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The optical analogues of Bloch oscillations and their associated Wannier-Stark ladders have been recently analyzed. In this paper we propose an elastic realization of these ladders, employing for this purpose the torsional vibrations of specially designed one-dimensional elastic systems. We have measured, for the first time, the ladder wave amplitudes, which are not directly accessible either in the quantum mechanical or optical cases. The wave amplitudes are spatially localized and coincide rather well with theoretically predicted amplitudes. The rods we analyze can be used to localize different frequencies in different parts of the elastic systems and viceversa. PACS numbers: 43.35.+d,63.20.Pw,43.40.Cw Recently, undulatory systems showing analogues of Bloch oscillations and Wannier-Stark ladders (WSL) attracted increasing attention in several fields of physics [1,2,3,4,5]. As shown by Bloch, electrons in a periodic potential have extended solutions. The same is true for the behavior of an electron under the action of a static electric field. In contrast, and opposite to intuition, when both the periodic potential and the electric field are present, the solutions are localized; this is only true when band to band Zener tunneling is negligible or the system is short enough. The spectrum then shows equally spaced resonances known as Wannier-Stark ladders, the nearest-neighbor level spacing being proportional to the intensity of the external field [6]. In the time domain, the Wannier-Stark ladders yield the so called Bloch oscillations which consist in a counterintuitive effect where the electrons show an * Permanent address:

We discuss the existence of the electromagnetic Stark ladder in some optic systems by studying the propagation of light. The transmission coefficient is calculated by means of the transfer-matrix method. It is shown that although the transfer matrix is different from the quantum case it can give, in some particular configurations, a Stark-ladder resonance structure similar to the one observed in quantum systems. The relation between these resonances and a Fabry-Perot-like interference is discussed. Consideration is given to the observability of these ladders in the laboratory.

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