Fiber-laser frequency combs with subhertz relative linewidths.

Abstract

We investigate the comb linewidths of self-referenced, fiber-laser-based frequency combs by measuring the heterodyne beat signal between two independent frequency combs that are phase locked to a common cw optical reference. We demonstrate that the optical comb lines can exhibit instrument-limited, subhertz relative linewidths across the comb spectra from 1200 to 1720 nm with a residual integrated optical phase jitter of approximately 1 rad in a 60 mHz to 500 kHz bandwidth. The projected relative pulse timing jitter is approximately 1 fs. This performance approaches that of Ti:sapphire frequency combs.

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Fiber-laser frequency combs with subhertz relative
linewidths
W. C. Swann, J. J. McFerran, I. Coddington, and N. R. Newbury
National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305
I. Hartl and M. E. Fermann
IMRA America Inc., Ann Arbor, Michigan 48105-9774
P. S. Westbrook, J. W. Nicholson, and K. S. Feder
OFS Laboratories, 19 Schoolhouse Road, Somerset, New Jersey 08873
C. Langrock and M. M. Fejer
E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305
Received June 9, 2006; revised July 25, 2006; accepted July 26, 2006;
posted August 8, 2006 (Doc. ID 71822); published September 25, 2006
We investigate the comb linewidths of self-referenced, fiber-laser-based frequency combs by measuring the
heterodyne beat signal between two independent frequency combs that are phase locked to a common cw
optical reference. We demonstrate that the optical comb lines can exhibit instrument-limited, subhertz rela-
tive linewidths across the comb spectra from 1200 to 1720 nm with a residual integrated optical phase jitter
of ?1 rad in a 60 mHz to 500 kHz bandwidth. The projected relative pulse timing jitter is ?1 fs. This per-
formance approaches that of Ti:sapphire frequency combs. © 2006 Optical Society of America
OCIS codes: 120.3930, 320.7090, 140.3510.
The output of a femtosecond fiber laser consists of a
train of optical pulses at a repetition frequency fr. In
the frequency domain, this output is a comb of lines
at frequencies fn=nfr+fceo, where n is the mode num-
ber and fceois the carrier-envelope offset frequency.
Following the original work with femtosecond Ti:sap-
phire lasers,1,2fiber-laser combs have been stabilized
by phase-locking both frand fceoto a microwave ref-
erence,yieldingavaluable
metrology.3–6Fiber lasers have a number of advan-
tages over their Ti:sapphire cousins in that they are
more compact, are capable of turnkey, long-term op-
eration, are less expensive with lower power con-
sumption, are compatible with existing fiber optics,
and cover the telecommunication window. However,
while Ti:sapphire combs have exhibited subhertz
linewidths,7fiber-laser frequency comb linewidths
have until recently been at the kilohertz level or
higher. There is no fundamental reason for these
large linewidths,8and two combs with low-phase-
noise fceobeat notes have been described.9,10Here we
demonstrate that frcan be similarly narrowed by
phase locking one optical comb tooth to a cw optical
reference. We find that the comb lines can exhibit low
residual phase noise and subhertz relative linewidths
across the comb. A narrow-linewidth fiber-laser fre-
quency comb should find important applications in
metrologyfor low-phase-noise
precision optical spectroscopy, coherent Lidar,11fiber
transport of frequency standards,12,13and optical
clocks.
Following the work on Ti:sapphire combs by Bar-
tels et al.,7we compare two distinct fiber laser fre-
quency combs by phase locking a tooth of each comb
to a common, narrow cw reference laser while simul-
tool forfrequency
cw lasers, high-
taneously phase locking fceoby use of the standard
f-to-2f
technique.Although
complicated,14essentially the lock to the reference la-
ser fixes a central comb tooth by stabilizing the cavity
length while the offset frequency lock removes any
breathing motion of the comb about that central,
fixed tooth. In our experiments, two very different
frequency combs are phase-locked with an 8 MHz dif-
ference in their offset frequencies and a fixed integer
relationship between their repetition rates. The comb
outputs are combined, optically filtered, and detected
to generate an 8 MHz heterodyne beat from different
thedetails are
Fig. 1.
coupler. Inset, spectra of comb 1 (gray) and comb 2 (black).
Arrows indicate the location of the different optical band-
pass filter settings for the heterodyne measurements. (b)
Comb 1 (top) and comb 2 (bottom), along with the cw refer-
ence laser at 1550 nm ?194 THz?. The circled pairs contrib-
ute to the beat note at 8 MHz. (The number of contributing
pairs is ?400–4000, depending on the filter bandwidth.)
(a) Schematic of the experimental setup. FC, fiber
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0146-9592/06/203046-3/$15.00 © 2006 Optical Society of America

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spectral regions across the comb; the beat signal is
analyzed to give the residual linewidth and phase
noise. We obtain a coherent ?-function peak on the
heterodyne signal across the spectrum with a signal-
to-noise ratio of ?50 dB/Hz and a correspondingly
low integrated residual phase jitter of ?1 rad.
Figure 1 shows the experimental setup. Comb 1 is
basedonaFabry–Perot-type
oscillator.15Self-starting mode-locking operation is
stabilized by a saturable absorber mirror. The oscil-
lator intracavity dispersion is compensated by a
chirped fiber Bragg grating to near zero. The oscilla-
tor emits a pulse train with a repetition rate fr,1
?175 MHz and an optical bandwidth of ?60 nm.
Comb 2 is based on a stretched-pulse Er-fiber ring la-
ser with a repetition rate of fr,2?50 MHz and optical
bandwidth of 80 nm.10,16The combs were on separate
optical tables. Each laser emits between 5 and
10 mW, which is amplified in a bidirectional (comb 1)
or backward (comb 2) pumped Er-fiber amplifier. The
amplified output is spectrally broadened to an octave
in UV-enhanced highly nonlinear fiber.17
Each comb is stabilized to a common, 1550 nm cw
fiber laser by beating an individual, ?1 nW comb line
against the ?1 mW cw laser. The cw fiber laser line-
width was specified at ?2 kHz with slow drifts of
megahertz over minutes. The two beat signals are de-
tected at fbeat,1=58 MHz and fbeat,2=66 MHz, respec-
tively, upshifted with a common 1 GHz synthesizer,
divided by 64, and phase locked to two separate fre-
quency synthesizers by feeding back to the cavity
length with both a slow and a fast piezoelectric trans-
ducer (PZT). For comb 1, the two PZTs change the
saturable absorber mirror position with a feedback
bandwidth limited by resonances at 1 Hz and
70 kHz, respectively. For comb 2, the two PZTs
change the fiber length with a feedback bandwidth
limited by resonances at 5 and 45 kHz feedback, re-
spectively. The resulting in-loop phase noise spectra
are shown in Fig. 2(a), and the corresponding phase-
locked coherent peak is shown in Fig. 3. The low 1/f
shoulder in the phase noise at Fourier frequencies
?5 Hz is a result of phase noise on the frequency
synthesizers used in the optical phase lock. Despite
the very different design of the two fiber laser combs,
Er-soft-glass-fiber
the performance is very similar. To stabilize the re-
maining degree of freedom, the offset frequencies of
the two combs are phase locked to fceo,1=120 MHz
and fceo,2=112 MHz through feedback to the pump
power.9,10In each case, this phase lock results in a
strong coherent fceopeak with a signal-to-noise ratio
of 50–57 dB/Hz and a low phase noise [see Fig. 2(b)].
While Fig. 2 gives the residual, in-loop phase noise
of the two phase-locked signals, we are interested in
how this phase coherence is preserved across the
comb. To do this we set the combs’ repetition rates to
an integer ratio and compare coincident comb teeth
(offset by 8 MHz) across the spectrum. The repetition
ratedepends onboth
=?f1550±fbeat,i−fceo,i?/n1550,i, where f1550=c/1550 nm is
the frequency of the cw laser and n1550,iis an integer
identifying the nth mode nearest to f1550of the ith
comb.7Since both the fbeatand the fceosignals of the
two combs differ by 8 MHz, with the appropriate sign
choice the repetition rates of the two combs will have
a fixed integer relationship. For the cavity lengths of
the two combs, we can fix the repetition rates such
that 2fr,1=7fr,2. Adjusting the repetition-rate phase
between the two combs7ensures that every second
pulse of comb 1 and every seventh pulse of comb 2 ar-
rive coincidentally at the photodetector, generating
an 8 MHz heterodyne beat signal that is subse-
quently recorded with a digital fast Fourier trans-
form instrument. This beat signal represents the av-
erage relative linewidth of the collection of comb lines
transmitted by the optical filter (see Fig. 1).
Figure 3 demonstrates a strong coherent peak in
the heterodyne beat between the two combs at wave-
lengths of 1200±5, 1300±5, 1400±5, 1540±0.5,
1580±5, 1600±0.5, 1720±15 nm (see Fig. 1), where
±x indicates the 3 dB bandwidth of the optical filter.
This coherent peak approaches a ?-function with a
3 dB linewidth limited by either the spectrum ana-
lyzer or uncompensated drifts in any out-of-loop fi-
bers. In this case our coherent peak is instrument
limited to 300 mHz over the 48 s acquisition time.
The inset shows the heterodyne beat at 1720 nm for a
wider 1 MHz span, showing the coherent peak con-
fceo
and
fbeat
as
fr,i
Fig. 2.
lock between the cw reference laser and comb 1 (gray) and
comb 2 (black). The integrated phase noise of 0.94 and
0.35 rad, respectively, is dominated by the servo bumps at
high Fourier frequencies. Extrapolation to the Nyquist fre-
quencies of 92.5 and 25 MHz for the two combs gives inte-
grated phase noises of 0.53 and 1.21 rad. (b) In-loop phase
noise for fceofor comb 1 (gray) and comb 2 (black). The in-
tegrated phase noises are 1.5 and 1.0 rad, respectively.
(a) In-loop phase noise spectral densities for the
Fig. 3.
the comb and on fbeat,ibetween the combs and the cw ref-
erence laser (resolution bandwidth (RBW) of 0.3 Hz, acqui-
sition time 48 s). Inset, rf spectra on a 1 MHz span and log
scale for the heterodyne beat at 1720 nm ?RBW=3 kHz?.
(Color online) Spectra of the coherent peak across
October 15, 2006 / Vol. 31, No. 20 / OPTICS LETTERS
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taining 55% of the total power atop a broad noise
pedestal. This broad noise pedestal is seen on the
heterodyne beat at all wavelengths and is a direct re-
sult of phase noise. Indeed, for such a coherent lock,
the most physically meaningful measure of the coher-
ence is the phase noise power spectral density (PSD).
Figure 4 gives the phase noise PSDs, S????, as func-
tion of Fourier frequency, ?. The S???? are scaled cop-
ies of each other and are limited by the quality of the
optical phase locks, as is shown below. (Excess phase
noise from supercontinuum generation may exist as a
white-noise floor at large ? but was not explored
here). The frequency of the nth tooth is fn=nfr+fceo
=r?f1550+fbeat?+?1−r?fceo,
ranges from 0.9 to 1.3 for ? from 1200 to 1720 nm.
Therefore, its residual phase noise PSD is Sn???
=r2Sbeat???+?1−r?2Sceo????r2Sbeat???, since Sceois not
much larger than Sbeatand we assume negligible cor-
relations between Sbeatand Sceo. The residual phase
noisebetween the
??f?/f1550?2Sbeat,?=?1550/??2Sbeat,?,
Sbeat,??Sbeat,1+Sbeat,2, converting from n to ?. (Corre-
lated phase noise on the two combs, most notably
from frequency fluctuations of the free-running cw
reference laser, will not appear on S?) In this simple
approximation the optical lock stabilizes the relative
repetition rates to Sbeat,i/f1550
etition rate noise up to the appropriate optical fre-
quency yields S?. Figure 4(b) shows that the mea-
sured and predicted S? agree well, verifying the
simple approximations. The integrated phase jitter,
???
nally, returning to the rf heterodyne beat, the frac-
tional power in the coherent peak will be exp?−???
where
r?n/n1550
and
combs is
where
then
S?
f??c/?,
2
; multiplying this rep-
2=?0.06 Hz
0.5 MHzS????d???−2is shown in Fig. 4(c). Fi-
2?.18
The tight phase lock between the two combs im-
plies a low residual timing jitter. A reasonable upper
limit to this jitter on the pulse train of comb 2
is ?2?f1550?−1??0.06 Hz
Extrapolating to the Nyquist frequency of 25 MHz
from the measured white-phase-noise floor increases
the jitter to 1.12 fs. Of course, such a low timing jitter
remains to be demonstrated. Finally, the low phase
noise also translates into excellent relative frequency
stability; with a lower-noise frequency synthesizer
used in the optical phase lock for comb 2, the counted
fbeatand fceoboth exhibit a counter-limited standard
deviation of ?1 mHz at a 1 s gate time, giving a sta-
tistical error of 1 mHz/?c/1550 nm??5?10−18at 1 s,
which can certainly support the next generation of
optical clocks.
0.5 MHz?Sbeat,2???+Sceo,2????d??1/2=0.9 fs.
We acknowledge helpful discussions with S. Did-
dams and Q. Quraishi. N. R. Newbury’s email ad-
dress is nnewbury@boulder.nist.gov; I. Hartl’s is
ihartl@imra.com.
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Fig. 4.
=1200,1300,1400,1540,1580,1720 nm (top to bottom).
The PSDs above 1200 nm are offset by 10 dB from each
other for viewing clarity. (b) Comparison of the measured
(solid curve) and predicted (dotted curve) phase noise PSD
at 1720 nm, which are basically indistinguishable. Also
shown is the integrated phase noise, ???(dashed curve,
right axis), which reaches 0.9 rad. Extending the white-
phase-noise floor to 25 MHz yields a residual phase jitter of
1.03 rad. (c) Measured (squares) and predicted (curve) in-
tegrated phase jitter, ???, versus wavelength.
(Color online) (a) Phase noise PSDs at ?
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OPTICS LETTERS / Vol. 31, No. 20 / October 15, 2006