我們使用了幾何光學的思考模式，討論折射率分佈為步階式平板耦合器的耦合係數。我們舉出了在強耦合與弱耦合情形下的幾個範例，將計算結果與傳統耦合模理論以及E. Marcatili所提出的改良式耦合模理論來做比較。在弱耦合情況下，可以發現上述三種方法均得一致的結果；強耦合情形下，幾何光學法的計算結果與改
良式耦合理論較相近。而從範例裡的結果，我們推論幾何光學法可以得到較改良式耦合模理論準確的耦合係數。此外，幾何光學法中所使用的觀念、公式與計算都相當簡單。相對之下，改良式耦合理論在這些方面就顯得複雜的多。

為了詳細檢查各耦合平板不同傳播模式的相互耦合情形，我們探討了基模對基模以及第一激模對第一激模的交互耦合。於是，我們可以輕易的檢查耦合模的基本假設的正確性。經由我們所提出的例子裡可以看出，幾何光學法在分析平板型波導以及相關元件是非常強而有力的。在本論文研究中，我們同時證實了Goos- Hähnchen位移這個經常被忽略的現象，其實在分析二維波導結構是一非常有用且重要的物理參數。

Discussed are cross-coupling coefficients of two coupled step-index slabs using a ray-optic method. Calculations are made and compared with the so-called the conventional coupled-mode theory (CMT) and the improved CMT proposed by Marcatili. Here both weakly and strongly coupled slabs are illustrated and quantitatively compared. For weakly coupled slabs, excellent agreements among these three methods are found. For strongly coupled slabs, our ray-optic result can be close to that of the improved CMT. From illustrating examples, our ray-optic method demonstrates a better and accurate result in comparison with the improved CMT. Furthermore, the concept, formulation, and calculations of our ray-optic method turn out to be much simpler than those of the sophisticated improved CMT.

To examine the cross couplings of the guided modes in each of the coupled slabs in further detail, we investigate the cross coupling of the fundamental mode to the fundamental mode and of the first-excided mode to the first-excited mode. Accordingly, we can easily check the validity of the basic assumption of any a CMT. From our presented examples, it seems that our ray-optic method is a powerful approach in analyzing slab waveguides and related devices. In this work, we also demonstrate the usefulness and importance of an often neglected phenomenon Goos-Hähnchen shift in the analysis of step-index two dimensional slabs.

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