光子晶體(photonic crystal)是由週期性排列所組成的結構，經由適度的設計則具備控制光波傳遞的效果，而光子晶體吸引了學者做廣泛的研究。由於可藉由變數來設計光子晶體能隙的範圍，不計其數的文獻致力於光子晶體中的缺陷應用。近幾年，光子晶體的研究甚至延伸至傳導區獨特的新現象。
光子晶體除了有傳導模態(guide mode)外，還有輻射模態(radiation mode)，有別於傳導模態，輻射模態是指光無法在光子晶體內部傳導，若落在輻射模態之內的光入射光子晶體，將無法在光子晶體內部傳導，會輻射到晶體外部(external mode)。利用此一性質，將光子晶體置入多層的發光結構中，例如：LED、OLED等…，可提高光透射的效率。
本文將針對Archimedean-4[1]晶格由其基本性質到透射效率的應用做深入地探討，利用平面波展開法及有限元素法來檢視Archimedean-4的性質，使用其能帶密集的特性，來提升光透射的效果，並與常見之正方晶格、三角晶格以及蜂巢式晶格[2]做透射效率的比較，且考量其晶格內柱體的形狀變化以及晶格填充率與透射效率的影響，最後將光子晶體嵌入有機發光二極體(OLED)做實際上的模擬與驗證。

Photonic crystals (PhCs) are periodical structures in one or more dimensions. Suitably designed, photonic crystals have the ability to control the propagation of light. Following the pioneer work by Yablonovitch and John, PhCs have attracted extensive research interest over the last few decades. The photonic band gap can be purposely designed, and numerous researches in this field have taken that advantages and have been devoted to applications of the bandgap and defects in PhCs. For the past few years, it has been extended to new transmission phenomena.
The PhCs have both guide and radiation modes. The guide mode allows the lights to transmit internally. In contrast, the radiation mode refers to the phenomena in which the lights are not guided to transmit internally. Set the incident light in the radiation modes, then it would not propagate along the wave guide internally. Instead, the lights radiate and escape from the wave guide. By taking advantages of this feature, we can therefore enhance the efficiency of light extraction by embedding PhCs in the multiple radiating structures, such as LED and OLED, among others.
The proposed project aims at exploring design procedures and optimal designs that optimize the intensity of radiation mode at the cost of guide mode. We employ the energy band properties of Archimedean-4 lattices with the plane wave expansion method, the finite element method, and the finite-difference time-domain method. To employ density of bands on the figure of photonic crystal’s band gap, many parameters including, but not limited to, the lattice type, lattice period, the diameter of the hole or rod, materials, and the geometrical configurations, are taken into considerations. Upon completion of the proposed project, the optimal designs would contribute to saving the nature by making LED and OLED brighter while consuming less electric power.

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