Example of bianisotropic electromagnetic crystals: The spiral medium P. A. Belov, 1,2 C. R. Simovski, 1,2 and S. A. Tretyakov 1 1 Radio Laboratory, Helsinki University of Technology, P.O. Box 3000, FIN-02015 HUT, Finland 2 Physics Department, St. Petersburg Institute of Fine Mechanics and Optics, Sablinskaya 14, 197101, St. Petersburg, Russia Received 11 July 2002; published 23 May 2003 In this paper the electromagnetic properties of bianisotropic electromagnetic crystals are studied. The crys- tals are assumed to be rectangular lattices of perfectly conducting helicoidal spirals. The analytical theory of dispersion and plane-wave reflection refers to the case when the spiral step and the radius are small compared to the wavelengths in the host medium. The periods of the lattice can be arbitrary. Explicit closed-form expressions are derived for the effective material parameters of the medium in the low-frequency regime. The medium eigenmodes are elliptically polarized, and one of them propagates without interaction with the lattice. As to the other eigenmode, the lattice has strong spatial dispersion even at extremely low frequencies in the direction along the spiral axes. Numerical examples are given. An analogy between the spiral medium and the medium of loaded wires is indicated. DOI: 10.1103/PhysRevE.67.056622 PACS numbers: 41.20.Jb, 42.70.Qs, 77.22.Ch, 77.84.Lf I. INTRODUCTION Electromagnetic and photonic band-gap structures attract a lot of attention in view of many potential applications e.g., 1. Usually, these artificial media are formed as periodic arrangements of dielectric or conducting inclusions or voids in an isotropic matrix. The cell geometry is normally quite simple spheres, circular cylinders, etc.. We introduce the concept of bianisotropic or magnetoelectric electromag- netic crystals. In these structures, as in quasihomogeneous bianisotropic media, electric and magnetic fields are coupled through the medium response 2. In other words, electric fields cause both electric and magnetic polarizations, and also magnetic fields not only magnetize but also electrically polarize the medium. Obviously, more complicated proper- ties of the material allow more possibilities in the design of microwave or optical devices. The well-known optical activity phenomenon 3 was studied in composite chiral photonic crystals with a helical lattice of dielectric spheres in 4, using numerical modeling. Three-dimensional lattices sc, fcc, and bcc of dielectric spiral-shaped elements were considered in 5, and it was shown that the band-gap structure depends on the geometry of the elements, but not only on the lattice geometry. Micro- wave magnetoelectric coupling in media can be due to non- reciprocal properties of inclusions 3,6 or to the complicated geometrical structure of the medium 2. In this work we explore the second possibility and study a spiral medium,a periodic medium formed by long spiral ideally conducting inclusions helixes. The effective-medium regime of this medium was considered in 7. The special interest of the structure under consideration is based on its wide range of possible applications, beginning with the design of frequency and polarization filters and end- ing with the synthesis of high impedance surfaces in the microwave frequency region 8. To simplify the study with- out loss of general properties, we model helices as sets of connections of straight wires and coils, as depicted in Fig. 1, in the same manner as was done in 9. The same structure was also considered in 10 and its plasmonic behavior was revealed. In this paper we present an analytical model of a two- dimensional lattice of infinitely long and thin parallel per- fectly conducting helices. In this the structure the polariza- tions of the eigenwaves in the medium become elliptical due to bianisotropy effects. At the same time, these magnetoelec- tric coupling effects are combined with spatial dispersion effects as in electromagnetic or photonic crystals where the spatial resonances of the lattice determine the stop bands. Moreover, the helicoidal spirals have special resonant prop- erties the parallel resonance of the loop inductance and the interturn capacitance which lead to the resonant behavior of the whole medium at frequencies close to the helix indi- vidual resonance which is the antiresonance. The structure under consideration can potentially offer great opportunities for control of the dispersion properties of artificial materials, and it can possibly be used for prospective frequency and polarization filtering of the microwave signals. II. ANALYTICAL APPROACH Let the spiral medium be formed by a rectangular lattice of helicoidal spirals with periods a b , spiral pitch c, radius of a turn r, and radius of wires r 0 see Fig. 1. In this theory FIG. 1. Geometry of the spiral medium. PHYSICAL REVIEW E 67, 056622 2003 1063-651X/2003/675/0566226/$20.00 ©2003 The American Physical Society 67 056622-1 Reprinted with permission from P.A. Belov, C.R. Simovski, S.A. Tretyakov, Physical Review E 67, 056622 (2003). © 2003 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. 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