Etude des ondes rampantes sur un corps convexe vérifiant une condition ďimpédance par une méthode de développement asymptotique

We study the creeping waves propagating on a convex object, whose surface impedance is Z. To this end, we seek, by using an asymptotic expansion method, a solution of Maxwell equations, propagating along a geode sic, and satisfying Silver-Müller radiation condition at infinity, and the impedance boundary condition at the surface of the body. By using a geodesic coordinate system suited to the problem, we obtain a closed form solution. The electric and magnetic fields are given in term of the components of these fields along the binormal to the geodesic. We show that two types of creeping waves exist: the electric (resp. magnetic) type, with a non zero binormal component of the electric (resp magnetic) field. They are uncoupled, except in the vicinity of Z = 1, where a rotation of the polarization, similar to Rytov’s law, is evidenced.