無光闌自起動克爾透鏡鎖模雷射演變動力學之數值研究

Abstract

在本篇論文中，我們以ABCD矩陣建立描述鈦藍寶石鎖模雷射共振腔之模型 。在本模型中，我們可以同時考慮時間領域和空間領域所含之效應，包括 自聚焦，增益導引，自由空間傳播，介質色散，群速度色散補償，頻寬限 制，及自相位調變。先由此模型得出一穩定共振腔之解，再修改此模型之 增益飽合項，讓連續波模和克爾透鏡鎖模(KLM)並存，來觀察一虛光闌自 起動KLM雷射脈衝生成之情形。結果觀察到輸出脈衝寬度會有一轉折點出 現，推測為初始的脈衝能量造成之自相位調變和稜鏡色散補償兩效應造成 之脈衝壓縮到達極限，接著因自聚焦效應，造成KLM模之增益大於CW模， 導致脈衝能量上升，使脈衝繼續壓縮。最後KLM模獲得所有的增益介質中 所有的能量，造成CW模的消失，於是得到穩定輸出脈衝。 In this thesis, we have established a numerical model of kerr lens mode-locking(KLM) Ti:sapphire laser cavity by ABCD matrix. In this model, we can simultaneously consider the spatial and temporal effects including self-focusing, gain guiding, free space propagation, group velocity dispersion (GVD), bandwidth limiting, near resonance phase shift, nonlinear absorption and self-phase modulation (SPM). At first, We obtained a solution of a stable cavity, then modified the term of gain saturation to simulate the pulse grown of this laser by assumming CW mode and KLM mode coexisting. We found that there is a turing point in the time evolution of output pulsewidth, where GVD optimally compensates SPM to achieve the limitation of pulse compression. In consequence of self-focusing, the gain of KLM mode becomes larger than that of CW mode, and the pulse is further compressed by the rise of pulse energy. Finally, the KLM mode drains out all of the energy stored in the gain medium and quenchs CW mode, a steady-state solution of mode-locked pulse train is obtained.