用變分法來研究光固子的傳播行為

Abstract

我們發展了一套能適用於非守恆系統的變分理論，也利用 Mathematica 軟體發展了一套能在電腦上自動推導變分方程式的方法。我們利用這些工 具來研究光纖中光固子之傳播行為，包括單個光固子在有增益/損耗、濾 波及高階色散效應在光纖系統中的傳播特性，也包括兩個不同頻率或不同 偏振方向之光固子的碰撞行為。我們也做了直接數值模擬來驗證變分法的 準確性。我們發現在大部分的情形下，變分法都能給出更具物理意義、需 計算量較小、並且足夠準確之解答。 We have developed a variational method that can be applied to non-conservative systems. We have also developed a Mathematica program that can automatically generate variational equations directly on the computer. We use these tools to study soliton phenomena.The propagation of a single soliton with various effects as well as the collision of two frequency-demultiplexed or polarization- demultiplexed solitons are studied.Direct numercial simulation is also performed to verify the accuracy of our variational method. We find that in most cases the variational method can give more physical,more computationally efficient,and reasonably accurate answers.