In this work a set of simplified theories for predicting diffraction efficiencies of diffraction phase and triangular gratings are considered. The simplified theories applied are the scalar diffraction and the effective medium theories. These theories are used in a wide range of the value Λ/λ and for different angles of incidence. However, when 1 ≤ Λ/λ ≤ 10, the behaviour of the diffraction light is difficult to understand intuitively and the simplified theories are not accurate. The accuracy of these formalisms is compared with both rigorous coupled wave theory and the finite-difference time domain method. Regarding the RCWT, the influence of the number of harmonics considered in the Fourier basis in the accuracy of the model is analyzed for different surface-relief gratings. In all cases the FDTD method is used for validating the results of the rest of theories. The FDTD method permits to visualize the interaction between the electromagnetic fields within the whole structure providing reliable information in real time. The drawbacks related with the spatial and time resolution of the finite-difference methods has been avoided by means of massive parallel implementation based on graphics processing units. Furthermore, analysis of the performance of the parallel method is shown obtaining a severe improvement respect to the classical version of the FDTD method.This work was supported by the “Ministerio de Economía y Competitividad” of Spain under projects FIS2011-29803-C02-01 and FIS2011-29803-C02-02 and by the “Generalitat Valenciana” of Spain under project PROMETEO/2011/021
