Generalized Helmholtz Decomposition for Modal Analysis of Electromagnetic Problems in Inhomogeneous Media
Generalized Helmholtz Decomposition for Modal Analysis of Electromagnetic Problems in Inhomogeneous Media
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DOI：
10.1109/jmmct.2023.3305008
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发表时间：
2023-01
影响因子：
2.3
通讯作者：
Jie Zhu;T. Roth;Dong-Yeop Na;W. Chew
中科院分区：
文献类型：
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作者：
Jie Zhu;T. Roth;Dong-Yeop Na;W. Chew
基于势的广义Lorenz规范表述可以用于非均匀介质中电磁场的量子化。然而，人们经常面临的模式冗余时，发现本征模式从潜在的基础制定。在自由空间中，这可以通过与著名的亥姆霍兹分解的联系来解释。在这项工作中，我们推广了亥姆霍兹分解到它的广义形式，呼应使用广义洛伦兹规范在非均匀介质。利用数值量子化中常用的矢势公式，将电磁场本征值问题公式化。对微分算子的性质进行了数学分析。在连续空间和离散空间中证明了两类模态之间的相似性关系。数值验证了非均匀各向异性介质中两组模式的完备性和正交关系。这项工作作为一个基础，数值量子化的电磁场在非均匀介质与潜在的基础制定。
Potential-based formulation with generalized Lorenz gauge can be used in the quantization of electromagnetic fields in inhomogeneous media. However, one often faces the redundancy of modes when finding eigenmodes from potential-based formulation. In free space, this can be explained by the connection to the well-known Helmholtz decomposition. In this work, we generalize the Helmholtz decomposition to its generalized form, echoing the use of generalized Lorenz gauge in inhomogeneous media. We formulate electromagnetics eigenvalue problems using vector potential formulation which is often used in numerical quantization. The properties of the differential operators are mathematically analyzed. Orthogonality relations between the two classes of modes are proved in both continuous and discrete space. Completeness of two sets of modes and the orthogonality relations are numerically validated in inhomogeneous anisotropic media. This work serves as a foundation for numerical quantization of electromagnetic fields in inhomogeneous media with potential-based formulation.