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The introduction of a dielectric slab on slit and hole arrays allows the excitation of a peak of transmission even when the orientation of the electric field would in principle forbid high transmission. This is called anomalous extraordinary transmission and is and is associated with effective excitation of a surface wave inside a dielectrics supported by a perforated metal that is closely related to the phenomenon of surface waves on a grounded dielectric slab. The problem has been analyzed both from the diffraction and the engineering based equivalent circuit, with good agreement with numerical results. Measurements also show peaks of anomalous extraordinary transmission in millimeter and terahertz waves.