标题： 模展开和正交补在各向同性、各向异性和双各向异性介质中由外部源激发的复介质波导理论中的应用 显示英文标题

标题： Modal Expansions and Orthogonal Complements in the Theory of Complex Media Waveguide Excitation by External Sources for Isotropic, Anisotropic, and Bianisotropic Media

摘要： 一种统一的电磁动力学方法用于研究在具有各向异性介质的波导结构中由外部源激发的导引波。这种介质中的电、磁和磁电损耗的影响表现为本征模正交性的特殊形式，称为准正交关系。它反映了交叉功率流的存在，并且适用于通过该关系相互严格关联的任何一对模式。在无损耗波导的极限情况下，准正交关系仍然成立，得出传播（有源）模式的常规正交性和归一化关系，以及它们对非传播（无源）模式的推广。结果显示，波导结构的本征模集仅在激发源区域之外是完整的。在此区域内，场的模展开是不完整的，必须补充正交补场，以扩展由波导本征函数张成的适当希尔伯特空间。在激发源中包括外部体源（电流、场和介质扰动）和外部表面电流。此外，正交补场在体激发源的边界上产生有效的表面电流。通过确定源区域内模场展开的模幅度和正交补场，解决了由外部源激发波导的问题。模激发方程基于三种方法推导，即直接使用麦克斯韦方程，与常数变易数学方法的电磁动力学类比，以及共轭互易定理。 显示英文摘要

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.