Lorentz—Lorenz and Sellmeier Formulas in Irregular Gases

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Abstract
The integral equation expressing the condition of dynamical equilibrium of dipoles in an applied electromagnetic field is solved to determine the index of refraction for the ensemble-average wave in a media in which the polarizability varies irregularly. The solution closely follows that employed in the usual derivation of the Ewald—Oseen theorem for isotropic media. A Lorentz—Lorenz formula, modified by the appearance of an additional term, is determined. The additional term is real when the scale length of the irregularities is small compared to the wavelength. For larger irregularities, however, the correction leads to a complex index of refraction, expressing the attenuation due to scattering. Applying the concept of the depolarizing effect of electron—ion collisions, these results are extended to the case of an ionized gas. In this latter instance, a similar modification of the Sellmeier formula for the index of refraction is determined. Explicit formulas are given for the case of irregularities with scale large compared to a wavelength.

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