不規則柱狀波導之分析

Abstract

在本篇論文中提出一個近似的方法來分析任意形狀的介質波導. 不管它 的幾何形狀為何, 我們都可以把一個介質波導用內切圓和外接圓分成三個 部份, 最□面和最外面都是均勻的介質, 而中間的介質則是不均勻的. 我 們的近似方法就是將這介質的不均勻視為一個擾動的現象, 如此一來, 任 意形狀的波導我們便能將它視為一個擾動的柱狀介質波導, 而改用以有系 統的方法來分析. 以方形介質波導來說, 文獻中最低四個模的傳播常數跟 用這個近似方法所算出的最低四個模的傳播常數非常的接近. 這個方法所 用到的結構是在光纖光學□常用到的柱狀結構, 而且所需的層數不多, 所 以很容意可以引用也不需要太大的運算量. 最後我們也以同樣的方法分析 正三角形, 正五邊形, 正六邊形介質波導. In this thesis, we present an approximate method of analysis for dielectric waveguides of finite crosssection. Regardless of its geometrical configuration, a waveguide crosssection can always be divided into three regions by two concentric circles, such that the inner and outer regions are uniform in dielectric constant and the region in-between contains nonuniform dielectric constant. Our approach is to take the nonuniformity of the dielectric constant as a perturbation, so that a dielectric waveguide of any crosssection geometry can be regarded as a perturbed circular dielectric waveguide which can be treated in a systematic way. From the results, we find that the propagation constant of the lowest four modes of multi-layer concentric cylindrical dielectric waveguide achieve good agreement with the propagation constant of square dielectric waveguide performed by other methods. The structure applied here includes only cylindrical geometry used commonly in fiber optics, and not many layers are needed, so it is easy to implement and takes less CPU time. At last, we also use the structure to approximate dielectric waveguide with other shapes of crosssection, including equilateral triangle, equilateral pentagon, and equilateral hexagon.