Numerical calculations of the intrinsic electrostatic resonances of artificial dielectric heterostructures

In order to study the intrinsic electrostatic resonances (ERs) of artificial dielectric heterostructures, we develop an efficient effective-medium-based method for modeling the effective permittivity, with careful attention paid to several key factors controlling ERs. Our method relies on finite element modeling and is applicable to inclusions with complex boundaries, e.g., fractal inclusion. A series of isolated and square arrays of several types of negative-permittivity media is considered. The inclusion shapes investigated can be considered as cross sections of infinite three-dimensional objects, where the properties and characteristics are invariant along the perpendicular cross-sectional plane. The continuum model used in this work is accurate only if the homogeneous representation of the composite structure makes sense, i.e., quasistatic approximation. It is found, among the conclusions of the article, that the effective permittivity of the composite (lossless) structures versus surface fraction curves presents a sharp peak, which occurs precisely at ER. For lossy inclusions, the primary signature of the ER is seen in the peak in the imaginary part of the complex permittivity or as an inflexion in the curve of the real part of the complex permittivity. The focus in this effort is on the analysis of intrinsic ER as a function of the shape and permittivity of the inclusion. The variations in the effective permittivity related to the iteration number show the following hierarchy for Sierpinski's square and triangle: the higher the iteration number of the inclusion the smaller value of phi(2) corresponding to the ER. In the vicinity of the ER peak, field enhancement is observed, which consists of enormous changes in the local electric field. Differences between the ER characteristics for aperiodic and periodic orders through the introduction of localized voids in the structure are also noteworthy. In addition, our approach performs well for fractal-shaped inclusions, e.g., Siepinski square, for which we show that the ERs satisfy a similarity transformation. These calculations can aid in the discovery of new materials with optimized magnetoelectric structures whose ER may be manipulated by electromagnetic fields. (c) 2007 American Institute of Physics.