非均勻介質波導之分析

Abstract

有關能量藕合於兩曲形介質波導之間的問題,已早有嚴謹的數值方法。像 是階梯近似法, 配合著多模網路理論和模匹配程序, 已有相當好的數值結 果. 然而, 此方法是數值性的, 而且必須依賴大量的數值分析, 過程頗為 繁複, 實難成為一種解析性高的方法。 因此, 本論文便提出: 部份定數 近似法及WKB近似法, 此二種方法較前者簡易且解析性高。 此外, 我們還 提出另一種方法, 將原為非線性之波動方程式作線性近似, 使成為Airy方 程式, 來分析此問題。 我們根據這些數值結果分析了, 此定向藕合器之 藕合長度對能量傳遞的影響以及傳導長度對能量傳遞的影響。 希望藉由 這些解析性高的數值方法, 分析其它更多不同形狀之介質波導定向藕合器 。 There have been some rigious methods to analyze the problem of the energy coupling between two curved dielectric waveguide. For example, the method of staircase approximation combining with the builing block approach of multimode network theory and the mode-matching procedure. However, the method is numerical in nature and has to rely on extensive numerical analysis. In this work, we try to use two different approximate methods to analyze the nonuniform transition waveguide. One is the piecewise-constant method, which combines the building network of transmission line with EDC method. Another is the method of WKB approximation, which solves the Helmholtz equation of the wave propagation in the nonuniform transition region by simplifying the solution form. Furthermore, for the case of linear variation of the nonuniform dielectric, we utilize the Airy function to construct an exact solution, form which a set of bench mark results are extablished. Finally, numerical results are obtained by the two different methods to the analyses of effect of coupling length and effect of transition length. We attempt to solve much more the problems of the dielectric waveguides di- rectional couplers with any geometrical structure by these an- alytic methods.