We discuss propagation of symmetric and antisymmetric Josephson plasma waves in a slab of layered superconductor clad between two identical dielectrics. We predict two branches of surface waves in the terahertz frequency range, one above and another below the Josephson plasma frequency. Apart from this, there exists a discrete set of waveguide modes with electromagnetic fields oscillating across the slab thickness and decaying exponentially away from the slab. We consider the excitation of the predicted waves by means of the attenuated-total-reflection method.It is shown that for specific set of the parameters of the structure the excitation of the waveguide modes is accompanied by total suppression of specular reflection.
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