利用RLC共振電路研究介觀尺度下波的現象

Abstract

介觀物理是尺度介於巨觀與微觀的物理科學，要探討介觀物理的方法有許多種，一開始我們透過大面積孔徑面射型雷射(VCSELs)自發放射螢光光譜，來顯明量子彈子球檯量化能譜特徵的結果。並透過高解析度的光譜量測，在外加電流恰低於雷射出光截止電流時，VCSELs 螢光光譜將可明顯展現近千個具有狹小線寬的共振腔模態，同時我們對實驗所得相鄰本徵值進行統計，正三角形VCSEL的統計結果將遵循Poisson分布，而操場形VCSEL結果則呈現Wigner分布。 接下來利用二維的RLC共振電路來學習波函數的特性，同時也基於半導體業常用的電路模擬軟體HSPICE搭配C++程式語言設計一套虛擬共振腔模擬工具(Virtual Billiard Simulator)。並且利用此工具探討一維跟二維的有源波函數跟RLC共振電路的相對應關係，最後將此套工具的功能擴展到可以透過2D的圖案檔來建立任意形狀的共振腔參數及訊號輸入位置，讓此軟體可以更精準的模擬任何共振腔。

In this thesis , firstly, we report the results of manifesting signatures of quantum billiard quantized energy spectra from spontaneous emission spectra of large-aperture vertical cavity surface emitting lasers (VCSELs). Through the high-resolution measurement , nearly a thousand cavity modes with a narrow linewidth can be perfectly exhibited in the spontaneous emission spectrum just below the lasing threshold for VCSELs. Furthermore , we verify that the statistical analyses of the nearest-neighbor eigenvalue spacing distributions obey a Poisson distribution for an equilateral-triangular device and a Wigner distribution for a stadium-shaped device. Next, we propose that a two dimensional RLC resonance network may be used for fundamental studies of wave function properties. Based on HSPICE simulator and standard C++ language to generalized the virtual billiard simulator (VBS). We will demonstrate that this type of systems offer rich possibilities for experimental studies of wave functions and, in particular, current morphology and statistics. The square, equilateral-triangular and stadium shape geometry is suitable since there are both experimental in VCSELs results to compare with. We also explored the RLC resonance network circuits with wave chaos for the arbitrary-shape billiard.