Scattering by cylinder with anisotropic impedance

Scattering of plane waves by an isotropic cylinder with anisotropic coating is considered, for the design of radar reflectors and shaping of secondary fields. The corresponding boundary-value problem for the distribution of surface impedance is formulated in accordance with physical optics and reduced to a system of two equations with six unknowns, which leaves four degrees of freedom for combinations of resistances and reactances. Special cases are zero reactances only and zero resistances only, a more general case being rotation of the principal axis of the impedance tensor so that neither reactances nor resistances are zero. The problem is solved rigorously by the separation of variables method, for a cylinder of arbitrary cross-section inside a circumscribing circular cylinder with the smallest possible radius and with the Lorenz lemma in integral for applicable to the region between both cylindrical surfaces. Infinitesimally thin electric and magnetic current filaments as sources of the auxiliary field are placed first inside the inner cylinder and then outside the outer one.