Boundary Conditions and Edge States at Photonic Crystal Interface

S. Aleksandr, Kapaev Vladimir, Gorbatsevich Alexander, Friman Aleksandr
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Abstract

Modern nano-electronics faces a problem if reducing power losses and increasing signal transfer speed in interchip and intrachip interconnects. These demands can be satisfied with electrical/optical conversion and implementation of different types of optical interconnects. In the paper, a quantum mechanical theory of interfacial localized electronic states in envelope function approximation is generalized to the description of photonic modes in quasi-periodic media with an abrupt change of optical characteristics, which are localized near the interface. It is shown that there exist both donor-like and acceptor-like photonic modes corresponding the levels in the photonic gap split off either the upper or lower edge of the photonic gap. The description of localized modes regarding envelope functions is presented, and the conditions of mode stability are studied. The possibility of fabricating photonic crystal interfaces with topologically nontrivial edge modes is discussed.
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光子晶体界面的边界条件和边缘态
现代纳米电子学面临着如何在片间和片内互连中降低功率损耗和提高信号传输速度的问题。这些需求可以通过电/光转换和实现不同类型的光互连来满足。本文将包络函数近似下的界面局域电子态量子力学理论推广到具有光学特性突变的准周期介质中在界面附近局域的光子模式的描述。结果表明,在光子隙的上边缘或下边缘分裂出的光子隙中,存在类给体光子模式和类受体光子模式。给出了包络函数的局部模态描述,并研究了模态稳定的条件。讨论了制造具有拓扑非平凡边缘模式的光子晶体界面的可能性。
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