Dynamical experimental studies of the diffraction efficiency, birefringence, and surface relief modulation were carried out on functionalized azopolymer films of p(DR1M-co-MMA) with a 12% mole fraction of DR1M. The gratings were recorded using two linearly polarized pump beams (lambda = 514.5 nm) either;with a parallel configuration (p + p) or (s+(-s)) or with orthogonal polarizations (p+s). A general Jones matricial approach in conjuction with real-time polarization analyses of the first order diffracted beam (S+1) appears to be a quite sensitive method to extract relevant parameters such as birefringence (Delta n) and surface relief modulation (2 Delta d). The phase matrices have been developed considering the pump polarization of the two interfering beams and taking into account the orientational "angular hole-burning" model under low pump irradiances. Numerical calculations allow us to extract the time variations of Delta n and 2 Delta d and to compare the various efficiencies in grating formation. The obtained values for Delta n are then compared with polarimetric measurements and the basic mechanisms or driving forces in the relief formation are also discussed in connection with recently proposed phenomenological models.