全方位介電質反射鏡能帶結構與禁制角度之研究

Abstract

本研究是以二維長方晶格光子晶體(photonic crystal)系統來模擬由多層介電材料組成的介電質反射鏡(dielectric mirror)，並以平面波展開法(plane-wave expansion)計算出其能帶結構以及能隙對應的禁制角度。我們採用頻率相關的等效折射率模型(effective index model)，透過司乃耳定律(Snell’s law)將傳統以波向量表示的能帶結構，換算成以入射角度表示的角度能帶結構(angular band structures)。我們將此方法應用至不同材料組成的多層介電質系統，計算出對應的角度能帶結構，並分析其具備全方位能隙的條件。此研究結果有助於評估介電質反射鏡的表現，並可作為未來設計全方位介電質反射鏡及其相關系統的參考依據。

In this report, we employed the plane-wave expansion method to study the dielectric mirror composed of two alternating dielectric materials. To include the case of oblique incidence, we modeled the system by a semi-infinite two-dimensional rectangular photonic crystal embedded in air. By introducing a frequency-dependent effective index model, we calculated the angular photonic band structure from the conventional projected band structures with the help of Snell’s law so that we can examine how the photonic band gaps vary with the incidence angle directly. We applied this approach to study several examples of different dielectric contrasts and analyzed the conditions for omnidirectional reflection. The results are helpful in evaluating the performance of dielectric mirrors and provide a guideline in designing omnidirectional dielectric mirrors and their related applications.