Radiation and scattering from thin toroidally knotted wires

The electromagnetic radiation and scattering properties of thin knotted wires are considered in this paper. A special class of knots, called torus knots, are introduced for the purpose of this investigation. The parameterizations available for torus knots are used in conjunction with Maxwell´s equations to formulate useful mathematical representations for the fields radiated by these knots. These representations are then used to derive simple closed form far-field expressions for electrically small torus knots. The derivation of a new electric field integral equation (EFIE) suitable for analysis of toroidally knotted wires is also outlined. Finally, it is demonstrated that the well-known expressions for the electromagnetic fields radiated by a circular loop antenna (canonical unknot) may be obtained as degenerate forms of the more general torus knot field representations