| Summary: | 碩士 === 臺灣大學 === 應用力學研究所 === 98 === In this paper, we employ a plane wave expansion method to calculate the band structures of two-dimensional photonic crystals. For the types of photonic crystal, we have studied square lattice, triangular lattice, honeycomb lattice of circular columns, each connected to its nearest neighbors by rectangular rods.
We explore the relation of the radius r/a and the dielectric constant ε of rods, the width d/a of connecting rods to determine full band gaps. The dispersion curves for the TM and TE modes of the propagating electromagnetic waves have been analyzed separately. We found some characteristics of full band gaps :
(1)When TM and TE mode band gaps have approaching the same band edges, maximum full band gaps occur.
(2) Unlike the fundamental band gap which usually opens larger in low-lying bands, we obtain the maximum full band gap to open with high-lying bands. When changing the parameter, the dispersion curves around the full band gap are dense and flat. Material and geometry parameters can affect heavy photon state, but material parameter affect more than geometry parameters. The band structure exhibits a red shift phenomenon in frequency as the geometrical fill factor and material parameter increase. The width of band gaps have depends on the velocity of frequency shift.
(4)For honeycomb lattice, we added the connecting rods and obtain the full band gaps which are smaller than the full band gaps of no connecting rods.
(5) Band gaps of TE mode is very much more variation than band gaps of TM mode.
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