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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.