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Analysis of Tellegen H-Guides

Canto, João R. ; Paiva, C. R. ; Barbosa, A.

Analysis of Tellegen H-Guides, Proc IEEE AP-S/URSI International Symp., Charlston, United States, Vol. -, pp. - - -, June, 2009.

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Abstract
An isotropic nonreciprocal magnetoelectric metamaterial was suggested by Tellegen as early as 1948. An acceptable semi-microscopic picture of such a medium consists of
inclusions where a permanent electric dipole is tied – by a non-electromagnetic force – with a permanent magnetic dipole. The Tellegen parameter κ affects the phase of a propagating electric field and not its polarization, whereas the chiral parameter χ affects the polarization and not its phase. Furthermore, a linearly polarized plane wave propagating in a Tellegen media will present an angle between the electric and magnetic fields that differs from the right angle by ϑ , with sinϑ=κ εμ (I. V. Lindell et al., Electromagnetic Waves in Chiral and Bi-Isotropic Media, Artech House, Boston, 1994). Hence, Tellegen media can be used in the design of nonreciprocal devices for phase shifting and mode conversion. Although some claims that the so-called Post constraint would be violated by Tellegen media, it can be shown that «the Post constraint as a general dogma should be buried with all due honors» (F. W. Hehl and Yu. N. Obukhov, Phys. Lett. A, Vol. 334, Issue 4, pp. 249-259, January 2005). Although there is a
transformation that, for a sample of a uniform Tellegen material in free space, redefines fields so that the Tellegen material will look like a reciprocal isotropic medium, the surrounding free space will then look as a nonreciprocal Tellegen medium (A. Serdyukov
et al., Electromagnetics of Bi-anisotropic Materials: Theory and Applications, Gordon and Breach, Amsterdam, 2001). The influence of nonreciprocal bi-isotropic media on the propagation features of closed metallic waveguides, circular rods, and open slab waveguides has already been discussed in the literature (e.g., C. R. Paiva, A. L. Topa and A. M. Barbosa, Microwave and Opt.
Technol. Lett., Vol. 6, No. 3, pp. 182-185, March 1993). However, there is no closedform analytical solution to the problem of an H-guide containing Tellegen media due to the coupled equations that describe the transverse electromagnetic field. A full-wave
analysis of an H-guide containing chiral media has already been presented (A. L. Topa, C. R. Paiva and A. M. Barbosa, Proc. Conf. on Telecommunications – ConfTele, Peniche, Portugal, pp. 5-8, May 2007). However, as far as the authors are aware, no work
addressing H-Guides containing Tellegen media has yet been published. In this communication a rigorous analysis of a Tellegen H-guide will be presented. The approach is based on a transverse resonance method combined with a mode matching technique. The Bohren decomposition is used to obtain the modal equation of a parallelplate waveguide containing a Tellegen medium. Then, a mode matching approach is used to develop a full-wave analysis of the Tellegen H-guide. The guidance and leakage properties of the Tellegen H-guide are then analyzed and its potential applications are discussed.