Note on Frequency Shifts in Dispersing Media

Abstract

The propagation of a light wave through a dispersing medium is discussed. The absorption frequencies of the medium are shown to be the absorption frequencies of the coupled system formed by molecules contained in a cavity elongated in the direction of the electric intensity of the incident wave. The cavity is supposed to contain a large number of molecules and yet to be small compared to the wave-length.The absorption bands of the coupled system are discussed. For tenuous media the shift is small and of the order of the Lorentz-Lorenz shift. The modification introduced by the quantum theory consists in replacing the classical $\frac{{e}^{2}}{8{\ensuremath{\pi}}^{2}m\ensuremath{\nu}}$ by ${|x(\mathrm{I}, \mathrm{II})|}^{2}$ where $x(\mathrm{I},\mathrm{II})$ is the unperturbed matrix element of the polarization in the fixed direction $X$, the normal state is I, the excited state II. In this approximation the shift is obtained by replacing the classical $e$ by Dennison's effective charge. For regular arrangements of molecules, no broadening due to coupling is expected.For dense media there are additional effects even to the first order. These are: (1) the electrostatic interaction of a molecule with its neighbours due to its excitation, (2) the effect of the finite space extension of the $u_{\mathrm{I}}^{*}{u}_{\mathrm{II}}$ charge distribution. A comparison of the measured shifts in liquid HCl and HBr with the extrapolation of the Lorentz-Lorenz formula modified by ${|x(\mathrm{I}, \mathrm{II})|}^{2}$ is made. The observed shift is much too large to be explained without taking into account effects (1), (2). Particle exchange has been neglected.