Huang Chia-Chien
Department of Information Technology, Ling Tung University, Taichung, Taiwan, ROC.
Opt Express. 2008 Oct 27;16(22):17915-34. doi: 10.1364/oe.16.017915.
This work presents a novel full-vectorial imaginary-distance beam propagation method based on the multidomain pseudospectral scheme, for the first time, to study the modal characteristics of dielectric optical waveguides. The proposed method divides the transverse plane into several subdomains with uniform refractive indices, and expands the optical field in each subdomain in terms of a set of suitable basis functions. Accordingly, the complicated cross-coupling terms, which are required by the finite difference or finite element schemes, can be removed from the full-vectorial formulations. However, the coupling effect can be restored by matching the physical interface conditions. Moreover, to identify the higher-order modes, the residual traces of the preceding lower-order modes are subtracted from the calculated optical fields in each propagation step to suppress the rapid growth of the lower-order modes. Numerical examples of the two-dimensional slab waveguides demonstrate that the present approach yields a highly accurate propagation constant. When applied to three-dimensional rib waveguides the present scheme yields results that remarkably agree with the reliable values obtained from the modal transverse resonance method and finite element scheme.
这项工作首次提出了一种基于多域伪谱格式的新型全矢量虚距光束传播方法，用于研究介质光波导的模式特性。该方法将横向平面划分为几个具有均匀折射率的子域，并根据一组合适的基函数在每个子域中展开光场。因此，有限差分或有限元格式所需的复杂交叉耦合项可以从全矢量公式中消除。然而，通过匹配物理界面条件可以恢复耦合效应。此外，为了识别高阶模式，在每个传播步骤中从计算得到的光场中减去前序低阶模式的残余痕迹，以抑制低阶模式的快速增长。二维平板波导的数值例子表明，该方法能给出高精度的传播常数。当应用于三维肋形波导时，该方案得到的结果与从模式横向共振法和有限元格式获得的可靠值非常吻合。
