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Polarization gratings are nondepolarizing polarization elements that alter the polarization state of the transmitted light in a periodic way, yielding a polarization-dependent diffraction. Using both the Jones and Stokes formalisms, we demonstrate that the polarization states of the higher order waves do not depend on the polarization state of the incoming light and that they are fully characterized by the polarization grating vector. We furnish a general model for polarization gratings that can be advantageously used for their design and show that a chain of three polarization gratings is a achromatic in-line polarimeter. In addition, we show that polarization gratings can be used as a tool to measure polarization mode dispersion.