Dynamical experimental studies on the diffraction efficiencies and the formation of birefringence grating and surface relief gratings on doped and/or covalently bonded azobenzene derivatives containing polymer films were carried out using laser beams with different polarizations. From polarization analyses of the first-order (+/-1) diffracted beams, the contributions to the diffraction efficiency are separated into an anisotropic (or birefringence) part and a surface relief part. During the growth of the gratings the dynamical responses of both contributions appear to be quite distinct, and estimates of the time variations of the anisotropic phase shift, Delta phi, due to the induced birefringence and of the surface relief height, 2 Delta d. due to the polymer mass transport are obtained. Calculations and simulations of the theoretical expressions allow us to confirm the experimental findings and to reproduce all the observed polarized first-order diffraction curves with good agreement even when the surface relief is important in the covalently bonded azobenzene polymer films. In these functionalized systems we thus conclude that very efficient permanent surface relief gratings are formed using right-circular and left-circular interfering laser beams.