端泵固態雷射在簡併共振腔架構附近的非線性動力學研究

Abstract

我們使用柯林繞射積分和速率方程式研究擁有平凹共振腔的端泵固態雷射處於簡併共振腔架構附近的動態行為。當幫浦光斑大於基模光腰時，我們在架構參數g1g2約等於1/4和高Q值條件下發現傳播主導的雷射不穩和混沌的現象，g1g2約等於1/4附近的動態行為在以前是沒有被研究過的，我們稱傳播主導的不穩是因其行為像是在保守系統中的光束傳播行為。我們也得到和共振腔架構有關的V 型準週期不穩閥值曲線和幾種雷射不穩的分叉圖。而且，以前認為混沌不可能發生在簡併位置附近，但是我們確認了當雷射腔被調整到簡併位置附近時，由於光束和雷射增益的相互作用會促使雷射進入混沌狀態。 對於幫浦光斑小於基模光腰的情況，我們發現一種多光腰模態的雷射輸出，這種雷射模除了在平面鏡的光腰之外，又多了一個光腰，此光束在遠場形成多個同心圓光圈但近場則否，而且當此光束經過一個聚焦鏡，在鏡後會形成多光腰的情形，電腦模擬結果非常符合實驗觀察。此外，我們考慮了多光腰模光束同時具有光線及光波的特性，因而將它表示成空腔週期解的連續多趟電場的疊加，對於g1g2等於1/2採用兩趟疊加，而對於g1g2等於1/4和3/4則採用三趟疊加。 最後，我們發現對於幫浦光斑足夠小的情況，位在簡併位置兩旁總是會產生雷射不穩定的輸出情形，我們首先決定雷射不穩定區，並發現不穩的時序發展有週期性的，週期二的，和混沌的特徵，當腔長調動時，我們觀察到多種遠場橫模形狀，包括一種特別的對稱破缺現象以及輸出功率和其拍頻特徵關於簡併點的不對稱現象，電腦模擬結果指出這些不對稱的現象起因於熱透鏡效應。我們認為位於短腔的雷射不穩定是由一種組成雷射超模的橫模間之非線性交互作用而發生，位於長腔的雷射不穩定則是由雷射超模和其他橫模的非線性作用而產生。

We used Collin’s integral together with rate equations to study the nonlinear dynamics of an axially pumped solid-state laser operated near degenerate cavity configurations with a plano-concave cavity. When the pump size is larger than the fundamental mode size, we found propagation-dominant instabilities and chaos under the so-called good-cavity conditions near the 1/3-degenerate cavity configuration that had not previously been studied numerically. We call the propagation dominant because the laser behaves as a conservative system governed by beam propagation. We also obtained a V-shaped quasi-periodic threshold and a bifurcation diagram for classifying various instabilities that depends on cavity configuration. Although it had previously been predicted that chaos would be impossible under nearly degenerate conditions, we have recognized that the laser is transformed into chaos as a result of the interplay of beam propagation and gain dynamics as the cavity is tuned close to degeneracy. When the pump size is less than the fundamental mode size, we found that there are stationary modes called the multibeam-waist modes that show an additional beam waist besides the well-known waist on the flat mirror end near g1g2 = 1/4 and 3/4. The multibeam-waist mode possesses a small waist size without a ring structure in the near field on the flat mirror end; nevertheless, it has a far-field pattern with many concentric rings. When the specific modes propagate through a lens, they are capable of exhibiting multiple beam waists. The numerical results show good agreement with the experimental observations. Furthermore, by simultaneously considering the wavelike and raylike character of the multibeam-waist mode, we found that it can be represented as a superposition of N consecutive round-trip electric fields of period-N solution in the degenerate empty cavity, where N = 2 for g1g2 = 1/2 and N = 3 for g1g2 = 1/4, 3/4. Also due to small-size pumping, we found new instabilities and determined the unstable regions on each side of the degeneracy near g1g2 = 1/4. We illustrated the temporal behaviors including periodic self-pulsing, period-2 self-pulsing, and chaotic output. As the cavity is tuned, we observed various far-field mode patterns including an asymmetrical mode pattern, the asymmetric output power with respect to the point of degeneration, and the asymmetric beating frequencies beside the degeneracy. Our numerical results reveal that the thermal lens effect leads to these asymmetric phenomena. We ascribed the short-cavity instabilities to the interaction among the degenerate transverse modes that constitute a supermode by the gain dynamics. However, the spatiotemporal instabilities in the long-cavity side are ascribed to the interaction between the supermode and the other empty-cavity modes.