Finite-element simulation of the depolarization factor of arbitrarily shaped inclusions.

An understanding of the polarization characteristics is a prevailing issue in electrostatics and scattering theory and is also vital to the rational design of future dielectric nanostructures. In this work, a finite-element methodology has been applied to simulate two-phase heterostructures containing a polarizable dielectric inclusion. The inclusions investigated can be considered as arbitrarily shaped cross sections of infinite three-dimensional objects, where the properties and characteristics are invariant along the perpendicular cross-sectional plane. Given the paucity of experimental and numerical data, we set out to systematically investigate the trends that shape and permittivity contrast between the inclusion and the host matrix have on the depolarization factor (DF). The effect of the first-versus second-order concentration virial coefficient on the value of the DF is considered for a variety of inclusion shapes and a large set of material properties. Our findings suggest that the DF for such inclusions is highly tunable depending on the choice of these parameters. These results can provide a useful insight for the design of artificial two-phase heterostructures with specific polarization properties.