Generalized dispersion analysis of arbitrarily cut crystals with unknown orientation
To perform generalized dispersion analysis of arbitrarily cut crystals with a priori unknown orientation an appropriate set of spectra and evaluation scheme to reproduce the measured spectra is necessary. In this thesis a detailed procedure that respects the characteristic symmetries of each crystal system to perform generalized dispersion analysis and to calculate the dielectric tensor function is worked out. It is now no longer necessary to use the restriction of principal orientation as measurements on any crystal face of any orientation can be used as input for generalized dispersion analysis since the developed formalism is independent on the crystal symmetry. The measurement scheme is kept relatively simple, except for a (FT)IR-spectrometer and the polarizers no special equipment is necessary. The optimization routine is written in Matlab runs on a standard PC. The sample preparation comprises the optical polishing of three different crystal faces that are not coplanar to each other. The cut of the crystal into a cube is not mandatory, yet it facilitates the subsequent calculations. The minimal size of the crystal is restricted by the sample holder and the ability of a decent orientation of the crystal in the spectrometer. If the recorded spectra are desired to be reproducible with other samples of the same crystal it is advisable to determine the Miller indices of the crystal faces first. The most important step of the generalized dispersion analysis is a basis transformation from the laboratory frame to the one representing the principal axes of the crystal itself. The transformation is performed by applying an Euler matrix with three rotation angles to the dielectric tensor function. In this way, from enough measurements, the oscillator parameters can be determined and the dielectric tensor function in all directions can be calculated. The necessary number of spectra to gain reliable information about the dispersion parameters was investigated.