Peng Chao, Liang Yong, Sakai Kyosuke, Iwahashi Seita, Noda Susumu
Department of Electronic Science and Engineering, Kyoto University, Kyoto-Daigaku-Katsura, Kyoto 615-8510, Japan.
Opt Express. 2011 Nov 21;19(24):24672-86. doi: 10.1364/OE.19.024672.
The coupled-wave theory (CWT) is extended to a photonic crystal structure with arbitrary sidewalls, and a simple, fast, and effective model for the quantitatively analysis of the radiative characteristics of two-dimensional (2D) photonic-crystal surface-emitting lasers (PC-SELs) has been developed. For illustrating complicated coupling effects accurately, sufficient numbers of waves are included in the formulation, by considering their vertical field profiles. The radiation of band-edge modes is analyzed for two in-plane air-hole geometries, in the case of two types of sidewalls: i.e. "tapered case" and "tilted case." The results of CWT analysis agree well with the results of finite-difference time-domain (FDTD) numerical simulation. From the analytical solutions of the CWT, the symmetry properties of the band-edge modes are investigated. In-plane asymmetry of the air holes is crucial for achieving high output power because it causes partial constructive interference. Asymmetric air holes and tilted sidewalls help in inducing in-plane asymmetries. By breaking the symmetries with respect to the two orthogonal symmetric axes of the band-edge modes, the two factors can be tuned independently, so that the radiation power is enhanced while preserving the mode selectivity performance. Finally, top-down reactive ion etching (RIE) approach is suggested for the fabrication of such a structure.
耦合波理论（CWT）被扩展到具有任意侧壁的光子晶体结构，并且已经开发出一种简单、快速且有效的模型，用于定量分析二维（2D）光子晶体表面发射激光器（PC-SEL）的辐射特性。为了准确说明复杂的耦合效应，通过考虑其垂直场分布，在公式中包含了足够数量的波。针对两种面内气孔几何形状，在两种类型的侧壁情况下，即“锥形情况”和“倾斜情况”，分析了带边模式的辐射。CWT分析结果与有限差分时域（FDTD）数值模拟结果吻合良好。从CWT的解析解出发，研究了带边模式的对称性质。气孔的面内不对称性对于实现高输出功率至关重要，因为它会导致部分相长干涉。不对称气孔和倾斜侧壁有助于诱导面内不对称性。通过打破带边模式关于两个正交对称轴的对称性，可以独立调整这两个因素，从而在保持模式选择性性能的同时提高辐射功率。最后，建议采用自上而下的反应离子蚀刻（RIE）方法来制造这种结构。
