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本文用平面波展开法研究统计模态数目对能量的分布,进而求得光子态密度。光子晶体态密度的分布验证了存在光子带隙的范围,带隙随着填充比的变化而变化。文中研究了以Si、Ge及GaAs为背景的空气柱构成的二维三角格子光子晶体的能态密度随填充比f的变化。其结果表明,在f=0.3时,三角晶格能态密度在0.5818—0.4627Hz没有出现,为最大禁带,且GaAs比Si和Ge更易出现光子带隙。
In this paper, we study the distribution of energy by the number of statistical modes by plane wave expansion method, and then obtain the photon density. The distribution of state density of photonic crystals validates the existence of photonic bandgap, which changes with the filling ratio. In this paper, the energy density of two-dimensional triangular lattice photonic crystal composed of air column with Si, Ge and GaAs as the background changes with filling ratio f. The results show that at f = 0.3, the lattice energy density of the triangular lattice does not appear at 0.5818-0.4627 Hz, which is the maximum forbidden band, and the photon bandgap of GaAs is more likely than that of Si and Ge.