A comparative study of the electromagnetic behavior of two types of unbounded two-dimensional (2-D) photonic crystals (PCs) is presented. The first PC possesses a sinusoidal permittivity (SI) profile, while the second one, constituted of an array of dielectric rods in air, presents a sharp permittivity (SHA) profile. The dispersion relations of the two types of PCs, computed with the plane-wave method (PWM), are shown and compared. In particular, the evolution of the photonic bandgaps (PBGs) as a function of the permittivity contrast is investigated and discussed for both cases. The Green's functions derivation, by the efficient phased-array method (PAM) recently introduced, is briefly described, and numerical results for radiation patterns in the SI–PC and SHA–PC are shown and compared for different positions of the source within the crystal at a frequency lying inside the PBG. ©2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 24: 316–322, 2000.