The experimental set-valued index of refraction of dielectric and anelastic media

Abstract

The dielectric parameter, in the generalised Debye form, of all studied substances (Cole and Cole, 1941) contains a rational power of the imaginary frequency which implies that the index of refraction is a multivalued function of the frequency; the same property, concerning the stress strain relation, also applies to anelastic media (Bagley and Torvik, 1983a,b). The multivalued index of refraction implies then that the free modes of dielectric and anelastic media are split into a number of modes which depend on the exponent of the imaginary frequency. In order to estimate if it is possible to observe this splitting, this note computes the parameters appearing in the generalised Debye form of the dielectric parameters of many substances and also the complex anelastic parameter of an anelastic medium. The analysis of the data indicates that, depending on the accuracy of the experimental data, with few exceptions, the splitting is observable.