應用固態微單晶雷射研究量子彈子球檯之介觀波函數特性

Abstract

本論文將掺釹釩酸釔晶體設計成四菱柱、正三角柱、切邊圓柱等不同形狀的單塊晶體微型雷射腔，用以研究幾何光學(經典力學)與波動光學(量子力學)之間的關連性。由實驗的近場、遠場干涉圖案、雷射光出射角，可推得雷射腔內的波函數模態，再用量子力學同調相干態理論，成功地重建實驗觀測的近遠場圖案。幾何光學模態可由近場亮點數目、雷射光出射角推得，提供疊加同調波函數時所需參數，由分析光譜圖得之等效腔長也符合經典力學彈子球之週期性軌道長度。藉此實驗清楚地揭示同調波相干理論在聯繫經典力學與量子力學時扮演的角色。

Using monolithic microcavity lasers experimentally demonstrate the relation between geometrical optics (classical mechanics) and wave optics (quantum mechanics). The wave optical mode index can be obtained from near field patterns, far field interfere patterns and emission angle. With the quantum coherent state theory, we have successfully reconstructed the experimental patterns. The spatial positions of near field patterns, the emission angle and free spectrum range are in good agreement with predictions using the geometrical optics model. In the thesis, we clearly connect the wave function with the classical periodic trajectory in different shape of billiards using the representation of coherent stationary states theory.