In this paper the characteristics of millimeter-wave antenna composed of layered magnetic and dielectric slabs with different corrugation are described for the transverse electric mode. A corrugation of the upper magnetic layer contacts with air, and the lower surface of the dielectric slab having corrugation in matalized. The extinction coefficient clarifying the characteristics of the leakage wave is systematically derived by using the perturbation method combined with the multiple space scales. As an example the radiation efficiency becomes a value of about 89% by using the typical physical parameters in the frequency range from 52 to 54 GHz.