Scattering From Isotropic Connected Wire Medium Metamaterials: Three-, Two-, and One-Dimensional Cases

Scattering problems involving wire media are computationally intensive due to the spatially dispersive nature of homogenized wire media. In this work, an integro-differential equation based on a transport formulation is proposed instead of the convolution-form integral equation that directly arises from spatial dispersion. The integro-differential equation is much faster to solve than the convolution equation form, and its effectiveness is confirmed by solving several examples in one-, two-, and three-dimensions. As experimental confirmation of both the integro-differential equation formulation and the homogenized wire medium parameters, several isotropic connected wire medium spheres have been fabricated on a rapid-prototyping machine, and their measured extinction cross sections compared with simulation results. Wire parameters (period and diameter) are varied to the point where homogenization theory breaks down, which is reflected in the measurements.