This thesis reports on experimental demonstrations of a novel
direct frequency-comb spectroscopic technique for the measurement
of one- and two-photon excitation spectra. An
optical-frequency-comb generator emits a multitude of highly
coherent laser modes whose oscillation frequencies are evenly
spaced and uniquely determined by only two measurable and
adjustable radio-frequency parameters and the integer-valued mode
number. Direct frequency-comb spectroscopy can traditionally be
performed by scanning the comb lines of the frequency comb across
the transitions of interest and measuring a signal that is
proportional to the excitation by all comb lines in concert. Since
the modes that contribute to the excitation cannot be singled out,
transition frequencies can only be measured modulo the comb-line
spacing with this scheme. The so arising limitations are overcome
by the technique presented here, where the first frequency comb is
spatially overlapped with a second frequency comb. Both combs of
this so-called dual-comb setup are ideally identical except for
having different carrier-envelope frequencies and slightly
different repetition rates. The interference between the two combs
leads to beat notes between adjacent comb lines, forming pairs
(with one line from each comb) with an effectively modulated
excitation amplitudes. Consequently the probability of excitation
by any given comb-line pair is also modulated at the respective
beat-note frequency. These beat-note frequencies are spaced by the
repetition-rate difference and uniquely encode for individual
comb-line pairs, thus enabling the identification of the comb lines
causing an observed excitation. In a first demonstration,
Doppler-limited one-photon excitation spectra of the transitions
5S_{1/2}-5P_{3/2} (at 384 Thz/780 nm), 5P_{3/2}-5D_{3/2}, and
5P_{3/2}-5D_{5/2} (both at 386 Thz/776 nm), and two-photon spectra
of the 5S_{1/2}-5D_{5/2} (at 2x385 Thz/2x778 nm) transition,
agreeing well with simulated spectra, are simultaneously measured
for both stable Rb isotopes. Within an 18-s measurement time, a
spectral range of more than 10 THz (20 nm) is covered at a
signal-to-noise ratio (SNR) of up to 550. To my knowledge, this is
the first demonstration of both dual-comb-based two-photon
spectroscopy and fluorescence-based dual-comb spectroscopy. In a
follow-up experiment probing the same sample and two-photon
transitions, the Doppler-resolution limit is overcome by
implementation of an anti-resonant ring configuration. Cancellation
of the first-order Doppler effect makes it possible to resolve 33
hyperfine two-photon transitions. The highly resolved (1 MHz point
spacing), narrow transition-linewidth (5 MHz), accurate (systematic
uncertainty of ~340 kHz), high-SNR (10^4) spectra are shown to be
consistent with basic simulation-based predictions. As the spectral
span is, in principle, only limited by the bandwidths of the
excitation sources, the acquisition of Doppler-free two-photon
spectra spanning 10s of THz appears to be in reach. To my
knowledge, this is the first demonstration of Doppler-free
Fourier-transform spectroscopy. Lastly, the possibility of
extending the technique's scope to applications in the field of
biochemistry, such as two-photon microscopy, are explored. To that
end, first high-speed, low-resolution (>>1 GHz) experiments
are carried out identifying comb-stabilization requirements and
measurement constraints due to the limited dynamic range of the
presented highly multiplexed spectroscopic technique.
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