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Comparison of 2D and 3D Fourier modal methods for modeling subwayelength-structured silicon waveguides

机译：比较2D和3D傅里叶模态方法建模地铁结构的硅波导

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Frequency-domain Fourier modal methods have recently evolved into efficient tools for rigorous numerical modeling of a wide class of photonic and plasmonic structures and devices. In this contribution we describe the application of our 2D and 3D in-house tools, namely aperiodic rigorous coupled wave analysis (aRCWA) and bi-directional mode expansion propagation method using harmonic expansion (BEXX), on a recently described novel type of subwavelength grating (SWG) waveguides. They are created by means of periodically interlacing silicon segments with a superstrate material with a lower refractive index. It has been shown recently, both theoretically and experimentally, that for a suitable choice of SWG parameters such as grating period and duty cycle, the structure can support low-loss guided (Bloch) mode. Its effective index, mode profile and dispersion characteristics can thus be tailored to specific needs without the necessity of changing material composition. In our methods, either complex coordinate transformation or uniaxial anisotropic perfectly matched layers have been applied as efficient absorption boundary conditions. In order to reduce the number of expansion terms needed to reach required accuracy, the adaptive spatial resolution technique has been implemented. Structural symmetries of the devices can be fully utilized to this aim, too. Propagation constants of Bloch modes are also compared with those obtained with a full-vector film mode matching (FiMM) mode solver using the very simple effective medium theory (EMT).
机译：频域傅里叶模态方法近来已发展成为用于对各种光子和等离子体结构和设备进行严格数值建模的有效工具。在此贡献中，我们描述了我们的2D和3D内部工具在最近描述的新型亚波长光栅上的应用，即非周期性严格耦合波分析（aRCWA）和使用谐波扩展（BEXX）的双向模式扩展传播方法（SWG）波导。它们是通过周期性地将硅片段与折射率较低的覆层材料交织而成的。最近在理论上和实验上都表明，对于SWG参数（如光栅周期和占空比）的适当选择，该结构可以支持低损耗导引（Bloch）模式。因此，可以在不改变材料成分的情况下针对特定需求调整其有效折射率，模式轮廓和色散特性。在我们的方法中，复杂的坐标变换或单轴各向异性完美匹配的层已被用作有效的吸收边界条件。为了减少达到所需精度所需的扩展项的数量，已实施了自适应空间分辨率技术。装置的结构对称性也可以完全用于此目的。还使用非常简单的有效介质理论（EMT），将Bloch模式的传播常数与使用全矢量电影模式匹配（FiMM）模式求解器获得的常数进行比较。

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