Abstract

We study the density of states (DOS) in band gaps of ideal and disordered three-dimensional photonic crystals of finite size. The ideal crystal is a diamond lattice of resonant point scatterers (atoms) whereas the disordered one is obtained from it by displacing the scatterers by random distances in random directions. We find that DOS inside a band gap of the ideal crystal decreases as the inverse of the crystal size. Disorder narrows the band gap and DOS exhibits enhanced fluctuations near the new band edges. However, the average DOS still exhibits the same scaling with the crystal size within the remaining band gap. A phenomenological explanation of this scaling suggests that it should hold for one- and two-dimensional photonic crystals as well.

Graphical abstract

中文翻译：

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理想和无序光子晶体带隙内的状态密度的有限尺度缩放

摘要

我们研究有限大小的理想和无序三维光子晶体的带隙中的态密度（DOS）。理想的晶体是共振点散射体（原子）的菱形晶格，而无序晶体是通过将散射体沿随机方向移动任意距离而从中获得的。我们发现，理想晶体的带隙内的DOS随着晶体尺寸的倒数而减小。无序使能带隙变窄，DOS在新的能带边缘附近表现出更大的波动。但是，平均DOS在剩余带隙内仍具有与晶体尺寸相同的缩放比例。这种标度的现象学解释表明，它也应适用于一维和二维光子晶体。

图形概要