Radiation and scattering from thin toroidally knotted wires

The electromagnetic radiation and scattering properties of thin knotted wir es are considered in this paper. A special class of knots, called torus kno ts, are introduced for the purpose of this investigation. The parameterizat ions available for torus knots are used in conjunction with Maxwell's equat ions to formulate useful mathematical representations for the fields radiat ed by these knots. These representations are then used to derive simple clo sed form far-field expressions for electrically small torus knots, The deri vation of a new electric field integral equation (EFIE) suitable for analys is of toroidally knotted wires is also outlined in this paper. Finally, it is demonstrated that the well-known expressions for the electromagnetic fie lds radiated by a circular loop antenna (canonical unknot) may be obtained as degenerate forms of the more general torus knot field representations.