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The effects connected with the dynamical scattering of electromagnetic waves by weakly curved periodic layered media are discussed. A simple physical model is used to take into account the effects of the curvature in the framework of the dynamical theory of diffraction. A peculiar effect consisting of the possibility of a continuous sweep of the direction of the diffracted beam over a relatively wide angular range, under the control of the frequency of the incident wave, is seen and analyzed. The design of a device realizing such a frequency‐direction conversion in the frequency range of 82–107 GHz is presented and discussed as a prototype of a new possible class of instruments. © 1996 American Institute of Physics.