Abstract: The present invention relates to a crystal structure with three-dimensional photonic band gap which comprises a pile of alternate series of layers of distinct dielectric materials having a first and a second determined dielectric constant values, wherein said layers have a constant determined thickness and said pile forms a substantially rectangular parallelepipedal block, and a plurality of parallel channels provided through said block along a direction orthogonal to the main faces of said layers. Said channels are distributed according a two-dimensional lattice pattern and have a third determined dielectric constant value. The values for the dielectric constants as well as the relative geometric dimensions of said layers and said channels are selected so as to obtain said three-dimensional photonic band gap in a predetermined frequency range. The crystal structure is especially for use as an antenna substrate.