自從1998年T. W. Ebbesen等人分別在Natrue以及Physical Review B期刊上發表次波長金屬孔洞陣列的穿透光異常增強現象，並且引起之後廣泛相關的研究。目前次波長金屬孔洞的穿透光異常增強現象被認為是表面傳播電漿、表面局部電漿以及金屬波導模態的響應所造成。在這些機制中，表面局部電漿以及金屬波導模態都倚賴於金屬波導中的邊界條件。然而，到目前為止還缺乏一個適當數學模型來描述這些局部場形。 這篇論文中，我們使用電磁學理論分析了單一金屬狹縫以及金屬光柵。在單一金屬狹縫中，一個類似表面侷限電磁波的數學模型被提出並且稱呼為Surface modes in waveguide (SMW) 理論。這個SMW理論滿足奈米尺度真實金屬狹縫中的邊界條件。經由分析這個金屬狹縫中的電磁場，可以得到金屬狹縫中的傳播常數以及吸收係數。由SMW理論所得的傳撥常數以及吸收係數都使用Finite Difference Time Domain (FDTD) method 模擬得以驗證其高度的準確度。另外，我們使用SMW理論來修正已知的 Semi-analytical model 並且稱呼此修正後的模型為 Modified semi-analytical model (MSAM)。使用此MSAM模型可以用來分析金屬光柵的光學特性，例如異常的光穿透現象等。 It has been claimed that part of the mechanism of the transmission enhancement is due to the formation of propagating surface plasmon, localized surface plasmon and slit waveguide mode resonance. For these mechanisms, localized surface plasmon and waveguide mode is analysis rely on a suited boundary condition within the slit waveguide. However, until now, it lacks a suited mathematical expression of the localized fields. In this thesis, we analyzed both a single metallic slit and metallic grating using electromagnetic theorem. A mathematical expression of the localized field within the slit is assumed to be similar to the form of surface-confined electromagnetic field, called surface modes in waveguide (SMW). This SMW theory is suited for the boundary condition of a nano-scaled metallic slit with a thick thickness. Through analyzing the EM fields inside of the slit, the analytical solutions of the propagating wave vector inside the slit can be solved. It is shown that the SMW has a good agreement with the simulation of the FDTD method. In addition, a semi-analytical model for the analysis of a metallic grating is modified with SMW theory. We call it modified semi-analytical model (MSAM). By using the MSAM, the transmission anomaly of metallic grating can be well-predicted which is more accurate than current analytical theories for a metallic gratings.
