光子晶體平板微共振腔輻射特性之分析

Abstract

本論文以模擬方式探討光子晶體平板微共振腔的輻射特性。我們使用時域有限差分法作為數值模擬的工具。主要分析兩種結構，其一為「空氣-光子晶體-空氣」的懸空光子晶體；其二為「空氣-光子晶體-基板」，即光子晶體微共振腔下面有基板的結構，這較接近實際的元件。首先我們探討電偶極源與輻射率的關係。我們把以時域有限差分法求得的輻射率與由電偶極矩及電場內積關係式計算而得的輻射率作一比較。接著探討萃取效率與電偶極源的關係。有了輻射率與萃取效率，便可算出等效萃取率。因此，只要知道輻射率與電偶極源的關係，我們就可以在一個共振腔中放置很多電偶極源。我們在光子晶體平板微共振腔中每一個分割點上都放置一個隨機指向的電偶極源，藉此模擬實際上發光二極體的自發放光情況。總之，本研究應有助於增加發光二極體的輻射效率，並可應用於顯示與照明方面。

In this thesis, the radiation characteristics of photonic crystal slab microcavitiyes are numerically investigated. We use the finite-difference time-domain method as a simulation tool. Two structures are analyzed. One is an “air- photonic crystal- air” free-standing photonic crystal slab microcavity, and the other is an “air- photonic crystal- substrate” photonic crystal slab microcavity with substrate, which is similar to a real device. First, we investigate the relation between the radiation rate and the dipole source. We compare the radiation rate calculated by finite-difference time-domain method and that calculated by an analytic formula involving an inner product between the dipole moment and the electric field intensity. Then, we investigate the relation between the extraction efficiency and the dipole source. By multiplying the radiation rate and the extraction efficiency, we can obtain the effective extraction rate. Therefore, as we know the relation between the radiation rate and the dipole source, we can set multiple dipole sources in a microcavity. To simulate the spontaneous emission of a light-emitting diode, a randomly oriented dipole source is launched at each Yee cell of a microcavity. This study is helpful for increasing the radiation efficiency of light-emitting diodes and may be useful to the applications of display and lighting.