Abstract
在本論文中，我們從一直觀、簡易物理觀點出發，推導出光能量在洩 漏型及吸收型平面 波導中的衰減量 。分析原理是將此洩漏型或吸收型 平面波導等效地視為三層的平面波導結 構，藉由平面波在介面的反射及 全反射發生時所產生的側向位移(Goos-Hanchen shift)， 利用已知的 公式來計算此平面結構的反射率，由簡單的物理現象求出單位長度內的平 均碰撞 次數，進而得到光能量在上述結構中的衰減情形。此種分析方法 的優點在於其簡易性，省卻 一些繁複的數學函數、積分運算。且可應用 於多層的複雜波導結構中。論文中亦介紹已知的 分析公式，並比較不同 方法的優缺點。 這個簡易的分析步驟亦可延伸應用於覆蓋式側磨單磨光纖半耦合器中。分 析原理亦將此 結構的作用區域等效為一個三層的平面波導，經由適當地 修改相關的物理參數，即可得出光 能量在覆蓋式側磨單模光纖半耦合器 中的衰減量。前述的分析方法及另一嚴謹之耦合理論 分析方法所得之 結果，亦涵蓋於此論文中。我們提出的方法可以合理地解釋光在上述結構 傳播的特性。但因為假設仍過於簡略，未來必須進一步地改進這個缺失。 總而言之，本篇 介紹了一簡單、有趣的方法來探討光在洩漏型、吸收 型的平面波導及光纖波導中，傳輸時 能量的耗損。這個研究主題在設 計及分析光學元件上是相當重要的。 A simple, generalized method of analyzing the light transmission in leaky and absorbing planar waveguides is proposed in this thesis. We use a straightforward and intuitive manner to derive the analytical expression of the power transmission discussed. By utilizing the well-known law for the partial reflection of a plane wave at an interface and the Goos-Hanchen shift happened for the case of total internal reflection, the associated power transmission of the above structure is derived. Advantages of the present method are simple and applicable to multilayer structures with ease. For comparisons, the existing formula for this waveguiding structures is overviewed, and numerical calculations are compared well with our and the other method. An extension of this approach is applied to a medium-clad side-polished single-mode fiber. Calculations based on our simplified method and an expression derived from the sophisticated coupled-mode theory are also made. Our results can explain the behaviors of the light transmission in the above structure. It is still far from satisfaction because some assumptions are made too rough, however. Further works in this subject are needed. In summary, this thesis introduces a simple and interesting approach to analyze the light transmission in leaky and absorbing planar and fiber-optic waveguides. The previous subject is important in designing and analyzing optical waveguide components.