具高自發輻射因子的半導體微小共振腔雷射之特性研究

Abstract

在本論文中，我們將詳述如何製作具有高自發輻射因子的半導體微小共振腔雷射，並對此種雷射的特性作研究。其中包括了雷射的工作波長，自發輻射因子，與雷射的遠場光場分佈。除了波長為1.5 mm的雷射外，我們也首次成功的開發了波長在0.66 mm的雷射。此微小共振腔的雷射模態可藉由三度空間中whispering-gallery mode (WGM)的波動方程式經由等效折射率的方式，將問題簡化為只需兩個指標的兩度空間問題。其中一個指標與光場徑向分佈r有關，另一個則和光場在方位角f相關。當雷射共振腔較大時，我們曾發現有趣的多模競爭，但是當微共振腔的體積減小後，雷射便可達成單模輸出。微共振腔雷射的高自發輻射因子b，是反比於共振腔內的共振模數目。我們也由單模雷射速率方程式推導出量測雷射激發與輸出光強的關係，而作曲線擬合可直接得到雷射的b值。經研究不同大小的微共振腔之b值後，我們確定了b值與雷射共振腔大小的關係。 在遠場光強分佈上，微共振腔雷射在與圓盤雷射所在平面的垂直向量z的夾角q方向的發散角遠小於具有同一寬度的邊射型雷射的發散角。由傅氏光學來看，遠近場的光場分佈為一傅氏轉換，因此在厚度比波長小的近場面所得到的遠場發散角將會大於180度。不過在圓柱座標下，我們可推導出一個純量波動方程式，其中的遠場發散角還含有一個Hm (kr R )2的因子在分母部份，因此使得發散角變小。光強在f方向則呈現在圓周上有m個光強極大值，m代表的是共振模在共振腔內繞一圈所作全反射的次實驗上，輸出光為在共振腔平面的線性偏極光。

In this dissertation, we fabricate high spontaneous emission factor semiconductor microcavity lasers and study their lasing properties such as the resonant wavelength, spontaneous emission factors, and far-field emission distributions. We also succeed on extending the operation wavelength region of these microcavity lasers from 1.5 mm to 0.66 mm. Interesting mode competition is observed for larger cavity volume lasers while the cavity volume is only a few times of cubic wavelength, single mode lasing can be achieved. We develop a method to deduce the spontaneous emission factor b from the experimental light output versus pumping intensity curves based on a single-mode rate equation analysis. Comparison of the b values for microcavities with different cavity volumes clearly indicates b is inversely proportional to the cavity volume. Here we follow the conventional (r,f,q) notation in the cylindrical coordinate. We find that the far-field emission in the q direction for microdisk and microring laser has a narrow Gaussian distribution and the FWHM of the angular spread qFWHM is much smaller than that of a planar source with the same thickness. Based on a scalar diffraction theory in the cylindrical coordinate, an analytic expression for qFWHM is derived. The results exhibit an additional Hankel function factor difference when compared with the case of a planar boundary. This factor narrows the angle spreading in the q direction and is a function of the disk diameter. On the other hand, the far-field emission in the f direction shows a m-peaks quasi-periodic distribution around the circumference, where m is the azimuthal index. The polarization of emission is linearly polarized along the f direction from measurement.