A Coherent Frequency Comb in the Extreme Ultraviolet

In the course of this work, a system was designed and developed to
nonlinearily convert a femtosecond frequency comb laser into the
extreme ultraviolet (XUV) spectral range (120-30 nm). The optical
frequency comb, for which the nobel prize 2005 was awarded to John
Hall and Theodor W. Hänsch, has become an indispensable tool for
high precision spectroscopy. With the aid of a mode locked
femtosecond laser it is possible to directly and phase coherently
link the radio frequency domain and the frequency range of visible
light. Today's most accurate time standard, the cesium atomic clock
operates in the former and therefore it became possible for the
first time to compare arbitrary optical frequencies with our
primary time standard and measure them with 15 digits of accuracy.
Among other things, this method allowed one of the most accurate
test of quantum electrodynamics (QED) today in the course of the
determination of the 1S-2S transition frequency of atomic hydrogen
that is carried out in one of our labs. But also experiments in the
field of ultrafast physics rely on the frequency comb technique to
generate precisely controlled optical waveforms. An especially
intriguing possibility is to exploit the unique combination of high
peak power in the megawatt range and the high spectral quality (on
the order of 10^14) of single comb modes of a femtosecond frequency
comb. To this end, in the method presented in this thesis, the
femtosecond pulse train is coupled to an optical resonator of high
finesse. With this trick, the field strength inside the resonator
exceeds the driving lasers field by almost an order of magnitude.
Enough to efficiently drive a nonlinear process of high order
inside a medium of xenon atoms. As a result harmonics of the
driving frequency comb up to 15\nth order are generated. The
obtained field contains photons with energies exceeding 20~eV, a
spectral region which is not or only hard to access by conventional
continuous laser source. Therefore the presented XUV frequency comb
source brings direct frequency measurements at such high photon
energies into the realm of possibility for the first time. In
particular, an improved version of the demonstrated source will be
used to take the next step in an experiment with a long tradition
in our group, the 1S-2S spectroscopy of atomic hydrogen. The
generated frequency comb in the vicinity of 60~nm wave length will
be used to probe the 1S-2S transition in singly charged helium, a
hydrogen like system with larger nuclear charge. From such a
measurement it can be expected that, compared to hydrogen,
relativistic corrections from the QED theory become more important
as the system has higher energies in general. For this reason this
could lead to a test of QED with increased sensitivity. Other
applications of such a compact and relatively simple coherent
source of XUV radiation could be high resolution spectroscopy, XUV
holography, but could also lie in the research area of ultrafast
physics.