AbstractTo detach large vectorial full-wave electromagnetic scattering problems from the specific, dissimilar b'/> Wilson basis expansions of electromagnetic wavefields: a suitable framework for fiber optics
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Wilson basis expansions of electromagnetic wavefields: a suitable framework for fiber optics

机译：电磁波场的威尔逊基础扩展：光纤的合适框架

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AbstractTo detach large vectorial full-wave electromagnetic scattering problems from the specific, dissimilar bases that are typically associated with the optical waveguiding structures comprising an optical interface, we propose and demonstrate the expansion of wavefields in a single universal Wilson basis. We construct a Wilson basis by following the derivation in the paper by Daubechies, Jaffard and Journé. This basis features exponentially decaying basis functions in both the spatial and spectral domain. The strong localization in phase-space, with basis functions that strongly resemble wavefields, allow for efficient expansions of high-frequency electromagnetic fields. In a Wilson basis, the interface scattering problem is effectively separated from the physical configuration. For the evaluation of multiple, laterally displaced interface configurations, one may reuse electromagnetic fields in the Wilson basis, because the translation operator is sparse and diagonally dominant. We consider actual reflection-transmission problems comprising optical fibers and homogeneous media in the Wilson basis framework in a companion paper. There, the localization in the spectral domain aids the conversion of the numerical scheme to generate electromagnetic fields in homogeneous media due to Wilson-basis discretized electromagnetic sources. In this paper, we review the Wilson basis construction, demonstrate the expansion of modal electromagnetic fields in an optical fiber, and complex-source beams that are tilted with respect to the optical axis. Even for largely tilted beams (up to 60°), despite being highly oscillatory in the cross-sectional plane, the fields are well represented by a finite number of higher-order Wilson basis functions.
机译： Abstract 将大型矢量全波电磁散射问题与特定的，不相似的基类分离我们通常建议并演示在单个通用Wilson基础上扩展波场的方法，这些方法通常与包含光学接口的光学波导结构相关联。我们遵循Daubechies，Jaffard和Journé在论文中的推导，构建了Wilson基础。该基础在空间和光谱域中均具有指数衰减的基础函数。相空间中的强局部化具有与波场非常相似的基本功能，可以有效扩展高频电磁场。以威尔逊为基础，可以有效地将界面散射问题与物理配置分开。为了评估多个横向位移的界面配置，可以平移威尔逊基础的电磁场，因为平移运算符稀疏且对角线占优势。我们在随附的论文中考虑了威尔逊基础框架中包括光纤和均匀介质的实际反射传输问题。在那里，由于威尔逊基离散电磁源，在频谱域中的定位有助于数值方案的转换以在均质介质中生成电磁场。在本文中，我们回顾了威尔逊基础结构，演示了光纤中模态电磁场的扩展以及相对于光轴倾斜的复源光束。即使对于较大倾斜的光束（高达60°），尽管在横截面上高度振荡，但这些场都可以由有限数量的高阶Wilson基函数很好地表示。

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