Three theorems on zero backscattering

A body of revolution (BOR) which is axially symmetric in terms of both geometric and material properties is considered. It consists of simply or multiply connected impenetrable portions characterized by an impedance boundary condition with a relative surface impedance η=±1, and by penetrable (and possibly inhomogeneous) portions characterized either by scalar permittivity, scalar permeability and chiral admittance, or by uniaxial permittivity and permeability tensors. For an axially incident plane wave, two theorems are stated in which sufficient conditions are imposed on the constitutive parameters to ensure a zero backscattered field. A third theorem is concerned with the superposition of two structures, each of which individually yields zero backscattering