在此篇論文中我們討論以光纖高階模的反常色散作為光纖的色散補償，以此方法做色散補償相較於其他方式其優點有：較小的非線性效應、可調的色散曲線與非靠近截止頻率的反常色散。因此，這樣的色散補償架構非常適合用於高功率的全光纖雷射系統。此架構所需的元件有二：模態轉換器與設計過的色散補償光纖。
在模態轉換器的設計上，傳統的方式是使用固定周期的光柵，使光柵週期符合光纖模態之拍長度(beat length)，達到全功率之模態轉換的效果。此方法的缺點為對製程的錯誤容忍度低且頻寬較小。而近來光學與量子的相似性已被發現，因此我們可以透過以往用於量子控制的絕熱理論於波導理論中。透過使用絕熱理論設計出的模態轉換器，可達到良好的製程錯誤容忍度與較大的頻寬，但一般需較長的元件長度以符合絕熱條件，此缺點可於模態轉換器中多加一道光柵來改善。而此篇論文中進一步將描述模態轉換器的算符於三維空間中旋轉，使此元件能簡化為一道光柵，使我們的模態轉換器達到短距離高頻寬與大製程錯誤容忍度。
另外在色散補償光纖的設計與分析上，我們建立了一套基於有限差分法的分析工具，藉由此工具分析與設計具有核心與外環的光纖，使光纖在高階模達到合適的反常色散，作為色散補償之用。

In our research, we develop a fiber dispersion compensation module based on higher-order modes. By using higher order modes, we can obtain smaller nonlinear effect, tailorable dispersion curve, therefore, this module is very compatible with the high power laser module. The key components of this module are the mode converter and a well-designed dispersion compensation fiber.
By using long period grating (LPG), designing the coupling region of a resonant mode converter to the half of the beat length, we can achieve total power mode conversion. This kind of mode converter is easier to fabricate but having less error tolerance and narrow bandwidth. Recently, the analogies between quantum theory and waveguide optics has been investigated. From this, we can develop the mode converter with better error tolerance through adiabatic theory which has been used in the quantum control. For the adiabatic following mode converter, the device length must be long enough to satisfy the adiabatic condition. We can add the counter-diabatic term into the mode converter design to get the improvement but it requires an extra step in fabrication. Therefore, we introduce the rotation method of Hamiltonain to simplify the fabrication process into one step. For dispersion compensation, we propose to use the fiber with core-ring-trench structure to get the tailarable dispersion curve in the LP02 mode. We develop a finite-difference-based numerical tool to design and analyze these kinds of fibers.

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