B=μH+x (35.13b) where x is the chiral parameter. Media characterized by the constitutive relations, Eqs. (35. 12)and(3513),are Media in motion were the first bianisotropic media to receive attention in electromagnetic theory. In 1888 Roentgen discovered that a moving dielectric becomes magnetized when it is placed in an electric field. In 1905 Wilson showed that a dielectric in a uniform magnetic field becomes electrically polarized. Almost any medium becomes bianisotropic when it is in motion The bianisotropic description of material has fundamental importance from the point of view of relativity The principle of relativity postulates that all physical laws of nature must be characterized by mathematical equations that are form-invariant from one observer to the other. For electromagnetic theory, the Maxwell quations are form-invariant with respect to all observers, although the numerical values of the field quantities may vary from one observer to another. The constitutive relations are form-invariant when they are written in bianisotropic form. Constitutive matrices Constitutive relations in the most general form can be written as = P.e+L (35.14a) M·E+Q·cB (35.14b) where c=3x 10 m/s is the velocity of light in vacuum, and P, Q, L, and M are all 3 x 3 matrices. Their elements are called constitutive parameters. In the definition of the constitutive relations, the constitutive matrices L and M relate electric and magnetic fields. When L and M are not identically zero, the medium is bianisotropic. When there is no coupling between electric and magnetic fields, L= M=0 and the medium is anisotropic. For an anisotropic medium, if P=ceI and=Q=(1/qu)I with I denoting the 3 x 3 unit matrix, the medium is isotropic. The reason that we write constitutive relations in the present form is based on relativistic considerations. First, the fields E and c B form a single tensor in four-dimensional space, and so do (D and H. Second, constitutive relations written in the form Eq.(35. 14)are Lorentz-covariant. Equation(35. 14)can be rewritten in the form H (35.15a) and C is a6x6 constitutive matrix: (35.15b) which has the dimension of admittance c 2000 by CRC Press LLC© 2000 by CRC Press LLC (35.13a) (35.13b) where c is the chiral parameter. Media characterized by the constitutive relations, Eqs. (35.12) and (35.13), are biisotropic media. Media in motion were the first bianisotropic media to receive attention in electromagnetic theory. In 1888, Roentgen discovered that a moving dielectric becomes magnetized when it is placed in an electric field. In 1905, Wilson showed that a moving dielectric in a uniform magnetic field becomes electrically polarized. Almost any medium becomes bianisotropic when it is in motion. The bianisotropic description of material has fundamental importance from the point of view of relativity. The principle of relativity postulates that all physical laws of nature must be characterized by mathematical equations that are form-invariant from one observer to the other. For electromagnetic theory, the Maxwell equations are form-invariant with respect to all observers, although the numerical values of the field quantities may vary from one observer to another. The constitutive relations are form-invariant when they are written in bianisotropic form. Constitutive Matrices Constitutive relations in the most general form can be written as (35.14a) (35.14b) where c = 3 ¥ 108 m/s is the velocity of light in vacuum, and , , , and are all 3 ¥ 3 matrices. Their elements are called constitutive parameters. In the definition of the constitutive relations, the constitutive matrices an d relate electric and magnetic fields. When an d are not identically zero, the medium is bianisotropic. When there is no coupling between electric and magnetic fields, = = 0 and the medium is anisotropic. For an anisotropic medium, if = ce and =Q = (1/cm) with denoting the 3 ¥ 3 unit matrix, the medium is isotropic. The reason that we write constitutive relations in the present form is based on relativistic considerations. First, the fields and c form a single tensor in four-dimensional space, and so do c and . Second, constitutive relations written in the form Eq. (35.14) are Lorentz-covariant. Equation (35.14) can be rewritten in the form (35.15a) and is a 6 ¥ 6 constitutive matrix: (35.15b) which has the dimension of admittance. D E H t = e – c ¶ ¶ B H E t = + m c ¶ ¶ cD P E L cB = × +× H M E Q cB = ×+× P Q L M L M L M L M P I I I E – B – D H cD H C E cB È Î Í ˘ ˚ ˙ = × È Î Í ˘ ˚ ˙ C C P L M Q = È Î Í Í ˘ ˚ ˙ ˙