<p>We report on conditions of invariance of the transmitted pattern in the propagation through a periodic waveguide, the incident wave having no effect on the intensity pattern of the transmitted field. This phenomenon is reminiscent of that observed when illuminating a disordered medium in the regime of Anderson localization, as a consequence of the contribution of a single transmission eigenchannel to the transmitted wave. It is shown that the freezing of the transmitted wave is not intrinsically related to the disorder and that, whatever the frequency, it can also be observed in a regular, periodic system, provided that at most one Bloch mode is propagating. Moreover, while all localized modes in a disordered medium are exponentially decaying, our periodic waveguide system offers the possibility of observing the freezing with propagating waves, hence without the counterpart of having a very low energy transmission.</p>