Dispersion Analysis of Perpendicular Modes Using a Hybrid Two-Trace Two-Dimensional (2T2D) Smart Error Sum

Using linear dichroism theory, one would assume that a z-cut of a uniaxial crystal is equivalent to an x-cut to determine the perpendicular component of the dielectric tensor and the corresponding oscillator parameters. However, Fresnel's equations show that the effect of interfaces in the form of the continuity relations of the different components of the electric field must be considered. A consequence of the continuity relations is that perpendicular modes increase less significantly in strength with increasing angle of incidence than expected. This is a consequence of the fact that it is the inverse of the perpendicular component of the dielectric function that increasingly becomes important with a growing angle of incidence. An inverse dielectric function, however, has typically much smaller values than the dielectric function. An additional consequence is that perpendicular modes are blueshifted and coupled in such a way that oscillator strength is transferred to the higher wavenumber mode. Thus, the spectral signatures of perpendicular modes are often weak and masked by the parallel modes when two modes overlap. Accordingly, to enable dispersion analysis, it is suggested to use a hybrid of the conventional residual sum of squares and the two-trace two-dimensional (2T2D) smart error sum, which can correct systematic multiplicable errors in the experimental spectrum. As demonstrated for fresnoite (Ba₂TiSi₂O₈), this is an important step toward determining the perpendicular component of the dielectric tensor and the corresponding oscillator parameters using dispersion analysis, since asynchronous 2T2D correlation spectra are, in particular, sensitive to perpendicular modes.