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It is shown that far- and near-field effects, which are similar to those arising in transmission through finite-thickness photonic crystals (PCs) with structural defects, can be obtained in the conventional defect-free dielectric square-lattice PCs. Multiple narrow peaks of total transmission can appear within a frequency range, where the noncircular isofrequency dispersion contours of one type are quickly transformed for a higher-order Floquet-Bloch wave to the noncircular contours of the other type, leading to a frequency-domain passband being very narrow within a certain range of variation of the angles of incidence. In this regime, the mirror reflectance of the equivalent Fabry-Pérot resonator takes rather large values, which correspond to large values of Q factor and group index of refraction, strong field localization, and good isolation of the transmission peaks from each other. In some examples presented, Q factor exceeds 10^4.