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Peters, Elisabeth (2011): Experimental and theoretical investigation of direct frequency comb spectroscopy. Dissertation, LMU München: Faculty of Physics
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Abstract

This thesis reports on theoretical and experimental examination of two-photon direct frequency comb spectroscopy (DFCS) using atomic two-level systems. This method is a very promising tool to extend optical spectroscopy into the short wavelength region where only few cw laser sources exist. The high peak intensities of pulsed lasers facilitate efficient nonlinear conversion into frequency regions which are so far unexplored, for example by high harmonic generation (HHG). DFCS is based on theoretical work in the 1970s which showed that a pulse train of a mode-locked laser drives a two-photon transition as efficient as a cw laser of same average power. Thereby the effective line width is determined by the narrow width of a single comb mode rather than by the spectral width of a single pulse. In this way a frequency comb combines the spectral purity of a cw laser with the high peak intensity of a pulsed laser. To demonstrate the capability of a nonlinearly converted frequency comb for DFCS, the absolute frequency of a two-photon transition in $^{24}$Mg at 431~nm was measured in a first experiment. The accuracies of the values could be improved by more than two orders of magnitude with respect to previously reported values. Furthermore two crucial effects which affect the transition rates were analyzed quantitatively for the first time: the impact of a linear chirp and non-centered spectral envelope on the spectroscopy. In general the pulses of a nonlinear converted frequency comb are not bandwidth limited leading to a partially destructive pairwise addition of modes. To describe the impact of a linear chirp a theoretical model was developed and verified experimentally using two-photon spectroscopy on cesium. Moreover, theory and experiment have shown a Gaussian decrease in the transition rate with increasing detuning of the laser spectrum. %Another important aspect is the centering of the laser spectrum with respect to the atomic transition. Theory and experiment show here a Gaussian decrease in the transition rate with increasing detuning. Finally the progress of $1S - 3S$ spectroscopy in hydrogen is presented. This transition is a promising candidate for a test of bound state quantum electrodynamics. Using cw lasers the required wavelength of 205~nm is hard to generate, making this transition to an eligible system for DFCS. Beside the experimental achievements also the lessons learned from Cs and Mg spectroscopy and their consequences for the H spectroscopy are discussed. In the scope of this work a frequency quadrupled laser system was extended and improved, providing ps frequency combs of high average power and good beam profile at 820~nm, 410~nm and 205~nm. An overall output power of max. 100~mW is now available at 205~nm, the up to date highest power generated by SHG. Moreover for H spectroscopy a new spectrometer was designed and built.