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Abstract

The ultra-high precision spectroscopy of highly charged ions (HCI) paves way for a new
atomic clock standard. To match the larger transition energies in HCI, a near-infrared
(NIR) frequency comb operating at 100 MHz is extended into the extreme ultraviolet
(XUV) regime via high harmonic generation (HHG) inside a femtosecond-enhancement
cavity (fsEC). Large HHG yield is favored by correct coupling of the incident beam to
the desired Gaussian mode of the fsEC. Optimal alignment induces a small focus size,
reduces residue plasma between pulses, and allows for the desired focus intensity of
up to ~10¹⁴ W=cm². Manual mode optimization can be time consuming, prone to error,
and requires far off-resonance operation. This thesis concentrates on the automatic
mode optimization. A hill climb (HC) algorithm is adapted for close to resonance operation
and demonstrates intensity gain of up to 300% in less than 100 iterations, while
correcting for resonance shifts and successfully depleting higher order transverse electromagnetic
modes (TEM) in favor of the desired Gaussian mode.