On electromagnetic waves in isotropic media with dielectric relaxation

In some previous papers one of us discussed dielectric relaxation phenomena from the point of view of nonequilibrium thermodynamics. If the theory is linearized one may derive a dynamical constitutive equation (relaxation equation) which has the form of a linear relation among the electric field E, the polarization P, the first derivatives with respect to time of E and P and the second derivative with respect to time of P. The Debye equation for dielectric relaxation in polar liquids and the De Groot-Mazur equation (obtained by these authors with the aid of methods which are also based on nonequilibrium thermodynamics) are special cases of the more general equation of which the structure has been described above. It is the purpose of the present paper to investigate the propagation and damping of electromagnetic waves. We consider the case in which the dielectric relaxation may be described by the above mentioned relaxation equation derived by one of us, the case in which the Debye equation may be used and the case in which one may apply the De Groot-Mazur equation. We derive solutions of the relaxation equations which also satisfy Maxwell's equations. We limit ourselves to plane waves of a single frequency in isotropic homogeneous linear media with vanishing electric conductivity. It is also assumed that the media are at rest. From thermodynamic arguments several inequalities are derived for the coefficients which occur in the relaxation equations. Explicit expressions are given for the complex wave vector, the complex dielectric permeability and for the phase velocity of the waves. All these quantities are functions of the frequency ¿ of the waves. For ¿¿0 the complex permeability e(compl) ¿ e(eq) where e(eq) is the equilibrium value of the permeability for static fields. If ¿¿8 we find e(compl) ¿ 1 except for the case of the Debye equation. This is due to the fact that a part of the polarization changes in a reversible way in media for which the Debye equation holds.