本研究中，我們設計二維以及三維光束直進之結構，將提出一個新的二維六角晶格的光子晶體波導結構，以達成準直輸出的光束。藉由運用平面波展開法，與有限時域差分法，針對二維結構做數值模擬與分析。本研究中也以有限時域差分法為基礎，提出新的光損耗與反射率之計算方法，可計算出各結構的反射率與傳輸損耗。除此之外，本研究以貝色光束的概念，分析探討三維環型之光子晶體波結構。使光侷限於該結構的中央，形成一圓形對稱之環型波導，光束更加準直，能量傳遞距離更長。準直且具指向性之光源可以提升光子晶體波導耦合進入傳統波導的耦合效率，也可以應用於光子晶體超高功率雷射，以取代介電材料之透鏡，使雷射有直進、超細光束與低耗損之特性，若滿足電磁波在方向性上之要求，可以運用於高指向微波天線。

In this work, we propose a novel output design of the photonic-crystal waveguides (PCWG) structures to investigate the enhancement of the collimated beam that was radiated from PCWG. First, we design novel two-dimensional PCWGs in hexagonal lattice. We simulate and analyze different structures by using the finite-difference time-domain numerical method and the plane wave expansion method. Based on the finite-difference time-domain numerical method, we propose a novel method to calculate the propagation loss and reflection for PCWGs. This method can be applied on single or multimode low-loss PCWGs. On the concept of the Bessel beam, we analyze and discuss the three-dimensional radial PCWG to enhance the collimated beam and propagation distance. The collimated emission is attractive for enhancing the coupling efficiency of light from PCWG into conventional dielectric waveguides, to control the emission direction of PC edge-emitting lasers, to apply to the high power laser to replace the dielectric lenses and to obtain the high collimated microwave beam.

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