Electromagnetic radiation and scattering from elliptical torus knots

Abstract

A mathematically rigorous approach for combining knot theory with Maxwell's theory of electromagnetism was reported by Werner (see IEEE Antennas and Propagation Society International Symposium Digest, vol.2, p.1468-71, Montreal, Canada, 1997). This analysis methodology was initially used to investigate the electromagnetic characteristics of a special class of knots, known as (p,q)-torus knots. A convenient set of parametric representations was developed by Werner for this particular family of knots by making use of the fact that they may be constructed on the surface of a standard circular torus in R/sup 3/. These parameterizations were then used in combination with Maxwell's equations to derive vector potential and field expressions which describe the radiation and scattering of electromagnetic waves from circular (p,q)-torus knots.