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Two-dimensional scattering of a periodic array of circular homogeneous and gyrotropic-type cylinders embedded in an isotropic dielectric slab is studied using the T-matrix of an isolated circular cylinder and the lattice sums. The T-matrix of a single circular gyrotropic cylinder is given numerically and then the generalized reflection and transmission matrices for the embedded array are obtained using the T-matrix and lattice sums. The harmonic fields in each of the four regions are given analytically. Numerical results of the power reflection and transmission coefficients based on the fundamental mode and the near-scattered field distribution are shown and discussed.