束縛態是指波被局部或完全的束縛在某特定頻段中，換言之決定系統內是否存在著束縛態可由特定頻段做判定，若頻段坐落於連續頻譜之中，則此束縛態將有兩種情形，一種是有能量洩漏的共振模態，是為局部性束縛之離散共振模態，一種是無共振模態，是為連續頻譜中的束縛態(Bound states in the continuum, BIC)。而BICs又可藉由其生成的機制不同分成被對稱性保護之束縛態(symmetry-protected BICs)以及非對稱性保護之束縛態(non-symmetry-protected / accidental BICs)等兩種。
BICs生成之相關研究於近年不斷地被提出，例如利用光子-電漿子系統或電漿子-電介質結構系統加以混合形成一種hybrid BICs，而現下也能夠將研究之成果廣泛應用於光感測、雷射及濾波等領域。亦可嘗試透過金屬導體、光子晶體等材質產生表面電漿極化(surface plasmon polaritons, SPPs)以生成BICs，但由於金屬高損耗特性，於是僅以SPP方式所生成的Quality factor通常不明顯。進一步考慮SPP機制下形成的局部表面電漿共振(Localized Surface plasmon resonance, LSPR)，因其電磁場震盪方式與生成於特定頻段等特性，可將其視為一種侷限態，藉由模擬與研究討論SPP與LSPR相互影響並生成BICs的可能及原因。
本論文研究使用有限差分時域法進行數值模擬，並以單一介面之奈米凹槽週期性結構、有限長薄板之奈米週期性結構等兩種系統分別討論兩種系統下，能帶結構上各個模態的分佈情形、相互的影響以及BICs的產生。於單一介面之奈米凹槽週期性結構之模擬結果可發現在特定頻段中若SPP傳播模態與LSPR侷限態同時產生、共存，其中亦有High Q factor的存在，此High Q factor點即此系統所產生的一種非對稱性保護之束縛態(accidental BICs)。於有限長薄板之奈米週期性結構之模體結果可發現在特定頻段中若SPP傳播模態與各階LSPR侷限態同時生成、重疊，且對應階數LSPR之Linewidth足夠窄則可產生High Q factor，而這些High Q factor點上的SPP與奇數、偶數階LSPR各自之週期結構對稱性發現SPP傳播模態與奇數階LSPR等兩模態震盪於金屬結構左右之震盪電荷分佈方式不同，使兩模態相互干涉、相消產生了accidental cancellation，進而生成非對稱性保護之束縛態(accidental BICs)。

Bound state means that the wave is completely bound in a specific frequency band, in other words, whether a bound state exists in the system can be determined by a specific mode with infinite quality factor. If the frequency band is located in the continuous spectrum, there are two situations, one is a resonance mode with energy leakage, which is a discrete resonance mode with finite quality factor, and the other is a mode decoupled to the outside with infinite quality factor, which is called Bound states in the continuum (BIC). BICs can be divided into two types: symmetry-protected BICs and non-symmetry-protected/accidental BICs.
Researches related to the generation of BICs have been continuously proposed in recent years. For example, the plasmonics and dielectric structure are mixed to form a hybrid BICs. The BIC research can also be widely used in the fields of optical sensing, laser and filtering. In this work, we try to generate surface plasmon polaritons (SPPs) BICs in periodic metallic structure. Due to the high material loss characteristics of metal, plasmonic modes typically have low quality factor. BIC in plasmonic can eliminate the optical loss and lead to high quality factor only limited by the material absorption. First, we try to find the symmetric protected BICs. Further considering the localized surface plasmon resonance (LSPR) along with the SPP, the accidental BIC due to the cancellation of LSP and SPP radiation can be found. Finally we discuss the possible mechanisms for the generation of BICs under the interaction of SPP and LSPR.
In this thesis, we use Finite-Difference Time-Domain method to numerically simulate Nano grooved periodic structure at a single interface and Nano periodic structure of finite-length metal slab. In the two systems, the field distribution of each mode at different k point on the band structure, the mutual influence of LSPR and SPP on the generation of BICs are discussed.
In the nano grooved periodic structure with a single SPP interface, the accidental BICs with High Q factor can be found that if the SPP propagation mode and the LSPR occur simultaneously in a specific frequency band. In the nano metallic periodic structure with finite-length thin metal slab, both symmetry protected BIC and accidental BIC can be found. Symmetry protected BICs are found at the  and X point. Accidental BIC are found when + SPP propagation mode and the odd LSPR mode of the metallic slab occur simultaneously. The charge oscillation symmetry of the SPP mode and the odd-order LSPR mode are opposite and lead to the cancellation of each radiation, resulting in the accidental BICs.

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