大面積面射型雷射的螢光光譜與時空動力之研究: 量子渾沌的顯現

Abstract

本文將大面積面射型雷射 (broad-area VCSELs) 操作從未達閾值至遠比閾值高的條件，用以研究其基本性質及其在理論物理的探究。首先，透過高解析光譜儀的量測，得知面射型雷射快被激發時，螢光光譜可呈現出近千個極窄線寬的空腔模態，進一步理論分析發現螢光光譜可以應用於類比研究量子系統的能級密度。而由於赫姆霍茲方程式 (Helmholtz equation) 及與時間無關薛丁格方程式 (time-independent Schrödinger equation) 存在數學的相似性，面射型雷射的橫向模態可應用於類比研究量子系統的波函數，我們因而製作各種幾何形狀的大面積面射型雷射，觀察其主要橫向模態。此外，近軸光學波動方程式 (paraxial wave equation) 跟與時間有關薛丁格方程式 (time-dependent Schrödinger equation) 也存在高度的數學等價性，使得面射型雷射的激發模態在空間的傳播還可以用來類比研究物質波經過暫態反應後隨時間的變化行為(diffraction in time)。另一方面，操場型面射型雷射的模態選擇機制，也利用實驗歸納了解。我們還針對混亂模態 (chaotic mode) 及座落在不穩定古典軌跡模態 (scarred mode) 進行強度統計分析，以更定量的方式區別這兩種模態。最後，我們觀察大面積面射型雷射在遠高於閾值條件時的偏振穩定性，實驗結果呈現，當雷射操作在高階模態時，面射型雷射的空腔邊界是決定激發模態的偏振穩定性的重要因素。

Basic properties as well as applications in physics research of broad-area VCSELs from below to far above threshold are thoroughly investigated. Firstly, the high-resolution measurement demonstrates that over a thousand cavity modes with a narrow linewidth can be perfectly exhibited in the subthreshold emission spectra. Further analyses of the obtained spectra confirm that the subthreshold emission spectra of broad-area VCSELs can be exploited to analogously investigate the energy spectra of the 2D quantum billiards. In addition, due the analogy between Helmholtz equation and time-independent Schrödinger equation, transverse wave patterns of oxide-confined VCSELs enable us to visualize the wave functions of the 2D quantum billiards with the same lateral shapes. Therefore, typical lasing modes for VCSELs with various cavity shapes are explored. Furthermore, since paraxial wave equation and time-dependent Schrödinger equation are highly equivalent in mathematics, free space propagation of lasing modes for VCSELs can be use to analogously study diffraction in time effect which is one of the most relevant quantum transient phenomena in matter waves. Mode selection mechanism for stadium-shaped VCSELs is also experimentally studied. We then perform statistical analysis to quantitatively understand characteristics of experimental chaotic and scarred wave patterns. Finally, polarization dynamics of broad-area VCSELs far above threshold are considered. Experimental results reveal that cavity geometry plays a significant role for polarization stability of the lasing mode that has large frequency detuning.