具有長週期光纖光柵之分析

Abstract

本論文主要主題為研究光在長週期光纖光柵中傳導之情形，利用光在光纖中之耦合特性，探討光纖之各參數 Λ、n1、a1、a2、z、σ(z)n1 和光柵相位移時的改變對其透射率頻譜影響變化之情形。 對於光在光纖中之耦合特性，可利用馬克斯威爾方程推導出波動方程式，藉由耦合模態理論進而得到長週期光纖光柵之耦合方程。為了更方便分析長週期光柵，則將其耦合方程式解出一個通解，並將其通解整理成一個轉換矩陣。經由這個轉換矩陣，我們就能夠改變其各個參數模擬出透射率頻譜的變化和光柵之相位移對透射率影響之情形。最後，藉由所得到透射率對共振波長、頻寬和大小的變化，就可以設計一些元件和設備。

The topic of this paper is to study the transmittance of light in a long periodic fiber grating. By means of the couple characteristics of a light in the fiber, effect of Λ、n1、a1、a2、z、σ(z)n1 and phase shift of fiber to the transmittance frequency spectral is discussed. About the couple characteristics of a light in the fiber, Maxwell’s equation is used to determine wave equation, and also by couple mode theory to get the couple equation of long periodic fiber grating. In order to analyze long periodic fiber grating conveniently, the couple equation is applied to find a general solution, and turn the general solution into the form of transfer matrix. According to this transfer matrix, the parameters is changed to simulate the variety of transmittance frequency spectrum and the phase shift of fiber grating to transmittance of light in a long periodic fiber grating. Finally, by means of the variety of transmission, bandwidth and resonant wavelength of fiber grating can be applied to design some instruments and devices.