ABSTRACT
This chapter presents the basic theory of magnetoinductive (MI) waves. It deals with the magnetic coupling between two elements. Although in general quite complicated, the properties of metamaterial elements can be in many cases described by only three parameters: self-inductance, self-capacitance, and self-resistance. The coupling between magnetic metamaterial elements leads to propagation of MI waves. The chapter presents the discussion of their properties with one-dimensional arrays for which interaction between only nearest neighbors. It explores the treatment, first, by including higher-order interactions and, second, by considering two- and three-dimensional arrays. Changing the resonant frequency of the elements and the coupling between them it is possible to tailor the dispersion of MI waves in coupled arrays. Interaction of electromagnetic waves with magnetic metamaterials was considered in a number of studies. The customary approach is based on an effective medium theory, where the interaction is described in terms of an effective magnetic permeability.
