We predict the existence of evanescent modes with unlocked phases in two-dimensional (2D) dielectric periodic structures. Contrary to what is known for one-dimensional structures, where evanescent fields lock to the host modulation, we show that in 2D systems a new class of evanescent modes exists with an unlocked real part of the wave vector. Hence, beams constructed from such unlocked evanescent waves can exhibit spatial effects. A significant focalization of a beam propagating within the band gap of a flat photonic crystal slab is also shown. The predicted phenomenon is expected to be generic for spatially modulated materials.