Dispersion relations for liquid crystals using the anisotropic Lorentz model with geometrical effects

The dispersion relations for the refraction indices and extinction coefficients of an ordered system of anisotropic molecules are derived, taking into account absorption near the resonance frequencies and the molecular geometrical form factor. The derivation is based on a combination of the anisotropic Lorentz oscillator dispersion model and the generalized Lorentz-Lorentz (LL) relationship. This relationship is shown to be consistent with the isotropic limit. The geometrical form tensor (GFT) distinguishes this relationship from the LL and the Calusius-Mossotti equations valid for isotropic media. Far from the absorption bands the dispersion relationships are shown to converge to those of Sellmeier-type dispersion relationships for transparent dielectrics that can be expanded into generalized Cauchy-type series. The principal values of the GFT are shown to cause a red shift to the resonance wavelengths that can be found from measurements in the disordered phase. Experimental data are presented based on published works as well as measurements using a spectroscopic retardation technique, and excellent agreement is obtained with the theoretical calculations on several LC materials.