Determination of the complex dielectric tensor of triclinic crystals: theory

Abstract

Theoretical expressions are derived for normal-incidence reflectances at three faces of a cube, cut from a triclinic crystal, for any desired orientation of crystallographic axes relative to the cube edges. The reflectances are expressed in terms of the components of the complex dielectric tensor of the crystal referred to the cube axes. Also presented is a suitable dispersion formula in which each component of the dielectric tensor, referred to the fixed cube axes, is given as a sum of the contributions of all crystal oscillators, each multiplied by products of the direction cosines of the oscillator axis relative to the cube axes. A least-squares-fitting procedure, based on the variation of the oscillator parameters and the direction cosines, can be used to obtain the best match of the measured and calculated reflectances, over a wide frequency range, and thereby to determine the dielectric tensor as a function of frequency.