The electromagnetic fields of elliptical torus knots

The electromagnetic radiation and scattering properties of thin perfectly conducting knotted wires are investigated. A particular class of knots, which we call elliptical torus knots, are introduced for the purposes of this investigation. These knots derive their name from the fact that they may be constructed on the surface of a virtual torus which has an elliptical cross section. The parameterizations which describe the curves of these knots are more general than any which have been considered in previous studies and, therefore, provide more flexibility in the design of knotted wire scatterers. A moment method technique is applied to model the backscattering from an elliptical trefoil knot as a function of frequency, polarization, and incidence angle.