以有限元素法分析光子晶體光纖之模態特性

Abstract

為了瞭解在光子學領域上日益重要的光子晶體光纖之模態特性，我們採用高精準度的曲線式混合基底元素之全向量有限元素特徵值解法以及虛軸波束傳播法來進行分析。由於有限元素法使用非均勻切割的曲線形元素，是故可精確分析屬複雜結構的光子晶體光纖。本論文分析了數種光子晶體光纖。首先分析光子晶體光纖耦合器之模態及其耦合強度，分析結果呈現和傳統的耦合器一致的趨勢。接著，分析空氣纖心的光子能隙光纖其損耗、群速色散、和有效模態面積，藉由增加空氣洞環的數目、提高空氣洞半徑對洞間距的比例或是適當設計空氣纖心的形狀，損耗可以降低。最後，我們分析短波長時光子晶體光纖的頻譜特徵，頻譜圖可由圓柱孔洞的直徑和填充在內之液體的折射係數決定。其導波機制可藉由視此光子晶體光纖為一抗諧振反射光纖的解析理論來解釋，此解析理論可精準預測相關數值結果。

In order to comprehend the properties of photonic crystal fibers (PCFs), which play a more and more important role in photonics applications, a variety of PCFs are investigated by using a high-accuracy full-vectorial finite element (FE) mode solver and the finite element imaginary distance beam propagation method (FE-ID-BPM) based on curvilinear hybrid edge/nodal elements. Because of the utilization of the nonuniform element division and the curvilinear elements, PCFs having complex structures can be analyzed accurately. In this thesis, several PCFs are discussed in detail. First, the propagating characteristics and the coupling strength of twin-core PCFs are studied and explained. It is observed that the computed results of twin-core PCFs have similar trends with those of conventional fiber couplers. Next, the analysis of air-core photonic bandgap fibers (PBGFs) is performed through calculating the con nement losses, the group velocity dispersions, and the effective mode areas. It is demonstrated that the con nement losses can be reduced by increasing the number of air-hole rings, raising the diameter to hole pitch ratio, or appropriately designing the air-core shape. Finally, we analyze the loss spectra of PCFs especially at shorter wavelengths. The numerical results show that the loss spectra are strongly determined by the size of the cylinder inclusions and the refractive index of the liquid lled in these inclusions of the PCFs. Besides the numerical investigation, an analytical theory which treats the PCFs as antiresonant reflecting optical waveguides is adopted to explain the guiding mechanism. Calculated wavelength dependence of the effective refractive indices of the guided modes is well predicted by the analytical theory.