复介质理论中的模展开和正交补各向同性、各向异性和双各向异性介质的外激励波导
Modal Expansions and Orthogonal Complements in the Theory of Complex Media Waveguide Excitation by External Sources for Isotropic, Anisotropic, and Bianisotropic Media
摘要：
本文提出了一种求解双各向异性介质波导结构中外源激励导波问题的统一电动力学方法。在这种介质中，电损耗、磁损耗和磁电损耗的影响以本征模正交性的特殊形式表现出来，称为准正交性关系。它反映了交叉功率流的存在，并且对于任何一对通过这种关系刚性地彼此连接的模式。准正交关系仍然是真实的，在无损耗波导的限制情况下，产生的传播（有源）模式的正交性和归一化的习惯关系，也是他们的推广非传播（无功）模式。结果表明，波导结构的本征模集只有在激励源区域之外才是完备的。在这个区域内，场的模式展开是不完整的，必须用正交互补场来补充，正交互补场扩展了波导本征函数所跨越的适当希尔伯特空间。在激励源中，有外部体源（电流、场和介质扰动）和外部表面电流。此外，正交互补场在体激励源边界产生有效表面电流。通过确定模式场展开的模式振幅和源区域内的正交互补场，解决了由外部源激励波导的问题。模式激励方程推导的基础上三种方法应用麦克斯韦方程组的直接使用，电动力学模拟的数学方法的变化的常数，和共轭互易定理。
英文摘要：
A unified electrodynamic approach to the guided wave excitation by external sources in the waveguiding structures with bianisotropic media is developed. Effect of electric, magnetic, and magneto- electric losses in such media manifests itself in the special form of eigenmode orthogonality referred to as the quasi-orthogonality relation. It reflects the existence of the cross-power flow and for any pair of modes which are rigidly linked to each other by this relation. The quasi-orthogonality relation remains true in the limiting case of lossless waveguides yielding the customary relations of orthogonality and normalization for propagating (active) modes and also their generalization for nonpropagating (reactive) modes. It is shown that the eigenmode set for a waveguiding structure is complete only outside the region of exciting sources. Inside this region the modal expansions of fields are incomplete and must be supplemented with the orthogonal complementary fields which extend the proper Hilbert space spanned by waveguide eigenfunctions. Among exciting sources there are the external bulk sources (currents, fields, and medium perturbations) and the external surface currents. Besides, the orthogonal complementary fields generate the effective surface currents on boundaries of the bulk exciting sources. The problem of waveguide excitation by external sources is solved by means of determining both the mode amplitudes for the modal field expansions and the orthogonal complementary fields inside the source region. The equations of mode excitation are derived on the basis of three approaches applying the direct use of Maxwell's equations, the electrodynamic analogy with the mathematical method of variation of constants, and the conjugate reciprocity theorem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
