金属基质中孔周期阵列的光子能带结构：超越准静态近似的紧束缚
Photonic band structures of periodic arrays of pores in a metallic host: tight-binding beyond the quasistatic approximation
摘要：
我们已经计算了光子能带结构的金属反蛋白石和周期性线性链的球形孔在金属主机，低于等离子体频率$ω_{\text{p}}$。在这两种情况下，我们使用紧束缚近似，假设Drude介电函数的金属成分，但没有准静态近似。紧束缚模式是单腔横磁（TM）模式的线性组合。对于反蛋白石结构，最低模式是类似于那些从fcc晶体中的三个简并原子p-态构造。对于线性链，在与波长相比的小球的极限中，结果是绝缘主体中的金属球的色散关系的“逆”，如由Brongersma \textit{et al.} [Phys.\修订版本\ B \textbf{62}，R16356（2000）]。由于这些模式的电磁场在金属中呈指数衰减，因此与空气中的金属球阵列的情况相比，没有辐射损失。我们认为，这种紧束缚的方法来光子能带结构的金属逆材料可能是一个有用的方法，研究光子晶体含有金属成分，甚至超越准静态近似。
英文摘要：
We have calculated the photonic band structures of metallic inverse opals and of periodic linear chains of spherical pores in a metallic host, below a plasma frequency $ω_{\text{p}}$. In both cases, we use a tight-binding approximation, assuming a Drude dielectric function for the metallic component, but without making the quasistatic approximation. The tight-binding modes are linear combinations of the single-cavity transverse magnetic (TM) modes. For the inverse-opal structures, the lowest modes are analogous to those constructed from the three degenerate atomic p-states in fcc crystals. For the linear chains, in the limit of small spheres compared to a wavelength, the results are the "inverse" of the dispersion relation for metal spheres in an insulating host, as calculated by Brongersma \textit{et al.} [Phys.\ Rev.\ B \textbf{62}, R16356 (2000)]. Because the electromagnetic fields of these modes decay exponentially in the metal, there are no radiative losses, in contrast to the case of arrays of metallic spheres in air. We suggest that this tight-binding approach to photonic band structures of such metallic inverse materials may be a useful approach for studying photonic crystals containing metallic components, even beyond the quasistatic approximation.
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