Focalization of evanescent beams

We predict and show the existence of unlocked evanescent waves in two dimensional periodic structures. In a one dimensional periodic structure an evanescent mode are located either at the center or at the boundary of the Brillouin Zone, and the real part of wave-vectors is locked either to zero or to the modulation vector of the periodicity. However, we report an unexpected observation that this is not the case in 2D or 3D PhCs where "unlocked" complex modes can be predicted. As an interesting consequence, due to their “complex” character, or, equivalently, due to their phase freedom, beams constructed from such evanescent waves can show focalization effects. Indeed, we numerically simulate the propagation of such beams in the bandgap of PhC slabs, and we find significant focalization.