以摻釹釩酸釔雷射晶體產生Laguerre-Gaussian模態疊加之研究

Abstract

雷射共振腔系統提供了比傳統固態雷射更多元的變化性，藉由腔長與激發源(pumping source)離軸變化可產生各式各樣的雷射本徵態。本論文主要研究的方向為c-cut Nd：YVO4(摻釹釩酸釔)雷射所產生的三維六點環形模態。此種雷射模態為Laguerre-Gaussian modes疊加而成，其本徵態在特定的條件下，雷射模態在遠場時會產生左旋光(left-handed light)與右旋光(right-handed light)。而在近場時因為幾何光束會有重疊的情況，此時會產生單一光點同時擁有左旋與右旋光的現象。在單一的固態雷射系統能同時產生左旋光與右旋光是一件非常特別的情形，應用上能發展於冷原子系統(cold atom system)相關的研究中。 雷射共振腔裝置可以從理論推知各種穩定簡併態的相位延遲δ(phase retardation)。藉由c-cut Nd：YVO4的雙折射特性，可以將ne與no帶入雙折射理論公式計算出等效折射率neff，如此一來即可了解相位延遲δ下的折射角θ值。理論上能符合簡併共振腔條件的折射角存在很多組，本實驗也確實完整找到每一組對照的相位延遲δ之圖像。藉由理論計算能先訂出實驗的目標，接著透過實驗去驗證理論上的計算。藉由四分之一波片與線偏振片的配合檢驗與多次實驗觀察，確定了三維六點環形模態同時具有「左旋圓偏振和右旋圓偏振」的模態。由計算得到實驗與理論的相位延遲δ值相互比較的結果發現實驗與理論計算相當吻合。並且確認了多組不同階數的情形。

本實驗一併對不同三維模態進行觀察，在本文後段中將展現橢圓形或是複合形式的模態，並觀察其相關光學特性。藉由實驗與理論的相互印證，能更加的了解此種特殊的雷射模態形成的物理機制，在未來基礎科學的研究應用上能給予相當的貢獻與啟發。

The laser cavity system mentioned in the thesis is different from the traditional solid state laser. We can manipulate the pump offset to generate a variety of the laser beams with complex spatial structures. We investigate the geometric beams generated from a c-cut Nd:YVO4 laser. The Nd:YVO4 acts as a birefringence crystal. In this work, we focused on six spots of the circular geometric mode. In the far field, the structured laser beam is left-handed circularly polarized and right-handed circularly polarized at the same time. This particular property has many applications, like cold atom system. The phase retardation (δ) of a stable geometric mode can be derived by the birefringence theory. According to the birefringence property of Nd:YVO4, the effective refractive index neff can be calculated by the coefficient ne and no. It leads to get the refraction angle θ of the geometric mode. In the numerical simulation, we fit twelve orders of six spots of circular geometric modes and get the patterns. In the experiment we use the quarter-wave plate (QWP) and the linear plate(LP) to detect the laser polarization. Experimental results reveal that a geometric mode possesses circularly polarized states in opposite directions at the same time and the superposition of orthogonally polarized geometric beams can be generated systematically by controlling the off-axis magnitude. The numerical results have a good agreement with the experimental results. The research may make some contributions for the application of structured beams.