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Generalized Impedance Conditions on the Boundary of a Nonscattering Cylinder


E.V. Chernokozhin

The solution to the inverse scattering problem of determining the impedance on the surface of an infinite cylinder from the field measured in the far zone is known rather well. In particular, the surface impedance of a nonscattering cylinder can be found. A cylinder is termed nonscattering if the scattered field under the incidence of a given plane electromagnetic wave is zero. However, the surface impedance making a cylinder nonscattering substantially depends on the direction of incidence. This fact is more evident when the cylinder is not circular. In the given paper, the possibility to generalize the impedance conditions on the boundary of a nonscattering cylinder in order to eliminate the dependence on the direction of incidence is suggested. The case of H-polarization is considered. The incident field on the surface of a cylinder is expanded in the proper surface harmonics, which are understood as eigenfunctions of Green’s function for the second boundary value problem for the Helmholtz equation in the cross section of the cylinder. The ratios between the corresponding expansion coefficients of the magnetic and electric fields are referred to as impedances of proper surface harmonics. Then the condition of zero scattering is expressed in terms of these partial impedances. This result is illustrated by the example of a nonscattering elliptic cylinder, for which the conditions of zero scattering are calculated explicitly in terms of the Mathieu functions

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