  We calculate analytically the spectra of plasma waves and electromagnetic
waves (EMW) in metallic photonic crystal consisting of the parallel thin
infinite metallic cylinders embedded in the dielectric media. The axes of
metallic cylinders form a regular square lattice in a plane perpendicular to
them. The metal inside the cylinders is assumed to be in the high frequency
regime $\omega \tau >> 1$, where $\tau$ is the relaxation time. The proposed
analytical theory is based upon small parameters $f << 1$, where $f$ is the
volume fraction of the metal, and $kR << 1$, where $k$ is the wave vector and
$R$ is the radius of the cylinder. It is shown that there are five different
branches of the EMW that cover all frequency range under consideration except
one very small omnidirectional gap in the vicinity of the frequency of the
surface plasmon. However, at some directions of propagation and polarizations
the gap may be much larger. The reflection and refraction of the EMW is also
considered. The general theory of refraction is proposed which is complicated
by the spatial dispersion of the dielectric constant, and one particular
geometry of the incident EMW is considered.
