光子晶体中的共振诱导效应
Resonance-Induced Effects in Photonic Crystals
摘要：
对于一个简单的面心立方光子晶体的均匀介质球的情况下，我们研究在何种程度上单球米氏共振频率与带隙和是否可以扩大由于附近的共振间隙的宽度。与某些建议相反，可能不会产生惊人的效果。当球体的介电常数$ε_s$大于背景介质的介电常数$ε_b$时，则对于任何填充分数$f$，存在临界$ε_c$，在该临界$ε_c$之上，最低的米氏谐振频率落在（111）晶体方向上的最低的停止间隙内，接近其中间间隙频率。如果是$ε_s <ε_b$，则米氏谐振与（111）截止带隙和全带隙两者之间的对应关系不遵循这样的规则模式。如果米氏共振频率接近间隙边缘，则可以观察到相对间隙宽度由$\approx 5%$共振引起的加宽。
英文摘要：
For the case of a simple face-centered-cubic photonic crystal of homogeneous dielectric spheres, we examine to what extent single-sphere Mie resonance frequencies are related to band gaps and whether the width of a gap can be enlarged due to nearby resonances. Contrary to some suggestions, no spectacular effects may be expected. When the dielectric constant of the spheres $ε_s$ is greater than the dielectric constant $ε_b$ of the background medium, then for any filling fraction $f$ there exists a critical $ε_c$ above which the lowest lying Mie resonance frequency falls inside the lowest stop gap in the (111) crystal direction, close to its midgap frequency. If $ε_s <ε_b$, the correspondence between Mie resonances and both the (111) stop gap and a full gap does not follow such a regular pattern. If the Mie resonance frequency is close to a gap edge, one can observe a resonance-induced widening of a relative gap width by $\approx 5%$.
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