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Hyperbolic materials are artificially engineered composite media which allow innovative optical properties that could lead to significant advances in numerous breakthrough technologies. However, these properties are conventionally studied…

Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material…

Here, we present an overview of recent developments in the characterization of electromagnetic and quantum metamaterials using effective medium methods. It is highlighted that both electromagnetic and electronic systems can be homogenized…

We present a general framework for the homogenisation theory of space-time metamaterials. By mapping to a frame co-moving with the space-time modulation, we derive analytical formulae for the effective material parameters for travelling…

Here, we present an overview of a first principles homogenization theory of periodic metamaterials. It is shown that in a rather general context it is possible to formally introduce effective parameters that describe the time evolution of…

Recent years have seen considerable research success in the field of dynamic homogenization which seeks to define frequency dependent effective properties for heterogeneous composites for the purpose of studying wave propagation. There is…

Effective medium theory replaces a given fine-scale heterostructure with a homogeneous one in such a way that the physically measurable quantities, e.g. reaction fields and losses, remain approximately the same. This Letter shows that the…

It is well known that defining a local refractive index for a metamaterial requires that the wavelength be large with respect to the scale of its microscopic structure (generally the period). However, the converse does not hold. There are…

We analyze the reflection and transmission coefficients calculated from transfer matrix simulations on finite lenghts of electromagnetic metamaterials, to determine the effective permittivity and permeability. We perform this analysis on…

In the homogenization of composite metamaterials the role played by the relative positions of the wires and resonators is not well understood, though essential. We present a general argument which shows that the homogenization of such…

Recent experiments on temporal reflection in transmission line metamaterials and theoretical treatments of dispersive time-varying media have unearthed the fundamental role of modulation mechanisms on the interface conditions, underpinning…

We derive from first principles an accurate homogenized description of periodic metamaterials made of magnetodielectric inclusions, highlighting and overcoming relevant limitations of standard homogenization methods. We obtain closed-form…

A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…

Electromagnetic (EM) composites have stimulated tremendous fundamental and practical interests owing to their flexible electromagnetic properties and extensive potential engineering applications. Hence, it is necessary to systematically…

In the work, a modified effective medium theory is constructed for calculating the effective properties of thermoelectric composites with different values of percolation thresholds. It is shown that even at concentrations beyond the…

Classical theory of crystals states that a medium to be considered homogeneous must satisfy the following requirements: a) the dimension of the elementary cell must be much smaller than the incident wavelength; b) the sample must contain a…

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the…

In this work, we develop a new systematic and self-consistent approach to homogenize arbitrary non-magnetic periodic metamaterials. The proposed method does not rely on the solution of an eigenvalue problem and can fully characterize the…

In this paper we develop homogenization theory for spatiotemporally modulated wire medium. We first solve for the modal waves that are supported by this composite medium, we show peculiar properties such as extraordinary waves that…

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…