  We consider transverse propagation of electromagnetic waves through a
two-dimensional composite material containing a periodic rectangular array of
circular cylinders. Propagation of waves is described by the Helmholtz equation
with the continuity conditions the tangential components of the electric and
magnetic fields on the boundaries of the cylinders. We assume that the
dimensionless wave frequency $\nu \ll 1$ that allows us to view the governing
equation as a perturbation of the Laplace equation. We show that the
eigenfunctions and the eigenvalues are even analytic functions of the magnitude
of the quasimomentum vector and provide a rigorously justified asymptotic
expansion the tensor of effective properties. We also determine explicitly a
frequency correction term to the tensor of effective properties.
