We examine the properties of the defect modes arising in the zero-effective phase (zero-φ ) gap when a dielectric defect layer is introduced in a one-dimensional photonic crystal containing single negative materials. We show that the defect modes inside the zero-φ gap can be as sensitive to the incidence angle as those inside the Bragg gap. In addition, adjusting the properties of the dielectric defect layer can control the frequencies and the number of defect modes. We present a brief design of a polarization-independent spatial filter based on those defects. The proposed spatial filter can work at dual carrier frequencies with low-pass and wide-pass characteristics. Our results can help improve the performance of microwave devices independent of the source wave polarization.