or isotropic or anisotropic media, the constitutive relations relate the two electric field vectors and the two magnetic field vectors by either a scalar or a tensor. Such media become polarized when placed in an electric field and become magnetized when placed in a magnetic field. A bianisotropic medium provides the cross oupling between the electric and magnetic fields. The constitutive relations for a bianisotropic medium can be written as D=E·E H E+∈·H (35.10b) When placed in an electric or a magnetic field, a bianisotropic medium becomes both polarized and magnetized. Magnetoelectric materials, theoretically predicted by Dzyaloshinskii and by Landau and Lifshitz, were observed experimentally in 1960 by Astrov in antiferromagnetic chromium oxide. The constitutive relations that Dzyaloshinskii proposed for chromium oxide have the following form D=0∈0·E+050·H 351la) 00 B=050·E+|0u0·H (35.1b) 00μ effect. Rado proved that the effect is not restricted to antiferromagnetics fe an exhibit the magnetoelectric It was then shown by Indenbom and by Birss that 58 magnetic crystal classes magnetic gallium iron oxide is also magnetoelectric Biisotropic Media In 1948, the gyrator was introduced by Tellegen as a new element, in addition to the resistor, the capacitor, the inductor, and the ideal transformer, for describing a network. To realize his new network element, Tellegen conceived of a medium possessing constitutive relations of the form D=∈E+H (35.12a) B= 5E+HH where $/ue is nearly equal to 1. Tellegen considered that the model of the medium had elements possessin permanent electric and magnetic dipoles parallel or antiparallel to each other, so that an applied electric field that aligns the electric dipoles simultaneously aligns the magnetic dipoles, and a magnetic field that aligns the magnetic dipoles simultaneously aligns the electric dipoles. Tellegen also wrote general constitutive relations Eq(35.10)and examined the symmetry properties by energy conservation Chiral media, which include many classes of sugar solutions, amino acids, DNA, and natural substances, have the following con c 2000 by CRC Press LLC© 2000 by CRC Press LLC For isotropic or anisotropic media, the constitutive relations relate the two electric field vectors and the two magnetic field vectors by either a scalar or a tensor. Such media become polarized when placed in an electric field and become magnetized when placed in a magnetic field. A bianisotropic medium provides the cross coupling between the electric and magnetic fields. The constitutive relations for a bianisotropic medium can be written as (35.10a) (35.10b) When placed in an electric or a magnetic field, a bianisotropic medium becomes both polarized and magnetized. Magnetoelectric materials, theoretically predicted by Dzyaloshinskii and by Landau and Lifshitz, were observed experimentally in 1960 by Astrov in antiferromagnetic chromium oxide. The constitutive relations that Dzyaloshinskii proposed for chromium oxide have the following form: (35.11a) (35.11b) It was then shown by Indenbom and by Birss that 58 magnetic crystal classes can exhibit the magnetoelectric effect. Rado proved that the effect is not restricted to antiferromagnetics; ferromagnetic gallium iron oxide is also magnetoelectric. Biisotropic Media In 1948, the gyrator was introduced by Tellegen as a new element, in addition to the resistor, the capacitor, the inductor, and the ideal transformer, for describing a network. To realize his new network element, Tellegen conceived of a medium possessing constitutive relations of the form (35.12a) (35.12b) where x2 /me is nearly equal to 1. Tellegen considered that the model of the medium had elements possessing permanent electric and magnetic dipoles parallel or antiparallel to each other, so that an applied electric field that aligns the electric dipoles simultaneously aligns the magnetic dipoles, and a magnetic field that aligns the magnetic dipoles simultaneously aligns the electric dipoles. Tellegen also wrote general constitutive relations Eq. (35.10) and examined the symmetry properties by energy conservation. Chiral media, which include many classes of sugar solutions, amino acids, DNA, and natural substances, have the following constitutive relations D EH =× +× e x B EH = × +× z e DEH BEH z z z z = È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ × + È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ × = È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ × + È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ × e e e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x x x x x x m m m D EH = + e x B EH = +m x