A Geometrical Approach to Duality Transformations for Tellegen Media

• Published in: IEEE transactions on microwave theory and techniques 2014-07, Vol.62 (7), p.1417-1428
• Main Authors: Prudencio, Filipa R., Matos, Sergio A., Paiva, Carlos R.
• Format: Article
• Language: English
• Subjects: Applied sciences; Biisotropic media; Circuit properties; Conformal mapping; Couplings; duality transformation; Electric, optical and optoelectronic circuits; Electromagnetics; Electronics; Exact sciences and technology; Isotropic media; Magnetoelectric effects; Materials; Media; Microwave circuits, microwave integrated circuits, microwave transmission lines, submillimeter wave circuits; Microwaves; Photonic crystals; Refractive index; stereographic projection; Tellegen media; Transformations; Transformations (mathematics); Waveguides
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2014.2326108

Duality transformations are of key importance in the study of Tellegen (i.e., achiral and nonreciprocal biisotropic) media: they often can reduce electromagnetic problems with both Tellegen media and simple isotropic media (SIMs), to simpler problems just with SIMs. Here, we generalize known results and derive the most general classes of Tellegen media that can be reduced, under the same duality transformation, to SIMs. Furthermore, it is shown that a family of isorefractive Tellegen media can be completely mapped onto the Riemann sphere where duality transformations are conformal mappings. Depending on their geometrical action in the Riemann sphere the duality transformations are then classified as: 1) generalized rotations; 2) Lorentz boosts; or 3) Galilean boosts. Applications include a wide range of structures containing Tellegen media: from (open and closed) waveguides to photonic crystals.