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In this paper, we analyze the birefringence effect in circular photonic crystals (CphCs). The studied CphCs are dielectric rings (DRs) and photonic crystals with cylindrical air holes arranged in circular patterns. The dielectric concentric circular patterns admit two preferred propagation directions defined by an extraordinary and an ordinary refractive index, representing two electric field polarizations. These electric fields are diffracted inside the crystal or are localized in a central microcavity region. We prove the induced artificial anisotropy in DRs through the geometrical equivalence with the corresponding thin-film multilayer structure. The equivalence is obtained through the geometrical synthesis of the wavefront propagation inside the artificial anisotropic structure. As applications, we analyze a Si/SiO2 DR Bragg reflector and a GaAs CphC microcavity resonator. The Bragg theory is validated by numerical time-domain approaches that are well suited to solve scattering problems. The microcavity resonance analysis and the Q -factor evaluation are performed by the finite-element method modeling.