Spatial modifications of a Gaussian beam incident on a diffraction grating

When a fundamental Gaussian beam at microwave frequency is incident on a reflection grating, there are spatial modifications such as lateral shift for the reflected and diffracted beam and generation of higher order Gaussian modes. Different parameters of the incident beam such as waist radius, beam frequency, incident angle, and polarization direction affect the spatial modifications differently. We trace the beam propagation and central ray position by simulation and find how these parameters influence the beam modifications.