We study the propagation of waves in a periodic array of absorbing layers. We report an anomalous increase of wave transmission through the structure related to a decrease of the absorption around the Bragg frequencies. The effect is first discussed in terms of a generic coupled wave model extended to include losses, and its predictions can be applied to different types of waves propagating in media with periodic modulation of the losses at the wavelength scale. The particular case of sound waves in an array of porous layers embedded in air is considered. An experiment designed to test the predictions demonstrates the existence of the enhanced transmission band.

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