雙曲色散超材料具有奇特的雙曲色散特性，在入射波長遠大於雙曲色散超材料的晶格大小時，其光學性質可由等效介質理論描述和預測。因此，我們利用表面電漿耦合來計算雙曲色散超材料的電漿子能帶結構以預測更準確的光學性質，該理論適用於任意晶格大小。我們透過計算雙曲色散超材料的表面阻抗，預測在帶隙中表面態的存在。藉由改變晶格中金屬與介電質的比例，雙曲色散超材料能分別與金屬、介電質或其他雙曲色散超材料形成表面態。我們更進一步找到帶隙中表面態的存在性與相鄰能帶的阻抗之間的密切關係，稱為塊材與邊緣對應。該塊材與邊緣對應關係適用於所有具有反轉對稱的雙曲色散超材料。最後，我們提出兩個實驗用以驗證表面態的存在，其一是利用寬頻入射光用棱鏡耦合出表面態並量測其反射率﹔其二是直接利用電子束直接激發表面態。

We first review the fundamental properties of the surface plasmon polariton (SPP) and the effective medium theory approach to hyperbolic metamaterials. Then we go beyond effective medium theory and calculate the plasmonic band structure of the one-dimensional hyperbolic metamaterial (1DHMM) based on the coupled SPPs. In the plasmonic band gap of 1DHMM, we scrutinize the existence of an interface state on three types of interfaces: dielectric/1DHMM, metal/1DHMM, and 1DHMM/1DHMM. The existence of the interface state is determined by the wave admittance of the 1DHMM in the gap region. Interestingly, we develope the rigorous relation between the existence of interface and the wave admittance in the band region, such relation is identified as the “bulk-interface correspondence” of
1DHMM. We further show that the “bulk-interface correspondence” holds for any 1DHMM with inversion symmetry. We also propose two potential experiments of exciting the interface states by using white light source and electron beam, respectively.

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