Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 159

The magnetoelectric materials are general bianisotropic electromagnetic materials with cross‐coupling of electric and magnetic fields. These materials have anisotropy for both the permittivity and permeability with additional cross‐coupling of the electric and magnetic field. In such materials, the electric flux density vector and also magnetic flux density depends on both applied and . It shows that in the bianisotropic materials, the fields not only generate an electric polarization but also create the magnetic polarization, i.e. magnetization. Similarly, fields applied to such materials create both magnetization and electric polarization. The constitutive relation relating four flux and field vectors for a linear magneto‐electric medium is expressed as follows [B.21–B.23]:

(4.2.14)

The above given four material parameter tensors , , , and describe the bianisotropic magnetoelectric materials. The tensors and are usual permittivity and permeability tensors, whereas and are magneto‐electric coupling tensors. In general, 36 complex material parameters are required to characterize bianisotropic materials. However, the material parameter matrix could be diagonalized. So, for the uniaxial bianisotropic, i.e. the magneto‐electric, materials, constitutive relations are written as follows [B.15, B.21]:

(4.2.15)

In the absence of cross‐coupling, i.e. for , the bianisotropic medium is reduced to an MD medium. Figure (4.5a) shows groups of general bianisotropic medium‐ isotropic, bi‐isotropic, biaxial anisotropic, and bianisotropic media [B.25]. Two cases have already been discussed.

The bi‐isotropic materials are isotropic materials also showing cross‐coupling of electric and magnetic fields. However, Fig. (4.5b) shows that the general bi‐isotropic medium has special forms – isotropic, Pasture, Tellegen, and bi‐isotropic. For general bi‐isotropic medium, the medium tensors are reduced to scalars, and the constitutive relations given by equation (4.2.14) are reduced to the following simpler form [B.23]:

(4.2.16)

where ξ²/με is nearly unity. The magnetoelectric coupling parameters ξ and ζ have two components: the chirality parameter κ (kappa) and the cross‐coupling parameter χ (chi). The chirality parameter κ measures the degree of the handedness of the medium. The parameter χ is due to the cross‐coupling of fields. It decides the reciprocity (χ = 0) and nonreciprocity (χ ≠ 0) of the medium, giving the reciprocal and nonreciprocal material medium, respectively. In absence of cross‐coupling, i.e. χ = 0, the parameters ξ and ζ are reduced to imaginary quantities, and the bi‐isotropic medium is reduced to a nonchiral simple isotropic medium for κ = 0 and to a chiral medium for κ ≠ 0. It is also known as Pasteur medium. It supports the left‐hand and right‐hand circularly polarized waves as the normal modes of propagation. It is a reciprocal medium. For κ = 0, χ ≠ 0 another medium, called Tellengen medium, is obtained. It is a nonreciprocal medium. The general bi‐isotropic medium has χ ≠ 0, κ ≠ 0. It is a nonreciprocal medium.

The gyrotropic medium and bianisotropic medium support left‐hand and right‐hand circularly polarized EM‐waves. However, there is a difference. The gyrotropic medium supports the Faraday rotation, i.e. rotation of linearly polarized wave while propagating in the medium, whereas bianisotropic medium does not support it [B.21].