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Because the penetration depth of light in the band gap is of the order of one lattice constant of a photonic crystal, structures such as circular photonic crystals CPC confine light. We show that an extension of the CPC concept to holes in any high-index material yields confinement only in the case that the hole size is varied jointly. Applying the Bloch-Floquet theorem in such a rotationally symmetric case leads to a decomposition of the Green's tensor. By using the photonic local density of states LDOS components in a CPC, the eigenfrequencies of localized cavity modes can be efficiently found.