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Metallic metamaterials with positive dielectric responses are promising as an alternative to dielectrics for the generation of Cerenkov radiation [J.-K. So et al., Appl. Phys. Lett. 97(15), 151107 (2010)]. We propose here by theoretical analysis a mechanism to couple out Cerenkov radiation from the slab surfaces in the transverse direction. The proposed method based on Brillouin-zone folding is to periodically modify the thickness of the metamaterial slab in the axial direction. Moreover, the intensity of the surface-coupled radiation by this mechanism shows an order-of-magnitude enhancement compared to that of ordinary Smith-Purcell radiation.

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