由共振腔決定虛光闌克爾鎖模雷射非線性動力學的研究

Abstract

本論文敘述我們實驗上研究虛光闌克爾鎖模雷射與共振腔有關非線性動力學的現象。首先為了探討虛光闌克爾鎖模雷射的機制，我們量測鈦藍寶石雷射連續波功率輸出時發現不連續的功率凹陷區域，虛光克爾鎖模就發生在這些不連續的區域並且伴隨著特殊的空間模態輸出。利用理論上線性疊加低階橫模的模態擬合量測到的虛光欄鎖模模態，我們認為克爾鎖模的模態是由基模與低階簡併的橫模相位鎖定所構成。由於所觀察到的鎖模模態已被廣泛的實驗上觀察到，這個發現將可做為虛光闌克爾鎖模的指引。 為了以實驗驗證我們理論上所預期的一些脈衝不穩定行為會發生在克爾鎖模雷射的特殊共振腔結構上，將雷射共振腔調整在G1G2=1/2與G1G2=1/4的位置，我們發現理論上預期的週期二與週期三的脈衝發生。推論其發生的原因可能是由克爾非線性效應引發低階共振所造成。將雷射調整在1/3簡併腔時並且選擇功率與共振腔微調為控制參數，我們觀察到由三個週期頻率的交互作用到渾沌狀態的詳細路徑。由於我們的雷射是操作在群速度非零的區域，所以明顯與先前報導將雷射操作在群速度為零，以致於雷射有最短的脈衝及最強的非線性克爾效應去造成渾沌狀態明顯不同，它與共振腔的相依性較大。 在不加飽和吸收體克爾鎖模雷射特定的群速度區域，我們第一次發現到此克爾鎖模雷射的諧頻鎖模現象。它是由瞬態動態增益所造成脈衝前移而形成。其次我們也觀察到了奈秒與皮秒等級多脈衝分裂現象。藉由觀察雷射在不同群速度色散區域波長、頻寬、脈衝平均寬度與脈衝峰值功率的分佈顯示多脈衝分裂發生在波長較短的區域。由鈦藍寶石雷射的增益分佈與我們雷射鏡片反射率鍍膜的頻寬限制推論，非對稱奈秒分裂的脈衝發生在功率損耗較大的地方。因此我們認為分裂的兩個脈衝將遭受到不同的損耗，並將此項加到增益的動力學理論，發現只要兩脈衝有微小的損耗差異就會造成穩定的奈秒非對稱脈衝。最後藉由基因演算法，精確的雙與三脈衝分裂的波形與相位被重建，由相位的二次微分我們發現兩脈衝中有很大非線性啾頻產生，為造成脈衝分裂的主要原因。

In this dissertation, we have experimentally studied the cavity configuration dependent nonlinear dynamics of the SAKLM Ti:sapphire. To study the mechanisms of the soft-aperture Ti:sapphire KLM, we have experimentally measured the CW output power as the cavity detuning and found the KLM occur at the discrete power dips corresponding to the degenerate configuration with the peculiar mode patterns. By spatially correlating the SAKLM mode patterns with the linear superposition of the selected transverse mode patterns, we found the SAKLM patterns are attributed to phase locking of the fundamental mode with the low order degenerate transverse modes. Because the beam patterns are widely reported in many laboratories, it is a variable guidance for the optimization of the SAKLM laser. To experimentally prove the theoretical prediction of the irregular behavior of KLM laser at the specific configurations, we operate the laser at G1G2=1/2 and G1G2=1/4 and find the period-2 and period-3 pulses. It is most likely resulting from the Kerr nonlinearity induced the low order resonance as our theoretical prediction. By choosing the pump power and cavity detuning as the control parameter while the cavity is operated around the 1/3-degenerate configuration, the detail route from the three-frequency interaction to chaos is observed. The laser is operated within the nonzero GVD region as our theoretical prediction so that it is obvious different from the larger nonlinearity induced chaos when the laser is at the zero GVD regime and the shortest pulse. The harmonic mode locking is first observed at the specific GVD in the KLM laser without saturable absorber due to the pulse drift by the gain dynamics. In addition, the multiple nanosecond and femtosecond splitting pulses are also experimentally noted. An investigation of the laser operated in these regimes in terms of wavelength, bandwidth, pulsewidth, average, and peak powers as functions of group velocity dispersion shows that unequally spaced pulses take place at shorter wavelength than that of equally spaced pulses. In conjunction with the information of gain profile for amplifying medium and wavelength-dependent bandwidth limited reflectance for mirrors suggest that the unequally nanosecond splitting pulse will undergo larger losses. By introduce a loss difference of the pulses into gain dynamic analysis, we find that multiple pulses with unequal spacing between the pulses can be achieved only with tiny loss differences. Finally, the retrieved envelope and phase from femotsecocnd-split two and three pulses can be obtained by the genetic algorithm (GA). A large nonlinear chirp is also observed between two pulses by the second order differentiation of retrieved phase. It might be the reason of the pulse splitting.