with a periodic constant of a 2 ( a < a 2 ). (a) a 2 = 3 a , (b) a 2 = 5 a , (c) a 2 = 7 a .

Fig. 6.
Fig. 6.

The defect modes- r 2 relationship, (a) a 2 = 3 a , (b) a 2 = 5 a , (c) a 2 = 7 a . The green shadow part denotes a single defect mode. The green line denotes a single polarization defect mode and a TE and TM overlap defect mode.

Fig. 7.
Fig. 7.

The representative defect modes in broad complete band gap where r 2 is the value shown by the green lines in Fig.6, in which a defect mode is TE and TM overlap defect mode. (a) a 2 = 3 a , the defect modes are incident angle dependent, and (b) a 2 = 7 a , the defect modes are incident angle independent. The frequency in the range of 0.382 to 0.462 is the complete band gap. The red solid lines denote the TM modes and blue dash lines denote the TE modes.

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