On the Volume-Dependence of the Index of Refraction from the Viewpoint of the Complex Dielectric Function and the Kramers−Kronig Relation

Abstract

How indices of refraction n(ω) of insulating solids are affected by the volume dilution of an optical entity and the mixing of different, noninteracting simple solid components was examined on the basis of the dielectric function ε₁(ω) + iε₂(ω). For closely related insulating solids with an identical composition and the formula unit volume V, the relation [ε₁(ω) − 1]V = constant was found by combining the relation ε₂(ω)V = constant with the Kramers−Kronig relation. This relation becomes [n²(ω) − 1]V = constant for the index of refraction n(ω) determined for the incident light with energy less than the band gap (i.e., ℏω < E_g). For a narrow range of change in the formula unit volume, the latter relation is well approximated by a linear relation between n and 1/V.