Measuring the Frequency of Light using Femtosecond Laser Pulses

In the course of this work a new technique to measure the frequency
of light has been developed, implemented and refined. For all time
and frequency measurements the SI second defined by the cesium
ground state hyperfine splitting near 9.2 GHz is the defined
standard of reference. Therefore in precision optical frequency
measurements optical frequencies on the order of several 100 THz –
too fast to be counted with any electronics – have to be compared
with radio frequencies on the order of a few GHz. The basic idea
here is to measure dierences between optical frequencies with the
help of frequency combs generated by the periodic pulse trains of
femtosecond lasers. The output spectrum of such a laser consists of
modes equally spaced by the repetition frequency of the pulses and
forms a convenient ruler in frequency space. Extending this
principle to the intervals between harmonics of the same optical
frequency f, in the most simple case the interval between f and 2f,
allows the absolute measurement of an optical frequency f = 2f − f.
To bridge the interval between an optical frequency f and its
second harmonic 2f a broad frequency comb with a width of several
100 THz is needed. This can be achieved with very short pulses (on
the order of 5 fs) or with moderately short pulses on the order of
a few 10 fs via self phase modulation in an optical fiber.
Especially suited for such massive broadening are so called
photonic crystal fibers. Here the light is guided in a very small
core (1-2 µm) surrounded by air holes. This development culminates
in the “single laser frequency chain” linking the radio frequency
domain with the optical domain with the help of just one fs laser,
a piece of fiber and some optics. Our optical frequency synthesizer
can be used to measure not only one but almost any optical
frequency with the same compact apparatus. Originally this project
has been initiated to perform precision spectroscopy on the 1S- 2S
transition in atomic hydrogen, a project with a long tradition in
our group, and yielded what is thus far the most precise optical
frequency measurement with a relative uncertainty of 1.8×10−14.
Hydrogen as the most simple bound system served and still serves as
an important cornerstone for tests of quantum physics, the
measurement of the 1S Lamb shift represents one of the most
accurate QED tests. Furthermore the Rydberg constant can be
determined very precisely from optical frequency measurements in
hydrogen. Soon it became obvious that this technique has a broad
applicability. In this work transition frequencies in cesium,
indium and molecular iodine have been measured. Besides that
principle tests on this technique have been conducted. The direct
comparison of two such frequency chains showed agreement on the
level of 5 × 10−16. Further applications besides precision
spectroscopy can be found in the time domain. There it is now
possible with this technique to control the phase evolution of
ultra short light pulses and perform optical waveform synthesis. As
optical clock work for future all optical clocks a fs frequency
chain transfers stability and accuracy from the optical to the rf
domain.