以全向量虛軸有限元素波束傳播法分析光子晶體光纖

Abstract

在本論文裡,我們採用以曲線混和型元素為基底的全向量有限元素虛軸波束傳播法搭配完美匹配層來精準地分析兩種以不同導波機制－修正型全反射導波與光子能隙導波－來導光的光子晶體光纖。 我們首先經由調整單極化單模態型光子晶體光纖耦合器內的大空氣洞與小空氣洞的半徑來了解其模態特性與耦合特性。從計算分析的結果我們發現耦合器的單極化單模態耦合區間的頻寬與位置可以藉由調整其結構中空氣洞的半徑大小來控制。從計算分析的結果我們也發現改變小空氣洞的半徑會比改變大空氣洞的半徑對耦合長度有更敏感的影響。接著，我們分析以空氣做為纖心的光子晶體能隙導光型的光纖。藉由三種不同的、尖角平滑化的多邊形可以更真實地模擬光纖的空氣洞的結構。我們對這種結構的光纖做了一系列完整的模態搜尋。從計算分析的結果我們證實了表面模態的存在，同時經由觀察搜尋出的模態頻譜，可以發現表面模態與纖心模態間有避免結合的現象發生。此外我們也找出了參考文獻中未提出的兩個模態。為了解此光纖結構的色散特性與損耗，本論文也計算出了一系列的結果，並從結果中發現色散曲線與損耗曲線在模態出現“避免結合”現象時，會受到強烈的影響。最後，為了解光纖周圍環繞的空氣洞環數對傳播模態的影響，本論文也探討了一個四個空氣環的結構，並對此結構執行一系列與先前的結構相同的參數分析，我們發現改變空氣環的數目，僅對光纖的損耗會產生影響，對光纖的模態頻譜則影響極小。

In this work, we adopt the full-vectorial finite element imaginary-distance beam propagation method (FE-ID-BPM) based on the curvilinear hybrid edge/nodal elements and the incorporated perfectly matched layers (PMLs) to accurately analyze two types of photonic crystal fibers (PCFs) guiding light by different mechanisms, the modified total internal reflection (TIR) and the photonic bandgap (PBG) guiding. We first analyze the modal characteristics as well as the coupling characteristics of a single-polarization single-mode PCF (SPSM-PCF) coupler through adjusting the diameters of the larger inner air holes and the smaller cladding air holes. From the simulation results, one can observe that the position and the width of the SPSM coupling region can be tailored through adjusting the hole diameters and the coupling length is more sensitive to the changing of the diameters of the smaller cladding air holes than those of the larger inner air holes. Next, we analyze an air-core photonic crystal bandgap fiber (PBGF) which more resembles the experimental structure due to the three types of polygons with their corners being smoothed by circles being used to approximate the air holes. We perform a complete searching for the propagation modes in this air-core PBGF. From the analysis results, the existence of the surface modes and the occurrence of the avoided crossings are confirmed. In addition, the confinement losses and the GVDs of the fundamental air-core mode of the air-core PBGF are also scrutinized and they are observed to be strongly modified by the presence of the avoided crossings. To understand the influence of the surrounding air-hole rings on the propagating modes, a four-ring PBGF is studied and the same numerical tests as in the six-ring PBGF are performed. We find that the real parts of the effective indices of the four-ring PBGF are very close to those of the six-ring PBGF while the confinement losses of the four-ring PBGF are much larger than those of the six-ring PBGF.