對二維光子晶體不同結構之研究

Abstract

本研究是以平面波展開法以及快速複利葉轉換法(FFT)計算二維平面之光子晶體能帶結構。我們先以理論計算圓形、方形以及三角形之介質柱呈正方形、三角形和六角形晶格等不同週期排列之光子晶體能帶。並藉由改變晶體填充率、介電質介電常數、介質柱形以及不同晶格排列方式，觀察能帶的變化情形。並將理論計算結果與學長所量測光子晶體實驗數據相驗證，得到不錯結果。

The photonic crystal exhibit forbidden frequency region where electromagnetic waves cannot propagate along any direction . There appears be great interest in finding out the band gaps.By the use of plane-wave expansion method and Fast-Fourier transform method, we have calculated 2-D photonic band structures . It has been theoretically calculated that photonic crystal structures consisting of periodic arrays of parallel dielectric rods of circular , rectangular or triangular crosssection , whose intersections with a perpendicular plane form a square、triangular or a hexagonal lattice. By theoretically calculations , the result showed that how the photonic band-gaps are affected by dielectric constant ,cross-sections of rods, lattice array andfilling factor. Besides, the calculated result is also in a good agreement with the measurement of the experiment at microwave frequency performed in our laboratory.