近年來，利用長周期光纖光柵(long-period fiber grating)頻譜特性，許多廣泛運用在光纖通訊系統的元件已經被提出，例如頻帶抑制濾波器(band rejection filters)，增益平坦器(gain flatteners)與色散補償器(dispersion compensators)。相較於布拉格光纖光柵(fiber Bragg gratings)，長周期光纖光柵擁有相當大的頻譜頻寬這是眾所皆知的。到目前為止，在光纖通訊元件的設計上，關於長周期光纖光柵的研究都是著重在核心模態(core mode，HE11)與低階纖殼模態(cladding modes)之間的耦合特性。很明顯的，使用長周期光纖光柵去設計擁有窄頻寬與符合分波多工標準(Wavelength Division Multiplexing standard ，WDM)的光通訊元件幾乎是不可能的，就更不用說符合高密度分波多工標準了(Dense Wavelength Division Multiplexing standard ，DWDM)。
在這本論文中，我們使用嚴謹的模態耦合理論(coupled-mode theory)詳盡的學習與量化長周期光纖光柵的頻譜特性，目的在提供具體設計窄頻寬光纖通訊元件的觀念。相較於由核心模態與纖殼模態之間耦合所導致的寬頻譜頻寬，我們將證明0.4的半功率頻寬(full width at half maximum，FWHM)是可以被達到的，只要長周期光纖光柵的週期是被適當的設計在選擇某個高階纖殼模態。然後，我們將進一步的應用這新的窄頻觀念來設計，架構在兩個平行長周期光纖光柵的窄頻寬光訊號塞取器(optical add-drop multiplexer ，OADM)。除此之外，為了使這個光訊號塞取器擁有最大的功率傳輸，我們也根據用來描述此原件操作原理的四模態藕合方程式，加以推導光訊號塞取器的結構參數，例如兩根平行光纖之間的距離與兩根長周期光纖光柵的長度。
對於在光纖式感測器上的應用，我們結合了傳統長周期光纖光柵感測器與目前光纖式表面電漿共振感測器(optical-fiber surface-plasmon-resonance sensor，SPR)的優點，並且進一步的提出了一個新型的光纖式表面電漿共振感測器。這個新型的表面電漿共振感測器簡單的利用了以適當周期設計，能使核心模態藕合至能激發表面電漿波(surface plasmon wave ，SPW)的纖核模態，的長周期光纖光柵，並且藉由監測操作在一固定波長上的傳輸核心模態功率來判定待測物(analyte)折射率的變動。就表面電漿波的激發，數值模擬的模型與量測設備設置的複雜度而言，很明顯的這個新型的光纖式表面電漿共振感測器是比目前架構在彎曲、拋光、單一模態的光纖式表面電漿共振感測器(bent polished single-mode SPR optical fiber)優越。在這本論文中，我們推導了存在於具四層結構表面電漿共振感測器的傳輸模態色散關係與非共軛形式的模態耦合方程式(unconjugated form of coupled-mode equations)。除此之外，為了大量增加分析此新型表面電漿共振感測器的效率，對於積分形式耦合係數(integration form of coupling constants)的進一步化簡是被提出。數值的結果將證明這個新型、簡單的架構真的能被用來實踐高靈敏度的強度感測器( highly sensitive amplitude sensor )。除此之外，藉由沈積一反射鏡在此光纖末端，這個新型的表面電漿共振感測器可以容易的改變為探針形式的光纖感測器。

In the recent years, utilizing the spectrum characteristic of long-period fiber grating (LPG), numerous components extensively applied on optical fiber communication system have been proposed such as band rejection filters, gain flatteners, and dispersion compensators. In contrast to fiber Bragg grating, it is well-known that the LPG has considerable spectrum bandwidth. So far, on the optical communication component design, the researches as to LPG are all to emphasize the coupling characteristic between core mode HE11 and low order cladding modes. Obviously, it is almost impossible to use LPG to design the optical communication components that possess the narrow bandwidth and conform Wavelength Division Multiplexing standard (WDM), not to mention Dense Wavelength Division Multiplexing standard (DWDM).
In this dissertation, we use strict coupled-mode theory to study and quantify the spectrum characteristic of LPG in detail with the aim of supplying a concrete concept to design narrow-bandwidth optical communication components. In contrast to the wide spectrum bandwidth resulting from the coupling between core mode and low order cladding modes, we will prove that a 0.4 nm FWHM can be achieved as long as the period of LPG is properly designed to choose some high order cladding. Then, we will further apply this new concept to design the narrow bandwidth optical add-drop multiplexer (OADM) based on two parallel LPGs. In addition, in order to obtain the maximal power transmission, we also derive the structure parameters of OADM such as the distance between two parallel fibers and the length of two LPGs according to four-mode coupled-mode equations.
As for the application on optical fiber sensor, we combine the advantages of traditional LPG sensor and present optical-fiber surface-plasmon-resonance (SPR) sensor and further propose a new type of optical-fiber SPR sensor. It simply employs a long-period fiber grating with proper period to couple a core mode (HE11) to the co-propagating cladding mode that can excite surface plasmon wave (SPW) and monitors the change of the transmitted core mode power, which is operating at a fixed wavelength, to determine the variation of the refractive index of analyte. As far as the excitation of SPW, the model of numerical simulation, and the complexity of measurement equipment are concerned, it is obvious that this new structure is superior to the proposed SPR sensor, consisting of a bent polished single-mode SPR optical fiber. In this dissertation, we derive the dispersion relation of guiding modes in this four-layer optical-fiber SPR sensor, and the unconjugated form of coupled-mode equations. In addition, in order to increase greatly the efficiency on analyzing this new SPR sensor, further simplifications on the integration form of coupling constants are proposed. The numerical results will demonstrate that this new and simple configuration may be used as a highly sensitive amplitude-sensor. Furthermore, it can be easily adapted for a SPR fiber optical probe by depositing a mirror on the fiber tip.

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