Far-field dot pattern generation is analyzed for a Gaussian beam source that illuminates a sinusoidal phase grating which is placed at a certain distance behind the beam waist. We obtain a bigger field of view with more numbers of points using a Gaussian beam in comparison to a plane wave illumination because of the initial curvature of the Gaussian beam. Light propagation modeling through the sinusoidal grating is carried out using different approximations for a thin and thick phase grating. Using thin element approximation (TEA), the complex field is carried out with low computational effort and accuracy. We compare TEA with more accurate methods, such as FFT-BPM and FDTD methods. For thin phase gratings, TEA can be used but for thick gratings, FDTD method is the only valid option. For thick phase gratings, the effect of reflection from phase grating on the field modulation increases and we use FDTD method to find the correct far field pattern distribution.