Yb:fiber systems serve as the basis for frequency combs at almost
any wavelength between the extreme ultraviolet and the mid-infrared
spectral regions.
even prevent mode-locking. However, in the oscillator design,
the dispersion is compensated to a slightly positive value by a
fiber Bragg-grating, which also serves as the output coupler.
Due to the availability of highly doped ytterbium gain
fibers, the repetition rate can now be scaled up to 1. 1 GHz
with this design. High repetition rates are not only beneficial
for spectroscopy—as this means a higher power per comb
mode—but also for other applications such as calibrating
astronomical spectrographs and low phase-noise RF generation. These applications still require passive filter cavities to
scale the repetition rate to tens of gigahertz. However, the
usage of high-repetition-rate oscillators significantly relaxes
the requirements for the external filter cavities.
For most practical applications, the pulse train from Yb:fiber
oscillators must be amplified to reach pulse energies of a few
nanojoules. Self-phase modulation is considered to be detrimental when amplifying frequency combs because it results
in amplitude-to-phase-noise conversion. One can realize
linear chirped pulse amplification by stretching the pulses in
depressed-cladding as well as standard fibers and amplifying
them in a cladding-pumped fiber amplifier. A fully integrated
setup, including compensation up to third-order dispersion,
can be developed by using a fiber coupler for pump light delivery. After recompression in a grating compressor, 80-fs pulses
at Watt-level average powers are possible.
The passive stability of this laser design is
reflected by a free-running f 0 linewidth of less
than 15 kHz. The noise performance is not
quantum-limited, but it is still subject to technical noise, mainly from the pump laser. Reducing
the relative intensity noise of the oscillator via a
feedback mechanism was shown to result in a further decrease in phase noise. This is highlighted
by the reduction of the f 0 and beat signals with
continuous wave (cw) lasers. The strong correlation between the pump laser’s intensity noise
spectrum and the comb’s frequency noise spectrum indicates that amplitude-to-frequency-noise
conversion in the oscillator is the dominant source
of noise. Amplitude noise is caused by the pump
laser as well as by quantum-noise contributions
dominating at higher sideband frequencies.
-0.4
-0.4
piezoelectric transducers are used to change the cavity length,
and hence, frep. This allows for phase noise compensation up to
sideband frequencies of 180 kHz, limited by acoustic resonances. Together with f 0-servomechanisms (servos) based on pump
power modulation, this gives a good set of control parameters.
In rare-earth doped fibers, the upper-state lifetime of the laser
transition is on the order of a few milliseconds, preventing
f 0-servos at high frequencies.
Significantly higher servo bandwidths can be realized
with electro- and acousto-optical modulators (EOM and
AOM). We used 1-mm long Li TaO3 crystal as an EOM in
the free-space section of the laser cavity. It acts as a frequency
transducer with a servo bandwidth of 390 kHz, directly
controlling the cavity length through its index change. A
200 MHz AOM with a servo bandwidth of 250 kHz was
implemented to serve as an f 0-actuator outside the cavity.
The phase-locking performance of this scheme is displayed in
the figure below, which shows the in-loop phase noise power
spectral density together with the integrated timing jitter, as
well as the in-loop beat signal.
Excellent locking performance was also achieved with
another stabilization scheme: phase-locking two comb teeth
to two different optical references. This is an alternative to
the use of self-referencing. These two methods of complete
0
(a)
Power [dBm]
- 20
- 40
0
Frequency [MHz]
Phase noise power
spectral density [rad2 / Hz]
10-6
10-8
10-10
0.4
101
(b)
0.2
0.1
Phase error [rad]
0
Frequency [Hz]105 103
0
(c)
Power [dBm]
- 20
- 40
Phase noise power
spectral density [rad2 / Hz]
10-6
(d)
10-10
10-8
0.4
0.2
Phase error [rad]
0
Phase-locking performance
In order to apply feedback for phase control to a
mode-locked oscillator, one must implement actuators for dynamic control of frep and f 0. Typically,
This frequency comb has high bandwidth transducers. (a, b) The beat signal
(100 kHz RBW) and phase noise power spectral density with the integrated
phase error for the f0-lock using an AOM. (c, d) The beat signal (100 kHz
RBW) and phase noise power spectral density with the integrated phase
error for the frep-lock to a cw laser at 698 nm using an intra-cavity EOM.
0 0.4
