Waves in anisotropic metamaterials comprised of finite L-C meshes

2D periodic lattices and finite grids of lumped L-C elements have been investigated to elucidate the mechanisms governing wave phenomena in this kind of metamaterial. Isofrequencies for a lattice unit cell and circuit simulations of finite meshes have shown that such a medium exhibits unusual properties of channeling power from a point source into pencil beams which can propagate only along specific trajectories. The beam direction varies with frequency, and at the resonance frequency ω = 1/(LC)¹2 /, the phase and group velocities of the transmitted wave are orthogonal. It is shown that the channeled beams do not obey the laws of geometrical optics (Snell´s law, Brewster angle, etc.) at the skewed interfaces of dissimilar meshes, and that beam scattering is governed by the local conditions of the phase synchronization and impedance matching. Finally a new physical planar L-C mesh unit cell arrangement has been designed and measured.