Affiliated with the
Communication & Space
Sciences Laboratory

Novel Electromagnetic Metamaterials

Scattering from Torus Knots

Two Views of a (2, 3)-Torus Knot,
which is Commonly Referred to as a Trefoil


..: References :..

1-) Radiation and Scattering from Thin Toroidally Knotted Wires
by Douglas H. Werner

ABSTRACT: 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 in this paper. 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.




2-) The Electromagnetic Fields of Elliptical Torus Knots
by Douglas H. Werner, D. M. Jones, and P. L. Werner

ABSTRACT: The electromagnetic radiation and scattering properties of thin perfectly conducting knotted wires are investigated in this paper. 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.




3-) Electromagnetic Radiation and Scattering from Elliptical Torus Knots
by Douglas H. Werner
1998 IEEE Antennas and Propagation Society International Symposium, Atlanta, Georgia, June 21-26.




4-) Polarization Selective Surfaces Composed of Trefoil Knot Elements
by J. v. Hagen, D. H. Werner, and R. Mittra

ABSTRACT: In this paper, we demonstrate that the trefoil knot has the unique property that its forward scattering for circularly polarized waves exhibits a strong dependence on the handedness of the polarization. Both a single knot element as well as an array of these knots show this property which could be used in a polarization-selective surface PSS.
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5-) Efficient MoM Analysis of Polarization Selective Surfaces Using Trefoil Knot Arrays
by J. v. Hagen, R. Mittra, D. H. Werner
1999 IEEE Antennas and Propagation Society International Symposium, Orlando, Florida, July 11-16.




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