本論文利用時域有限差分法(FDTD)來進行模擬主動元件與被動元件混成十字布拉格共振腔雷射。為確保光能夠在共振腔內有效的共振，對光柵耦合器進行模擬分析。先以理論算出二階光柵的週期，再利用模擬找出最適當的週期，讓光能夠以九十度角耦合進入波導或耦合出波導外。增加布拉格反射層於基板之上，有效的提高反射效率與降低損耗。
分析一階光柵長度與反射率之間的關係，將一階光柵反射器與二階光柵耦合器結合，控制一階光柵與二階光柵間距，可讓光耦合到空氣的反射率達99.9%。之後加入三五族(III-V)主動元件模擬雷射共振腔模態，並且針對不同的波長與不同的空間間隔分析其雷射共振腔之品質因子與光子生命週期。

In this thesis, we utilized the finite-difference-time-domain (FDTD) method to design a cross-coupled distributed bragg reflector (DBR) cavitie applied for hybrid lasers made on silicon waveguides. This cross-coupled DBR cavity consists of two pairs of DBR mirrors; one is fabricated on the silicon waveguide and the other is employed on the top and bottom of the waveguide, respectively. The top DRB mirror is made by III-V active layers. In order to guarantee light cross-resonating inside the cavity, a second-order grating on the silicon waveguide was designed first and optimized to have ideal orthogonal wave coupling between the two DBR pairs.
Second, a parameter scanning was conducted to find an optimal distance between the first- and the second-order gratings on the waveguide. Also, the gap spacing between the silicon waveguide and the III-V DBR mirror was examined. Finally, we concluded that the quality factor, resonant wavelength, photon lifetime, and mode profile of the cavity could be a function of the gap spacing. A mode hopping effect was also observed.

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