多層介質之表面波與體積模態分析

Abstract

本文主要在於討論激發表面電磁波的機制。我們知道最簡單可以激發表面模態的結構是單層介質層板波導，因此我們由此結構來觀察如何激發表面電磁波。我們利用橫向諧振法搭配轉移矩陣來解結構的色散關係式，並畫出色散曲線圖，在等效介電常數大於1的時候存在表面模態。接著另一側為了要利用週期性結構的禁帶，我們將 Rogers RO 5880(介電常數2.2)和矽(介電常數11.9)兩種材料排列成一組單位元，為了簡化計算繁複與實際應用等考量，選取五組單位元排列成多層介質的結構，希望能達到週期性結構的效果。解此多層介質單邊短路的色散曲線並與週期性結構的色散曲線重疊，可以找出表面模態在曲線上的位置。最後我們用電磁模擬軟體CST來輔助驗證我們的想法。

In this thesis, the mechanism of surface wave excitation is discussed. As we know, single-layered dielectric slab waveguide is the simplest structure that can excite surface wave, and this structure is utilized as the basic of our study. We use transverse resonance technique (TRT) incorporating transfer matrix to solve and plot the dispersion relation for a given structure. The surface mode exists when the effective dielectric constant is greater than one. Specifically, the periodic structure, which operates at the stop-band region, with unit cell consisting of two different materials is placed adjacent to the single layered dielectric slab. These materials are RO5880 and silicon. To simplify the computational cost and take practical fabrication into account, the infinite unit cells are truncated and reduced to five unit cells while the effect of periodic structure is still preserved. The dispersion curve of complete structure and the band structure of grating with infinite periodicity are graphically overlapped which can identify the location of surface mode. Finally the commercial electromagnetic package CST MWS is employed to verify the feasibility of this research.