Homogenization Models for a Simple Dielectric-Composite Slab upon Oblique Incidence

Four different models are applied to effectively describe a geometrically simple dielectric-composite slab. The corresponding model parameters, when the oblique incidence is taken into account, are retrieved based on the transmission and reflection data and compensated with the nonmagnetic assumption. The scattering parameters of each model with derived parameters for various angles of incidence are then analytically calculated using the forward propagation matrix method and compared with the simulated scattering parameters from the real composite slab. According to these comparisons, it is shown that spatial dispersion makes it challenging to achieve angle-independent parameters for the applied four models. Moreover, when a stratified model is employed to describe the composite slab of our interest under oblique incidence, the boundary layers need to be anisotropic. 1. Introduction Homogenization of a given composite whose heterogeneity scale is sufficiently small is a long-lasting problem of continuing interest [1–5]. In this so-called long-wavelength regime, various characterization techniques have been developed to determine the macroscopic constitutive properties of composites, for instance, different mixing formulas [1, 2, 6], field averaging method [7], and scattering parameter ( -parameter) retrievals [8–11]. It is usually sufficient in this regime to characterize the macroscopic electromagnetic properties of composites using the homogeneous and isotropic model with the effective permittivity and the effective permeability . However, in the study of metamaterials [5], homogenization is more challenging since the size of unit cell or the scale of geometrical detail is often an appreciable fraction of the effective wavelength inside the materials. Recent studies have revealed that, in such a metamaterial regime between the quasistatic one and the photonic crystal one, refractive index is well defined while wave impedance turns out to be less rigorous due to nonlocality or spatial dispersion [12–16]. This point evokes researchers to question the validity of classic homogenization theory in the metamaterial regime [13–16]. It was found, for instance, that, for a fishnet metamaterial, all retrieved parameters strongly depend on the angle of incidence (or lateral wave vector component) [16]. Nevertheless, these efforts concentrated on the case that either the structure under investigation is illuminated normally by a plane wave, or only the homogeneous model is used to approximate the macroscopic electromagnetic properties of the structure. If a