A semi-analytical approach for analyzing two-dimensional electromagnetic scattering by layered cylindrical arrays of circular rods distributed along concentrically layered circular rings is presented. The method uses the T-matrix of a circular rod in isolation, the reflection and transmission matrices of a cylindrical array expressed in terms of the cylindrical waves as the basis, and the generalized reflection and transmission matrices for a layered cylindrical structure. Using the method, the radiated field from a line source placed inside a cylindrical electromagnetic bandgap (EBG) structure with defects is numerically investigated. Numerical examples demonstrate that the three-layered EBG formed by circular rods of perfect conductor is effective for focusing a beam in the direction of missing rods.
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