Channelled waves in anisotropic mesh metamaterials

Channelled waves in 2D periodic anisotropic L-C mesh metamaterials have been investigated. Circuit simulation and the newly developed analytical model of a unit cell have demonstrated full qualitative agreement for both lossless and lossy cases. Isofrequencies for a lattice unit cell and the circuit simulations of finite meshes have shown that propagating waves are channelled from a point source as pencil beams which can travel only along specific trajectories. The beam direction varies with frequency, and at resonance frequency omega=1/(LC)^1/2, the phase and group velocities of the transmitted wave are orthogonal. The effect of losses was explored, and it is shown that losses can cause qualitative changes of the channelled wave type. It is shown that the channelled waves do not follow the laws of geometrical optics (Snell´s law, specular reflection and so on) at the interfaces of L-C meshes but are governed by the conditions of phase synchronism and impedance matching. Only in the special case of dual L-C and C-L meshes with the interface parallel to the axis of rectangular grid excited at the resonance frequency (X=1) do the channels follow the trajectories of optical rays. A planar mesh test cell has been designed and applied to retrieving the unit cell L-C parameters from the S-parameter measurements