三维面心立方晶格的光子带隙
Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices
摘要：
我们表明，光子模拟的Korringa-Kohn-Rostocker方法是一个可行的替代平面波方法来分析电磁波在一个三维的周期性介电晶格的频谱。首先，在均匀的介质球的fcc晶格的情况下，我们再现的主要特征的频谱通过平面波方法，即，对于足够高的介电对比度的一个完整的间隙打开之间的第八和第九频带的频谱中，如果球的介电常数$ε_s$低于介电常数$ε_b$的背景介质。如果为$ε_s> ε_b$，则在光谱中未发现间隙。在密排情况下，相对带隙宽度的最大值接近14%，并随着填充率的减小而单调减小。在光谱中完全能隙打开的最低介电对比度$ε_b/ε_s$被确定为8.13。最后，在一个面心立方晶格的涂层球的情况下，我们证明了一个合适的涂层可以提高间隙宽度高达50%。
英文摘要：
We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a viable alternative to the plane-wave method to analyze the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we reproduce the main features of the spectrum obtained by the plane wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eights and ninth bands if the dielectric constant $ε_s$ of spheres is lower than the dielectric constant $ε_b$ of the background medium. If $ε_s> ε_b$, no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast $ε_b/ε_s$ for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of an fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.
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