L3光子晶體微共振腔因為具有高品質因子(Quality factor)與低模態 體積(Mode volume)的優勢，在微共振腔的研究中受到重視。當共振腔 之間以消散波交換能量，能夠形成耦合共振腔，應用於高速雷射、光 波導以及光積體電路等元件，具有高度的潛能。文獻中顯示，L3共振 腔的基礎模態具有往30°方向傳播的消散波，因此本文以時域有限差分 法(FDTD)，研究兩個與三個L3光子晶體共振腔以30°的排列方式下，由 基礎模態所分裂的耦合模態。 我們的結果顯示雙重光子晶體共有兩個耦合模態，波長分裂量大約 為25nm。而模態的品質因子由3200~4200，偏振角度由84°~105°。三重 共振腔共有三個耦合模態，其波長的分裂量大約20nm。因模態不同， 品質因子有2400~3600、偏振角度有108°~77°的差異。文獻中指出，將 L3共振腔的孔柱外移可以提高品質因子，因此本研究雙重光子晶體經 孔柱外移0.15個晶格常數調變後，模態品質因子最高達11300。三重共 振腔的孔柱進行外移調變，發現孔柱外移0.10個晶格常數時，模態品質 因子最高可達5600。 我們對模態做動量空間的分析，發現孔柱外移會使模態漏光區域 (Leaky region)內電場分佈比例改變，而影響模態品質因子與偏振角度 的值。;L3 photonic crystal micro-cavity has been interested due to the advantages of high quality factor and low mode volume. Coupled cavity which allowing energy transfer by evanescent wave is considered to have potential applications to the fast laser,coupled cavity waveguide, and photonic circuits. Previous reported have emphasized on the fundamental mode studies of double-coupled-L3 cavity with the evanescent wave propagated in 30°. In this work, we will study the fundamental mode splitting of 30° propagation double-coupled-L3 cavity(DL3) and triple-coupled-L3 cavity (TL3) by using the finite-differential-time-domain (FDTD) calculations. Our calculations show that DL3 cavity has two coupled modes (bonding mode and anti-bonding mode). The wavelength splitting of these two couple modes are about 25nm. Their quality factors are in the range of 3200 to 4200, and polarization angles are about 84° to 105°. Further calculations showTL3 cavity has three coupled modes (one bonding mode and two anti-bonding modes), the wavelength splitting are about 20 nm. Theirquality factors and the polarization angles arein the range of 2400 to 3600 and 108°~ 77° respectively. The quality factor of DL3 cavity (or TL3 cavity) could be increased by outward-shifting the air hole beside cavity. Our calculations show that quality factors of DL3 cavitycould be up to 11300 as the air hole shiftingfor 0.15 lattice constant. For TL3 cavity, the quality factorscould be up to5600 as the air hole shifting for 0.10 lattice constant. By monitoring the electric field in k space, the reduction of the electric field within the leaky region could be found as the air hole shifting outward. Such a reduction was equivalent to less cavity loss, and it induced the increasing of quality factor.
