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Summary form only given. Optical bistability has raised a sustained interest in the 1990s. However it is commonly admitted that transverse mechanisms such as diffraction and carrier diffusion can seriously limit the applications developed in the frame of a plane wave (PW) analysis in increasing the energy consumption or introducing crosstalk mechanisms. In particular, several authors have predicted the existence of switching waves arising from the spatial coexistence of two different PW solutions, connected by an inhomogeneous intensity profile. We report on the first experimental observation of transverse switching waves in a passive resonator hosting a fast nonlinear active medium in a resonator composed by two Bragg mirrors.