In nanotechnology, porous materials play an important role in achieving new properties. In this work we examine the electromagnetic behavior of a system of cylindrical nanopores, aranged in a twodimmensional square lattice, at extremely low frequencies. Our geometry is considered a photonic crystal and then we use the plane wave expansion method to solve for the eigenvalues problem that arise after the Fourier transform of our initial representation, by doing so we actually find the dispersion relation that in turn gives us a tachyon-like spectrum to study .