中文摘要
在積體光學和光纖光學中，展示過很多的波導元件和函數。到目前為止所考慮的傳輸常數還有符合折射率的場強，如果要精確算出是非常複雜、難以計算的，為了處理這些基本的問題，我們應該利用一些從物理和數學角度提出的近似方法。
在本論文中，我們應用一種藉由研究波導結構中傳導模態的傳輸常數的近似方法，這個方法的來源很像熟悉的Lorentz reciprocity theorem。方程式用場強與折射係數寫出兩種不同波導中的傳輸常數的關係，雖然這個公式已經存在很久了，可是卻很少在文獻中被提起。為了瞭解這個近似方法的難易與好壞，我們把計算的近似結果與真正精確算出的數值比較。在我們提出的例子中，我們發現近似結果與精確數值的差異非常小，介於0.002%~0.0005%之間，也就是說這個式子在波導結構中的數值計算傳輸常數是非常近似的，因此很有可能可以通用在之前提過的問題上面。為了更準確的接近精確值，我們也會介紹反覆的近似方法。

Abstract
As far as the quantitative analyses of propagation constants are concerned, the corresponding index profiles, encountered in the real world, are too complicated which makes the exact results of the propagation constants in the wave-guiding structures unlikely. To handle this basic problem, we should resort to some kinds of approximations, either from physic or from mathematic points of view.
In this thesis, we apply an approximation method, which has a closed-form expression. The closed-form expression tells the relationship between the two propagation constants in each of two different waveguides. To check how good this approach is, we compare our approximate results with the exact values, if available. In our presented examples, we find that the discrepancies between the exact and the approximate results are rather small, to lie in between 0.002% and 0.0005%. In other words, the closed-form expression for quantitatively estimating propagation constants in wave-guiding structures is likely good, thereby possibly being universal in the problems addressed above. To get a closer result, we also introduce an iterative approach in this thesis as well.

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