Theory of Coupled Characteristic Modes

Abstract

A theory of coupled characteristic modes is developed for computing the eigenmodes of a coupled array using the modes of the isolated elements and the corresponding mutual interaction matrix. The systematic blending of the matrix block partitioning method and the orthogonal properties of the eigenvectors provide a generalized formulation considering the interaction of all the isolated modes. Later, closed-form solutions have been derived for the dominant coupled modes with the assumption of one-to-one mode coupling of the isolated elements. The idea has been further extended for two-to-two mode interaction modeling which conforms into a fourth-order generalized characteristic equation. The higher-order extension can be solved in a similar numerical process. Different examples have been considered to validate the proposed technique.