Phase gratings find useful application in array receivers as passive multiplexing devices in the local oscillator injection chain. In particular, the Dammann phase gating is one of the simplest class to model and manufacture, and can be used to generate multiple images of a single input beam in a quasi-optical system. It is a binary grating consisting of a regular arrangement of milled slots or recesses in some suitable transparent dielectric or conducting block of material. The basic operation of the phase grating can be understood in terms of Fourier optics. However, Gaussian beam mode analysis is a powerful tool when investigating the limitation of the grating in a real submillirneter system of finite throughput and bandwidth. This is especially the case when evaluating the coupling to an array of horn antenna feeds. In this paper we present the results of our investigation into the modelling of phase gratings using Gaussian beam modes analysis and discuss new experimental measurements.