General Theory on Artificial Metamaterials

Abstract

In this chapter, we present a general theory of effective media to establish the relationship between the local field responses on metamaterial structure and the macroscopical behaviors for artificial metamaterials composed of periodic resonant structures. By treating the unit cell of the periodic structure as a particle, we average the local field to define the local average permittivity and permeability for different unit structures and derive a general form of discrete Maxwell’s equations in macroscale. We obtain different wave modes in metamaterials including propagation mode, pure plasma mode, and resonant crystal bandgap mode. The distortion in the electromagnetic parameters has been well explained by the derived spatial dispersion model. Thus, the unfamiliar behaviors of metamaterials from the numerical S-parameter retrieval approach is further verified and described. The excellent agreements between the theoretical predictions and the numerical retrieval results indicate that the new defined model and method of analysis fit better to the physical structures and is thereafter a more advanced form of fitting formula for the effective electromagnetic parameters of metamaterials.