本論文主要為觀察TM波通過二維單狹縫（single slit）所產生的現象，雖然已有眾多研究著手於單狹縫或光柵結構激發的表面電漿（surface plasmon）現象[1-50]，但是在狹縫中的電磁場行為表現尚未有一完整合理的解釋，本研究發現，在次波長單狹縫的穿透率中金屬與完美導體皆有類似FP（Fabry-Perot）的共振峰，狹縫寬度的改變會造成有效折射率（effective refractive index）的變化，致使共振峰相較於用FP所估計的共振峰值較紅位移，我們利用FDTD及單狹縫理論解析解[27-28]也做了詳細的驗證。金屬與完美導體間也存在著顯著的不同，穿透率共振峰由表面電漿色散關係圖知會造成共振峰出現在紅移的位置，在單狹縫寬度極小（Very Narrow Slit）時，電磁波穿率行為是由表面電漿所主導，此時，狹縫中兩處空氣與金屬交界面所激發的表面電漿的耦合現象更明顯，共振峰因而出現在更紅移的位置，而當狹縫開孔寬度較寬時，金屬的表現才會趨近於完美導體。

This thesis is to study the transmission behavior of Transverse Magnetic (TM) wave through 2D single slit. Although there have been many research papers working on the excitation of surface plasmons in sub-wavelength single slits or periodical grating structures, there still lacks a complete explanation on the electromagnetic wave properties in such sub-wavelength structure. We use the finite-difference time-domain (FDTD) method and analytical solutions to make a detailed study on the transmission behavior of a single slit. Our study found that in the sub-wavelength slit of perfect electric conductor (PEC) or real metal, the transmission spectrum has resonant peaks similar to those found in the Fabry-Perot cavity. The slit width will affect the effective refractive index inside the slit channel, and will cause the red shift of the resonant peak. This red-shift is more significant for the real metal than the PEC single slits due to the dispersion relation of the surface plasmons generated on the real metal and dielectric interface. When the slit width becomes much smaller, there is a strong coupling between the two surface plasmon waves generated on the metal-dielectric interface on each side of the slit. This lead to further red shit behavior of the transmission resonant peak. When the slit width becomes large, the transmission behavior of the real metal and PEC will become similar.

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