光纖雷射混合式主動及被動鎖模與同步機制 之理論建模研究

Abstract

超快光纖雷射是應用於許多科學研究和產業研發之光電整合系統中的基本構建模組，有很好的研究價值。在本研究中，我們發展合適的理論模擬模型來具體地探討雙波長鎖模光纖雷射系統的被動式時序同步技術以及混合式(主動/被動)鎖模光纖雷射系統中從同步到非同步的不同鎖模操作態轉換現象。 關於雙波長鎖模光纖雷射時序同步技術之研究，摻鉺(Er-doped)和摻鐿(Yb-doped)鎖模光纖雷射可以藉由所提出的主附式(master-slave)架構來達到被動式同步的效果。我們利用數值計算來探討此被動同步系統中的光脈衝非線性動力學特性，藉由脈衝傳播模型來處理在共同傳播光纖部分中的脈衝碰撞狀況，並且使用鎖模雷射的Master equation模型來探討摻鉺雷射共振腔中脈衝的動力學演變。當此兩雷射的共振腔長度有些微不匹配時，我們根據計算結果指出Er雷射的光脈衝中心波長會經由在共同傳播光纖中兩種不同波段脈衝互相作用所產生的交叉相位調變(XPM)效應而產生改變，進而與注入的Yb光脈衝保持相同的光脈衝重複率。此外，由於光纖中色散作用所造成之脈衝寬度變化會導致XPM效應所產生的頻率調變函數對不同的起始碰撞相對時間位置變數的反對稱性特徵被改變，非線性脈衝傳播的準確數值模擬更顯必需。我們進一步藉由所發展的理論模型來探討分析此雙波長被動同步鎖模光纖雷射系統的相對時序雜訊特性，發現經由適當地調整兩脈衝的相對時間位置，相對時序雜訊抖動可以被有效率地抑制，並且所預測的物理特性也在實驗系統中得到驗證。在這裡所發展出的超低時序同步技術能用來獲得低於飛秒尺度的脈衝相對時序雜訊，提供了一個新方法能用來發展多種重要應用，包括同調脈衝合成技術與精確時序分配技術等。 在關於混合式(主動/被動)鎖模光纖雷射鎖模特性之研究中，我們理論性地探討混合式(主動/被動)鎖模光纖雷射在相位調變器的調變頻率被稍微錯開時所會產生的不同鎖模操作態轉換現象，此現象也可以廣義地視為雷射光脈衝序列與光調變訊號的時序同步效應。基於所使用的混合式鎖模雷射Master equation模型，在不同程度之錯開調變頻率與調變強度下，我們發現有三種截然不同的鎖模操作態，它們的狀態轉移圖也被首次準確計算與畫出。除此之外，我們也藉由變分法和單一高斯脈衝解的假設來解此Master equation模型，重要脈衝參數的演變方程式可被推導出，此變分模型可以用來與直接數值模擬所獲得的結果作比較以便釐清闡明關鍵的物理機制。我們更進一步透過計算不同鎖模操作態在穩態結果下的雷射增益，釐清了雷射在接近過度點的不穩定現象原因以及非線性飽和吸收效應對於穩定非同步鎖模操作態的重要性。這些發展出的分析方法可以示範出一套有效理論工具來解釋說明非線性混合式鎖模光纖雷射在調變頻率錯開效應下的動力學變化，並能準確預測此種雷射系統在不同操作條件下的運作性能。

Ultrafast fiber lasers can be employed as fundamental building blocks in many photonic systems for scientific research and industrial development. In this study, we develop appropriate simulation models to specifically investigate the essential properties of passive timing synchronization between two color mode-locked fiber lasers and the synchronous to asynchronous mode-locking state transition in hybrid (passive/active) mode-locked fiber laser systems. For the first objective of the research, the passive synchronization between the Er-doped and Yb-doped mode-locked fiber lasers is studied under the master-slave configuration. We numerically investigate the nonlinear optical dynamics of the passive synchronization system based on the pulse propagation model for the pulse collision in the common fiber section and the master equation model for modelling the dynamics of the Er laser cavity. When there is some mismatch of the cavity length, the computational results indicate that the central optical frequency of Er laser pulses may be shifted through the significant cross phase modulation (XPM) effect of the two color pulses interacted in the shared fiber section so as to maintain the same repetition rate with injecting Yb laser pulses. Additionally, since the pulse duration change by fiber dispersion can distort the anti-symmetric characteristics of the frequency modulation function caused by the XPM effect with respect to the relative timing position, accurate numerical simulation of the nonlinear pulse propagation effects will be critical. Furthermore, the relative timing jitters between the two passively synchronized mode-locked fiber lasers are analyzed based on the developed theoretical model. The relative timing jitter noises of the two synchronized lasers can be minimized by adjusting the relative pulse timing position and the predicted dependence agrees well with experimental observation. The presented ultra-low timing (< ~fs) synchronization technique provides an alternative approach to the development of many applications including the coherent pulse synthesis and precision timing distribution. For the second objective of the research, we theoretically investigate the different mode-locking operation states of a hybrid (active/passive) mode-locked fiber laser system with frequency detuning effects of active phase modulation. This may also be viewed as a timing synchronization problem between the laser pulse train and the optical modulation signal. Based on the master equation model of this hybrid mode-locked laser, we find three distinct mode-locking states and also determine their transition diagram under varying detuning frequency and modulation strength. Additionally, the evolution equations of essential pulse parameters are derived from the variational solution of the master equation under the single Gaussian pulse solution ansatz for the comparison of results and clarification of key physical mechanisms. The occurrence of laser instability near the transition points, and the importance of the nonlinear saturable absorption effect for stable asynchronous mode-locking operation are further clarified by examining the steady-state lasing gain as a function of the detuning modulation frequency. These presented analyses demonstrate an effective approach for the elucidation of the nonlinear mode-locked laser dynamics caused by the detuning effects and for the performance prediction of the studied laser system under different operation conditions.