Efficient MoM analysis of polarization selective surfaces using trefoil knot arrays

The electromagnetic properties of (p,q) torus knots consisting of perfectly conducting thin wires were investigated previously. The (2,3) or trefoil knot has the unique property that its forward scattering characteristics depend on the handedness of an incident circularly polarized wave. This property is conserved when placing the knots in an array. We describe an efficient method of moments (MoM) approach that is especially suited for the analysis of arrays comprised of these knots. In the MoM, solving the linear system of equations is the most time consuming part when the number of unknowns becomes large. For certain classes of problems, the use of preconditioning techniques allows us to reduce the solution time considerably. Array-type of structures can be efficiently analyzed when using the block-LU preconditioner, as outlined. Also, we present the spectral radius as a criterion for assessing the convergence of the method. Finally, we apply the block-LU method to investigate the electromagnetic scattering properties of a medium sized array of trefoil knots.