A complex plane analysis of dielectric response: Decomposition of ε_2 (ω) spectra into single lorentzian oscillators

In this thesis, a mathematical analysis of the dielectric function spectra for the dielectric crystals was performed within the framework of the linear optical dispersion theory. This analysis is a complex plane analysis. With this analysis, an analytical method was derived to separate the imaginary parts of dielectric functions into its fundamental components. The derived method is a method for seperating the spectra of dielectric functions into single Lorentzian oscilators. As it is known, the dielectric function, like other optical functions, is a complex function. A complex plane was formed using this feature of the dielectric function. While the real axis of the plane constructed from the real part of dielectric function, the imaginary axis is its imaginary part. In this plane, each loop of the function ε_2 (ε_1-1) which completed into a circle represents the linear optical response for a single Lorentzian oscillator. The resonance frequency, the energy, and the width and the half-width of abnormal dispersion of each Lorentzian oscillator can be calculated by analyzing the circles obtained for each loop. Using these calculated parameters, the probabilities of optical interband transitions can be calculated and their positions in the energy band diagram can be determined.