光子晶體結構是由週期性介電材料所組成，因為具有特殊的光子能帶，所以可以有效控制光波的傳播。本論文使用平面波展開法分析正方晶格的光子能隙，藉由時域耦合模態理論來設計光子晶體波導光能量分配器，並使用有限時域差分法模擬光波在分配器內的傳播情況，以探討分配器內波導的圓柱尺寸與傳遞係數的關係。此外，本論文亦對耦合共振光學波導的幾何結構進行建模與數值計算，由結果得知兩倍密四方晶格的排列方式在中心波長具有寬頻且高傳輸的特性。延伸此波導架構，本論文提出一個多模態的光子晶體光能量分光器，設計出同時兼具波導、分波與濾波能力的微米級光學元件，此研究成果應可用在日後的積體光子迴路設計中。 Photonic crystals are composed of periodic dielectric that has photonic band gap. It can effectively control the light of propagation. In this thesis, we analysis the band gaps of the square lattice photonic by plane wave expansion, and design of optical power divider by using time-domain coupled-mode theory. We simulated the light wave propagation in power divider by using finite-difference time-domain method. We also discussed the relationship of the cylindrical size and the transmission coefficient in the divider. Besides, We have simulated the structure of coupled-resonator optical waveguides. Simulation results show that the double dense cubic photonic crystals have wide high-transmission bandwidths near the center of wavelength. Further, we proposed the power splitter of multimode interference in photonic crystal waveguides. It is a nanometer scale of optical component and it has the ability to guide, split and filter. The results of this study should be applied for photonic integrated circuit in the future.
