Effective refractive index of a two-dimensional polycrystal

A relation of the effective refractive index $n^*=\sqrt{n_1n_2}$ of a two-dimensional polycrystalline dielectric film in the transparency region to the refractive indices $n_1$ and $n_2$ of crystallites at the positions of axes 1 and 2, respectively, of refraction ellipsoids of the crystallites in the plane of the film has been obtained. This relation and the relation $L^*=(L_1+L_2)/2$ between the components of the Lorentz tensors for the film and crystallites have been confirmed by comparison with experimental data for conjugate-polymer films with uniaxial domains.