Self-consistent task for radiation from a hole in a conducting screen to an open half-space

The homogeneous boundary-value problem of radiation from a circular hole in an ideally conducting infinite flat screen has been investigated. The formulation of a self-consistent radiation problem has been considered, on the basis of which the problem of synthesizing of sources creating a given radiation field can be formulated. The results of solving the self-consistent radiation problem obtained by the collocation method have been presented. The problem has been solved in various approximations for the case of a asymmetric field, when the collocation nodes are located along one ray. As a result of the calculation it has been obtained that for all field components, with the exception of Eρ, the qualitative dependence of the components on the radial coordinate remains independent on the number of collocation nodes. Starting with five collocation nodes, the qualitative dependence of the component Eρ on the radial remains unchanged, which indicates a good internal convergence of the solution of the problem.