Invariance of the speckle pattern of the transmitted wave in periodic waveguides.

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.