The performance of a simple microwave modulating retro-reflector based on a rotating corrugated metallic plate is analyzed theoretically and compared with laboratory measurements. Fields within the corrugations are described by waveguide modes and free-space fields by Floquet modes. The periodicity of the grooves is represented through the reciprocal lattice corresponding to the periodic structure. The accuracy of the calculation is analyzed as a function of the number of modes used to describe the electromagnetic field. Graphs are given for the design of a modulator for any wavelength.