以嚴謹耦合波分析次波長光柵反射器

Abstract

在本篇論文中，我們將專注於利用嚴謹的耦合波展開法(rigorous coupled wave analysis, RCWA)這種廣泛被利用在電磁計算的數值方法設計並分析一維次波長的光柵反射器，目的是希望能夠不需要利用非常複雜的幾何結構就可以製造出良好反射器的效果。以實用的角度來講，反射器的反射效率將在共振腔的設計上扮演決定性的角色，並且，近二十年來，許多研究指出光柵式反射器確實有可能應用在面射型雷射(Vertical-cavity surface-emitting lasers, VCSELs)上。在我們的研究之中將分別找尋正向入射時TE與TM極化在不同折射率對比之下光柵反射器的結構參數，並且直接利用RCWA這種數值方法畫出場形以及分析電磁波的相位變化來討論為什麼這種次波長的光柵結構可以具有強反射的物理特性。在我們的模擬工作中，折射率對比將分類為高折射率對比、中等折射率對比、低折射率對比的狀況，並且在每個狀況中舉出若干範例。其中，我們對中等折射率對比和低折射率對比的狀況花費較多心力，經過模擬我們認為經過妥善的設計，儘管在折射率對比差異較小的狀況下仍然有可能利用光柵反射器製造出高反射。除了正向入射的研究之外，我們也嘗試討論沿光柵溝槽方向有一個夾角入射的情況，希望透過妥善的設計讓光柵反射器有讓電磁波在低吸收性損耗介質中傳導的可能。

In this thesis, we devote to design and study one-dimensional subwavelength grating reflector by rigorous coupled wave analysis (RCWA), which is a famous numerical method in electromagnetic problem calculation. Our goal is to make a high reflection efficiency device without complicate geometric structure. In view of practical applications, reflection efficiency of a reflector plays an important role in designing a resonance cavity. In addition, lots of researches in past two decades have shown that grating reflector is possible to be used in vertical-cavity surface-emitting lasers (VCSELs). In our research, we will first try to design the parameters of grating reflector under normal incidence in different refractive index contrast of grating for TE and TM polarization respectively; furthermore, we will plot the field patterns and observe the phase difference between incident, reflection and transmission waves by RCWA calculation in order to figure out why such device could be a nice reflector. In our simulation, refractive index contrast difference is classified as high index contrast, medium index contrast, and low index contrast cases and we will show at least one example in each case. Among them, we will pay more attention on medium index contrast and low index contrast cases. After simulation, we consider that it is still possible to obtain high reflection efficiency in low index contrast case by properly designing parameters of grating reflector. In addition to the case of normal incidence, we also try to study the case of incident waves has an angle between those parallel grating bars. We hope to find the possibility to guide wave in low absorption loss medium by properly designing this kind of grating reflector.