Convergence phenomenon in the solution of dichroic scattering problems by Galerkin's method

Abstract

The convergence problem that arises when the scattering problem of dichroic surfaces is solved numerically by means of Galerkin's method and Floquet's theorem is investigated. A theoretical discussion is outlined showing that a truncation of the infinite Floquet spectrum is actually equivalent to modifying the used basis functions. Examples of modified basis functions due to different Floquet-mode truncations and the effect on the numerical results are demonstrated for the particular cases of arrays of thin dipoles and crossed dipoles. Some useful truncation rules are also presented, and the theories are verified by comparing predicted values with experimental results obtained by waveguide simulator measurements