On metallic dispersion in the near infra-red

Kronig has recently attempted to derive a quantum theory of dispersion in metallic conductors, using as a basis the Bloch theory of the metallic state; a more rigorous formulation of the same line of thought has been given by Fujioka. In particular, Kronig has developed explicit formulæ for the coefficients of reflection and extinction and for the index of refraction of a metal in the so-called "transitional" region of the spectrum, where the period of the incident radiation is comparable with the mean time between two collisions of an electron with the metallic lattice. In order to obtain reasonable agreement with the room-temperature measurements of Försterling and Fréedericksz in the nera infra-red, it is necessary to assume a value for the electrical conductivity of the metal which is very much less than the value obtained by direct measurement. Kronig has suggested that this result may be due to the fact that the optical constants depend upon the properties of a thin surface layer of the metal, in which layer it is possible that the conductivity is diminished on account of boundary imperfections of the metallic lattice. It has already been shown, however, that even though this additional hypothesis be allowed, the formulæ in question are not consonant with the results of recent measurements on the high-temperature emissivities of metals in the near infra-red. the inadequacies of the quantum theory of the transitional region are more readily appreciated when it is realized that the formulæ for the optical constants derived therefrom are identical in scope with the formulæ of the dispersion theory of Drude, published in 1900. Kronig himself mentions that his formulæ tend, in the limit of zero frequency, to the classical, phenomenological relations which Drude derived in 1894; but it does not appear to have been pointed out hitherto that the Kronig formulæ are, in fact,identical with, and not merely asymptotic to, those of the later dispersion theory of Drude.