Diffraction of a wave by a cylindrical surface with discontinuous impedance

The principal term of the asymptotics is obtained for the two-dimensional problem of diffraction of a plane wave by a smooth cylinder with discontinuous impedance. A key domain in the vicinity of the light-shadow boundary (Fock region) is considered. It is assumed that the point of a jump of the surface impedance is placed near the light-shadow boundary. This gives rise to an intersection of the transition regions near the lightshadow terminator and in the vicinity of a ray reflected from the inhomogeneity of the boundary. The leading terms contain Fock integrals of a new type in addition to the standard ones. The asymptotics is simplified in the penumbral, illuminated, and shadowed regions. Asymptotic estimates of the integrals lead to a description of waves of a new type, which are absent for continuous impedance.