Complementary spherical surface screens

Abstract

Ideally conducting spherical screens (SS) are investigated in this work. Boundary conditions on the surface of the field inside the sphere and outside it give relations connecting the elements of the scattering matrix (SM) of SS. These relations make it possible to express 4 submatrices of the SS SM in terms of one submatrix. The problem of the relationship between the characteristics of additional SS is considered. This problem is an analogue of Babinet's problem on additional flat screens. Combining additional flat screens forms a perfectly conducting plane, and combining additional SS gives a perfectly conducting sphere. When establishing the relationship of the characteristics of additional SS, they are considered, on the one hand, as a system of two bodies. On the other hand, this system forms a perfectly conducting sphere, the SM of which is diagonal. Equating the SM of the system with the SM of an ideally conducting sphere gives the sought relationship between the SMs of additional SS. The results of numerical verification of the relationships for the SM of additional SS are presented. In numerical calculations, the dimensions of the SS SM, which are infinite in the general case, have to be limited, this leads to an error. It is shown that with an increase in the SM dimension, the error decreases, and the elements of the resulting matrix approach those of the SM of an ideally conducting sphere. This confirms the validity of the relations for the SM of additional SS. The interrelation of characteristics of additional SS obtained in this work is analogous to the Babinet principle for additional flat screens. We believe that it will turn out to be just as popular and useful in calculating spherical screens and antennas, as Babinet's principle for flat screens and flat antennas.