Transition Properties of f-electrons in Rare-earth Optical Materials
Abstract: The main purpose of this thesis is to theoretically study energy levels and intra-electronic transition intensities for various f-electron systems. The f-f electronic dipole transitions are parity-forbidden for a free ion but become non-zero when the ion is subject to a crystal-field. This is commonly described within the framework of Judd-Ofelt theory which accounts for the mixing of odd parity into the wave-functions.Some refinements and quantitative studies have been made by applying many-body perturbation theory, or the perturbed functions approach, to obtain effective dipole operators due to correlation, spin-orbit and higher order crystal-field effects not included in Judd-Ofelt theory. A software for the computation of f-electron multiplets and Stark levels was implemented and published as well.The single- and pair-functions used for the evaluation of intensity parameters were obtained by solving various inhomogeneous Schrödinger equations. The wave-functions and energies obtained by diagonalizing an effective Hamiltonian have been used together with the oscillator strength methods to simulate absorption spectrum. Consistent crystal-field parameters applied in some of the papers were obtained by fitting crystal polarizabilities to reflect the experimental Stark levels. The same crystal model was then used to generate odd crystal field parameters needed for the f-f transition intensities. The total effect of these refinements are spectral features that usually agree well with experimental findings. Some of these methods have also been applied and seen to be quite useful for the understanding of optical fiber amplifiers frequently used in today's optical networks.Finally, a finite-difference approach was applied for the Helium iso-electronic sequence. The exact wave-function was expanded in a sum of partial waves, and accurate ground- and excited state energies were obtained by using the iterative Arnoldi approach.
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