在本篇論文中，提出一個以Mueller matrix為架構的數學模型來評估摻鉺光纖大器(erbium-doped fiber amplifier)的極化模態色散(polarization mode dispersion, PMD)，摻鉺光纖大器透過泵機光源的調變後，會使自發性放射的能階帶具有調變訊號的特性，調變後的自發性放射可作為監控訊號光源以對於線上的量測極化模態色散。在本篇題出的數學模型中，使用方法皆為頻率領域(frequency domain)，省去了時間領域(time domain)方法的實驗架構不易安裝之缺點，透過數學模型配合瓊斯矩陣特徵值法(Jones matrix eigenvalue method)計算出的群速延遲差(differential group delay, DGD)，再以實驗邦加球法(Poincare’ arc method)驗證數學模型的正確性。
在實驗中，先固定入射光的極化狀態為線性60度，入射至摻鉺光纖大器的波長範圍在1542nm-1566nm之間，藉由量測所得的數據，運用至邦加球法中再跟極化分析儀所量得極化模態色散相以佐證。

In this paper, a mathematical model is proposed to evaluate the polarization mode dispersion (PMD) of erbium-doped fiber amplifier based on Mueller matrix. A Erbium-doped fiber amplifier (EDFA) modulated by a pumping source cause the energy gap of amplified spontaneous emission (ASE) getting the characteristic of modulating signal.
The modulated amplified spontaneous emission can be the polarization mode dispersion monitoring system. All the methods we used are based on frequency domain. It is better than the approaches based on time domain, due to the fact that the experimental structure is convenient. The differential group delay (DGD) we calculated by Jones matrix eigenvalue method can be proved by the Poincare’ arc method using Poincare’ arc method.
We fixed the polarization state of a tunable laser at 60 degree of linear polarization to incident in EDFA at the range of wavelength 1542nm-1566nm. The data we got from the experiment can be verified the polarization mode dispersion we measured.

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