連續頻譜中的束縛態(bound states in the continuum, BICs)是存在於連續頻譜中但在空間上被束縛住並擁有無限生命週期的一種特殊態，BICs可由形成機制的不同分成被對稱性保護(symmetry-protected)的BICs和沒有被對稱性保護(non-symmetry-protected)的BICs兩種，而近期的許多文獻都已在光子晶體中發現上述的兩種BICs且闡明其物理機制，也在實驗中做出並應用於雷射、感測等諸多方面，然而BICs也被預期會存在於金屬結構中，但尚未實現並完全了解其物理機制。
本篇論文中，我們使用有限差分時域法(Finite-Difference Time-Domain method, FDTD)數值模擬一維週期性電漿子晶體，並發現在特定條件下，金屬片左右兩面的表面電漿極化(surface plasmon polaritons, SPPs)主導的共振模態的輻射波會互相抵消而產生沒有被對稱性保護的quasi-BICs，並畫出電場、電荷分布圖驗證Plasmonic BICs是由odd modes SPPs主導的共振模態所形成的物理機制，然後測量品質因子、poynting vector和衰減係數驗證其為quasi-BICs，再畫出等效厚度下的SPP曲線進一步確認此物理機制無誤，接著微調金屬片的結構參數，結果顯示這些quasi-BICs不會消失且會沿著布理淵區(Brillouin zone)移動，這表明了BICs的拓樸電荷(topological charge)性質。然後延伸至雙層一維週期性電漿子晶體，發現兩金屬片內外會有電磁場密度不同的現象，雖然也會產生quasi-BICs，但由於輻射波抵消較差造成品質因子普遍不高。最後將模擬空間擴展至三維，由此布里淵區也擴展成二維空間，並發現quasi-BICs會隨著ky增加沿著kx方向移動，與三維介電質的現象大相逕庭，並提出Plasmonic BICs會出現在電漿子晶體色散曲線和等效厚度下SPP曲線交點的理論。

Bound states in the continuum are the special states that exist in the continuous spectrum but are bounded in space and have infinite lifetimes. According to different formation mechanisms, BICs can be categorized into symmetry-protected-BICs and non-symmetry-protected-BICs. Many recent papers have found the above two BICs in photonic crystals and clarified their physical mechanisms. BICs have also been made in experiments and applied to many aspects such as lasers and sensors. However, BICs are also expected to exist in metallic structures, but their physics mechanisms have not yet been realized and fully understood.
In this thesis, we use Finite-Difference Time-Domain method to numerically simulate one-dimensional periodic plasmonic crystals. We find that under certain conditions, the radiative waves of the resonance modes dominated by surface plasmon polaritons on both sides of metal bar will cancel each other and thereby generating high Q-factors. Next, we draw the field and charge distribution to verify that the physical mechanism of Plasmonic BICs is the resonance modes dominated by odd modes SPPs. We measure Poynting vector and attenuation coefficient and draw the SPP curve under the equivalent thickness to verify whether they are quasi-BICs. By further fine-tuning the structural parameters of the metallic bar, these quasi-BICs would not disappear and move along the Brillouin zone, which indicated the topological charges property of BICs. Then we extended the structures to the 1D periodic double-layers plasmonic crystals, it was found that there will be a different electromagnetic field density between two metal bar and outside, although quasi-BICs will also be produced, but quality factors are generally reduced due to poor radiation cancellation. Finally, we expanded the simulation to three-dimension, from which the Brillouin zone also expanded into two-dimensional k space. We found that quasi-BICs will move along kx direction with the increasing of ky, which is quite different from the isolated BIC phenomenon in 3D dielectrics. We proposed the theory that Plasmonic BICs will appear at the intersection of the plasmonic crystal dispersion curve and the SPP curve under equivalent thickness.

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