Controlling the dispersion of longitudinal waves via the affine deformation of the interlaced wire medium

We studied the dispersion properties of double interlaced wire metamaterials with geometry modified by affine transformation. That metamaterials were found to support eigenmodes with longitudinal polarization at low frequencies for all deformations. Due to the spatial dispersion the metamaterials isofrequency surfaces are centered at the Brillouin zone edges (rather than at $\Gamma$-point) and have the shape of ellipsoids. The refractive indices corresponding to the ellipsoids were analyzed both analytically and numerically.