This paper presents a novel analytical model for the analysis of the electromagnetic field radiation in grating couplers. As will be shown, the radiation pattern of the grating couplers can be described with appropriate accuracy as periodic structures. The obtained field distribution of the coupler can be modeled as a sequence of Fourier series for particular distance values, periodicities and wavelengths. This is compatible with the Floquet-Bloch theory of periodic structures. With this model all relevant parameters for the radiation pattern can be investigated. The results of the proposed analytical model are compared with simulation results for a wavelength of 1550 nm. The model can be used for any periodic structure.