Implementation and characterization of a stable
optical frequency distribution system
Birgitta Bernhardt,1,*
Theodor W. Hänsch,1
and Ronald Holzwarth 1
1Max-Planck-Institute for Quantum Optics, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
Abstract: An optical frequency distribution system has been developed that
continuously delivers a stable optical frequency of 268 THz (corresponding
to a wavelength of 1118 nm) to different experiments in our institute. For
that purpose, a continuous wave (cw) fiber laser has been stabilized onto a
frequency comb and distributed across the building by the use of a fiber
network. While the light propagates through the fiber, acoustic and thermal
effects counteract against the stability and accuracy of the system. However,
by employing proper stabilization methods a stability of 2 x 10−13
τ-1/2
is
achieved, limited by the available radio frequency (RF) reference.
Furthermore, the issue of counter-dependant results of the Allan deviation
was examined during the data evaluation.
©2009 Optical Society of America
OCIS codes: (140.3425) Laser stabilization; (140.3510) Lasers, fiber; (060.2360) Fiber optics
links and subsystems
References and links
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1. Introduction
Frequencies or alternatively time intervals are the physical parameters one can measure with
the highest precision. In order to tap the full potential of time and frequency measurements
one tries to deduce other physical parameters from this kind of measurements. In 1983, the
value of the speed of light was defined to be 8
02.99792458 10 m
sc = ∗ and so, measurements of
a wavelength were deduced from a frequency measurement. However, optical frequencies are
that large (several 100 THz) that they cannot be processed by existing counters. With the
invention of optical frequency combs, these high frequencies have been made accessible. This
new technology enables counting the fast oscillations of such a light wave by the
transformation of optical signals into signals in the radio frequency range. It enables the
implementation of optical counters for high precision spectroscopy and with it the validation
of fundamental physics theories like quantum electro dynamics [1]. The introduction of the
frequency combs also resulted in the realization of the first optical clock that has the potential
to reach the 10−18
level and already now is better than the best Cesium clocks by one order of
magnitude [2,3].
Due to the advancement of optical frequency standards and optical precision spectroscopy,
it becomes more and more important to have precise transfer methods available to compare
these optical standards with each other over long distances. For this reason, the
implementation and characterization of optical fiber networks for the transmission of
frequencies is subject of several studies [4–7].
For many experiments on the other hand, the ultimate demand for stability and accuracy is
not at all necessary. For laser cooling experiments for example, one typically needs a
wavelength accuracy on the order of 100 kHz and a laser line width on the same order. For
such experiments other factors like continuous availability and convenient wavelength
coverage are of importance. In this case, the optical frequency comb can act as a universal
optical frequency synthesizer where the output can be conveniently distributed by fiber
networks without the need for elaborate stabilization techniques.
In the course of the work presented here, we have designed and implemented such a
system and kept it in operation for extended periods of time. Design criteria and results will be
presented here.
2. Setup
2.1 Basic concept
The basic concept of the frequency distribution system relies on the generation of precisely
known optical frequencies with the help of a frequency comb generator and subsequent
distribution via optical fibers to different applications. In order to avoid complicated
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stabilization schemes, we link the optical frequency synthesizer directly to a RF reference (see
Fig. 1). The following subsections explain the particular components of the distribution
system.
Fig. 1. Basic concept of the distribution system.
2.2 The reference
Initially, the frequency comb was referenced to a commercially available Cesium clock with
high performance tube that has a specified stability of 12 1/25 10 τ− −× (Symmetricon model
5071A). In the meantime, our system could even be improved by the introduction of a
Hydrogen maser (CH1-75A, Stability: 2/113102 −−× τ ). This reference is among the most stable
RF reference sources that are commercially available and, with the comparison by GPS
signals, it is also one of the most accurate ones.
Fig. 2. Allan deviation of the references: Specifications of the Cs clock and the maser as well
as the verifying measurements of the Cs and maser stability, respectively.
The specifications of both references are shown in Fig. 2. The Allan deviation of the Cs
clock was verified by comparing it to the institute’s Hydrogen maser. Both upper curves show
that the measured data fit the manufacturer’s specification very well. The maser’s
specification (lower curve) could be checked by a long term recording of a beat note between
a diode laser stabilized to a ULE (ultra low expansion glass) high finesse cavity in vacuum
and a frequency comb referenced to the active H-maser [8]. The FP Allan deviation of this
beat note reaches a minimum of 153 10−× at 500 s. For longer times, the drift is ascribed to the
ageing process of the ULE glass and the thermal drift of the cavity.
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Fig. 3. Setup for the comb stability measurement, f0 and frep of the frequency combs are
stabilized via phase locked loops onto the H maser or the Cs clock.
2.3 The optical frequency synthesizer
An Erbium fiber based frequency comb generates a grid of exactly known optical reference
frequencies and serves in that way as the optical frequency synthesizer.
The pulse train emitted by a mode-locked femtosecond (fs) laser appears in the frequency
domain as a comb of equally spaced modes [9,10]. This frequency comb is completely
determined by two frequencies, f0 and frep. The offset frequency f0 is the comb's offset from
zero and is due to the phase shift between the electrical field and the pulse envelope after each
round trip in the cavity. The pulse repetition frequency frep corresponds to the spacing of the
comb modes and is linked to the cavity round trip time by frep = 1/T = vg/L, where vg is the
group velocity and L the cavity length of the laser. Because both frequencies f0 and frep are in
the radio frequency regime they can be controlled by established radio frequency techniques.
The comb is stabilized onto the Cesium clock or the Hydrogen maser as its offset and
repetition frequency are controlled via phase locked loops. To characterize the synthesizer’s
performance, a relative stability measurement was assembled without involving the fiber link.
This was realized by locking a cw laser onto an Er fiber comb and counting the beat signal
between this stabilized cw laser and a second similar Erbium fiber comb (see Fig. 3). Its
resulting Allan deviation is shown in Fig. 4. As can be seen, the frequency comb’s stability
reaches 10−16
in the long term regime. It is evident that, for τ > 4000 s, phase drifts are
limiting the measurement accuracy.
Fig. 4. Allan deviation of the frequency synthesizer.
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2.4 The distribution
In principle, there are two different possibilities of distributing the optical reference
frequency. On the one hand, the frequency comb can be directly distributed via a fiber
network. Note that in this case no dispersion compensation of the pulses is necessary. The
right comb modes have only to be filtered and detected for the phase lock at each end point
separately. The other possibility takes a cw source for the distribution which is stabilized onto
the frequency comb. There is the need of first stabilizing the cw source onto the frequency
comb before distributing it. However, this second method has two advantages: The
stabilization of the laser has to be done only once and the light source (frequency comb and
cw laser) can be placed in a quiet and undisturbed environment far away from the
experimental handling.
Nevertheless, we realized both options as can be seen in Fig. 5. In our first case, a stable
signal at a wavelength of 785 nm is required. For this purpose, the frequency comb is
frequency-doubled and distributed directly to the experiment (see Applications).
In our second realization method, the signal of a stabilized cw laser was distributed (see
Fig. 5, right panel). For this purpose, first, the power of the cw laser is enhanced by a fiber
amplifier, then, its output is split into two parts: a small part for the beat detection for the
stabilization of the fiber laser onto the frequency comb and a major part for the distribution
through the institute.
Fig. 5. Distributing the frequency comb (left) or single stabilized cw signals (right). The two
grey boxes indicate that these steps are optional - depending on the application after the
distribution. As it turns out in subsection 3.3, a Doppler correction is only required if the
application’s accuracy has to be better than 10−14.
The distributed optical reference frequency is realized by a commercial continuous wave
Yb fiber laser from Koheras at 1118 nm that is stabilized onto the comb via a beat
measurement and subsequent phase lock. In order to get enough power for the beat signal and
the two experiments, the laser output power of 10 mW is increased to about 100 mW by a
Ytterbium-doped fiber amplifier. Most of the amplifier output is split into two parts and
distributed through the institute via 70 m and 90 m long fibers to two different experiments.
Temperature fluctuations that occur inside the building result in a Doppler shift of the
frequency (see Section 3.3). This frequency shift can be corrected with the help of an acousto-
optical modulator.
Also another effect in the fibers has to be considered: The so-called Brillouin scattering is
the scattering of light in its backwards direction caused by acoustic waves inside the fiber. As
a result, it decreases the transmission of the light through the fiber. Hence, Brillouin scattering
is quite simple to demonstrate by measuring the transmission of the fiber in dependence of the
input power. For this test, the whole output power of the amplifier was used as fiber input.
The transmission of the fiber linearly increased with this input until an input value of about 80
mW. At this point, the transmitted power went into saturation. That means for the operation of
#112018 - $15.00 USD Received 27 May 2009; revised 6 Aug 2009; accepted 21 Aug 2009; published 8 Sep 2009
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the system, Brillouin scattering does not occur at the required intensities and fiber lengths
since the amplifier output of 100 mW is divided into two parts for the two experiments. The
maximum power that travels through the fiber is consequently only 50 mW and lies well
beneath the crucial threshold for Brillouin scattering.
Like already mentioned, the continuous-wave fiber laser is stabilized onto the comb via an
offset frequency phase lock. For this purpose, a beat signal fbeat is observed between a cw laser
and its nearest comb mode. The optical frequency of the laser can be expressed as
0opt rep beatf mf fν = + + [11]. The two laser beams of the comb and the cw laser are overlapped
with orthogonal polarization by a polarizing beam splitter and then projected onto the same
polarization axis via an adjustable polarizer. This tuneable polarizer consists of a polarizing
beam splitter and a 2
λ -plate. A grating directly in front of the diode pre-selects several modes
of the comb in order to get a better signal to noise ratio. The output of the photo detector is
mixed with the frequency of a local oscillator and fed into a proportional-integral controller.
Its output is used to readjust the piezo controller unit inside the cw laser. The controlled beat
frequency was recorded by several counters without death time and the corresponding Allan
deviation was calculated (see section 3).
2.5 Applications
In our first case, a stable signal at a wavelength of 785 nm is needed to stabilize a cavity for
the realization of a single photon source with Rb [12]. Up to now, the cavity was stabilized
with the help of transfer cavities. The new method makes the setup easier and long-term-
stable.
As the required signal of 785 nm lies beyond the spectral range of the comb, the comb first
has to be amplified and frequency-doubled before the distribution. After the distribution, a
Diode laser (DL100 by Toptica) is phase -locked onto the comb. The single photon source
cavity is then locked onto the diode laser by a Pound-Drever-Hall-lock [13].
At the second application end, high power lasers are stabilized onto the distributed optical
standard via a beat signal detection and an offset frequency lock. While until now a complex
stabilization of the high-power lasers onto optical resonances in iodine was necessary, this is
now superseded because the frequency standard is directly distributed into the laboratories
and the lasers can be stabilized with the much easier beat detection method. Of course, there
are several other applications these newly stable high power lasers can be used for, in our case
they cool Mg+ ions that are part of our precision spectroscopy experiment [14].
The stabilization method with a frequency comb can be used for any other arbitrary
application instead of laser cooling as long as the wavelength of the laser that is to be
stabilized lies within the excessively broad comb spectrum (1000 to 2450 nm), as already
mentioned. Since the used frequency comb is a fiber based one that makes it extremely
maintainable and enables a continuous operation of the frequency distribution system so that
the experiments can be supplied with the wavelength of 1118 nm day and night.
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Fig. 6. (a) Beat signal between cavity stabilized laser and frequency comb (Resolution
bandwidth: 47 kHz, Signal-to-noise ratio: 22 dB), (b) locked beat signal between transfer laser
and frequency comb (Resolution bandwidth: 10 kHz, Signal-to-noise ratio: 32 dB).
3 Verification and results
3.1 Short term stability
To characterize the line width of the frequency comb locked onto the H-Maser we have
observed a beat signal with a cw laser locked onto a high finesse cavity to reduce the line
width to the Hz level. This laser is used for precision spectroscopy of Hydrogen and is
described in [8] in detail. Since this laser has Hz level line width, the main contribution to the
observed line width of 275 kHz as shown in Fig. 6(a) can be attributed to the frequency comb.
With this knowledge we have designed a relatively sloppy lock of the transfer cw laser to
the comb. The transfer laser has already a relatively narrow short term line of 45 kHz.
Therefore a sloppy lock will be enough so that the transfer laser follows the frequency comb
within its jitter. The locked beat signal is shown in Fig. 6(b), it has a line width of 90 kHz as
observed with a spectrum analyzer in 1 ms sweep time and with a resolution bandwidth of 47
kHz.
3.2 Long term stability
Before distributing the optical frequency through the building, it should be verified that the
system actually runs stable. This was done by measuring the in-lock beat signal between the
laser and the frequency comb like described in the section 2.4. It has to be considered that the
counters that acquire the beat frequency can make mistakes: they can loose cycles of the beat
signal for example due to possible perturbations in the experimental environment. This results
in a discrete step in the phase. Before processing the data, it must be verified that these cycle
slips don’t distort the result. Cycle slips can be detected by an additional branch in the locking
loop with an auxiliary counter or phase detector that is installed only for cycle slip exposure
purposes. In our case, it was done by an extra phase detector that was read out simultaneously
to the counters. Every big jump in its output voltage (several Volts instead of mV) showed a
cycle slip and the corresponding false data points could be removed (see Fig. 7).
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Fig. 7. A change in the phase detector output voltage (a) identifies occurring cycle slips in the
frequency measurement (b).
Counter-dependant result in the Allan deviation
Out of the remaining, correct data, the Allan deviation was calculated. It is defined via the
square root of the Allan variance [15]
2 2
1
1( ) ( ) ,
2k k
y yσ τ +≡ − (1)
where the kth sample of the normalized frequency y(t), averaged over the measurement time
τ , is defined as
1
( ) .k
k
k
t
y y t dt
t
τ
τ
+
= ∫ (2)
This integral corresponds to a single (normalized) measurement of a traditional frequency
counter for a selected measurement time τ , usually called gate time. Such a traditional
frequency counter is for example the FXM counter from K&K Messtechnik that was also used
in our experiment. It takes only one value after each expired gate time. This kind of counters
is also referred to as Π -type counters. Its corresponding Allan deviation is shown by the blue
line in Fig. 8. As expected for phase locked signals, it has a time dependence of τ −1. Another
important feature of this counter that has to be emphasized is the fact that it has no dead time.
The Allan deviation as it is defined in Eq. (1) can only be derived by dead time free data.
We showed this issue by using also a second type of counter, the counter model 53131A
from Agilent (former HP). It averages the frequency value over the set gate time. These
counters are also called Λ -type counters because of their characteristic averaging method. In
contrast to the FXM counters, this special counter has a dead time where no data is acquired.
These different types of counters can affect now the final data evaluation if their different
averaging procedure is not taken into account. If one calculates the above shown Allan
deviation for the second, Λ -type counter, one gets a different, hence wrong result since the
Allan deviation is defined only for counters with a Π -type behaviour and without dead time
[16,17].
The different results out of the identical measurement setup can nicely be examined in Fig.
8. The Allan deviation extracted out of the FXM counter measurement is about two orders of
magnitude worse than the Allan deviation out of the HP measurement. This seems plausible
since the HP counter averages its acquired data during the gate time in contrast to the FXM
counter. This procedure makes the frequency appear more stable. But since the definition of
the Allan deviation only considers the phase of the starting point and the end point of every
gate time, only the FXM counter yields the true Allan deviation. Out of the averaged,
#112018 - $15.00 USD Received 27 May 2009; revised 6 Aug 2009; accepted 21 Aug 2009; published 8 Sep 2009
(C) 2009 OSA 14 September 2009 / Vol. 17, No. 19 / OPTICS EXPRESS 16856
juxtaposed HP counter data, one gets a falsified time dependence of τ -1/2 (green line in Fig. 8)
which one would expect for white frequency noise but not for phase noise. This is a result of
the inadequate type of counter (Λ -type) and the additional fact that the counter has dead
times after each measurement.
Another possibility is to measure with different gate times and to calculate the Allan
deviation for each gate time, separately (see black line in Fig. 8). At first sight, this results in a
more reasonable behaviour since it seems to decrease at least with the expected τ −1
dependence. But by looking more closely, the deviation starts to decrease with τ -3/2 for short
times (1 s < τ < 10 s), and flattens then with a τ −1 behaviour for higher gate times (τ > 10
s). This behaviour for short gate times aligns well with the paper by Dawkins et al. where it is
shown that Λ -type counters provide a different dependence in time, the so-called modified
Allan variance for white phase noise (Table 1 in [17]).
For large times τ > 100 s, even the correct Allan deviation extracted out of the FXM data
loses its typical τ −1 behavior what can easily be explained: At higher gate-times, cycle-slips
carry more and more weight. The procedure of eliminating these sources of error causes
nevertheless the deficit of the coherence in the data. This gives rise to this bending towards
longer gate times.
As a conclusion, the FXM measurement constitutes the most realistic result. Its values are
not the best - but the ones that resemble the Allan deviation at best. Because of its waiving of
averaging the data, it is the most preferable option for giving a statement about a signal’s
actual stability since it is the only counter that delivers the true Allan deviation. Only for
higher gate-times, it has to be considered that the increasing number of erased cycle-slips can
cause a loss of the data’s coherence which provides a divergence from the true Allan
deviation.
For all measurements, the beat frequency was placed to fbeat = 40 MHz and f0 and frep of
the frequency comb to 20 and 100 MHz, respectively.
Fig. 8. Locked beat signal at 40 MHz evaluated with different counters and different gate times.
Only the FXM measurement yields the “real” Allan deviation as defined in [15]
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(C) 2009 OSA 14 September 2009 / Vol. 17, No. 19 / OPTICS EXPRESS 16857
3.3 Temperature effects
There are several effects that already occur in the initial laboratory that affect the stability and
the accuracy of the distributed frequency: The acoustic level in the laboratory caused by the
many devices with fans results in a spectral broadening that decreases the stability. This
spectral broadening was avoided by putting the whole setup into a sonic-isolating box. This
box, additionally, has its own fundament in order to keep off the low-frequency oscillations of
the building.
The accuracy is reduced, for example, by temperature fluctuations. These variations cause
a change of the refraction index in the fibers and an alteration of the fiber length which results
in a shift of the distributed optical frequency.
These temperature flows in the laboratory were also avoided by the box as it is also
thermally isolating. The isolating effect is that eminent as it attenuates the oscillations of the
air conditioning in the lab from about 1 °C within 10 minutes to only 0.2 °C of temperature
change within 10 hours inside the box. That corresponds to a frequency change of only 11.9
mHz for the 14 m long fiber inside the box. The frequency change is given by the
equationdn n dL T
f kLdT L dT t
∆ ∆ = + ∆
. k is the wave number. dn
dTis the ratio between refraction
index change and temperature change and 1 dL
L dT is the thermal extension coefficient of the
fiber (in our case 1.2 × 10−5
°C−1
and 11.1 × 10−7
°C−1
, respectively). That small frequency
shift means a relative accuracy of 4.44 × 10−17
.
Fig. 9. (a) Temperature development in the lab and (b) corresponding position of the stepper
motor during the long time measurement.
Figure 9 shows the temperature changes in the isolation box during one week and how the
stepper motor that changes the cavity length of the frequency comb counteracts to keep the
fiber comb stable.
Besides the temperature fluctuations inside the laboratory, temperature drifts inside the
institute also occur. The 70 to 90 meters long fibers run through the institute from the lab
through a vertical cable chute up to the attic and from here again through cable chutes that
lead to the experiments' laboratories. Here the contribution to a frequency shift is considerably
higher as in the central comb laboratory since the fibers cannot be isolated that well against
temperature fluctuations and the fibers are essentially longer than their part in the distribution
laboratory. For example with a fiber length of 90 m and a temperature change of 1 °C per
hour, a frequency shift of 3 Hz emerges. That corresponds to a relative accuracy of 1.4× 10−14
.
However, this frequency shift can be corrected with the help of an acousto-optical modulator
(AOM). Figure 10(a) shows the schematic setup for this correction.
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(C) 2009 OSA 14 September 2009 / Vol. 17, No. 19 / OPTICS EXPRESS 16858
For the purpose of the Doppler cancellation, most of the light is frequency shifted by an
AOM (80 MHz) and travels through the long fiber. A part of the light that is now frequency
shifted by both the AOM and the Doppler Effect in the fiber is reflected back by a mirror.
This part again experiences the frequency shift while travelling through the fiber and the
AOM for a second time. Back in the lab, the double frequency-shifted light is overlapped with
the “original” light that was not shifted in its frequency and a beat signal is detected by a
photo diode. The detected signal is amplified to −4 dBm, mixed with the frequency of a local
oscillator (2× 80 MHz = 160 MHz, wit the same power level of −4 dBm) and is fed into a
phase locked loop that regulates the frequency that is applied to the AOM.
Figure 10(b) shows the frequency of the AOM driver that manipulates the AOM. It
oscillates around the 80 MHz with a time period of about 11.5 minutes. As it turned out, this
oscillation corresponds to the air conditioning in the destination lab where the light was
reflected back. As here, 25 m of the long fiber are placed, a main part of the fiber experiences
the oscillating temperature fluctuations in this laboratory what finally results in the frequency
shift.
As already mentioned above, a temperature change of 1 °C per hour corresponds to a
relative accuracy of 1.4× 10−14
. That means that a correction of the frequency shift is not
necessary for the applications as they only request an accuracy of 10−10
.
Fig. 10. (a) Setup of the Doppler shift correction, mirror M, beam splitter BS, photo diode PD,
mixer MX, local oscillator LO, acousto-optical modulator AOM, proportional integral
controller PI; (b) controlling frequency
4 Summary and outlook
We have set up an in-house optical frequency distribution system which works for long time
and in principle, the accuracy of the frequency distribution system could be improved up to
10−18
by the implementation of an optical clock as prospective reference signal for the
frequency comb instead of the Hydrogen maser [18]. For the moment, the accuracy of the
frequency distribution system of 2 × 10−15
for 1000 s is much more than sufficient as the
demand for the two experiments is only 10−10
.
#112018 - $15.00 USD Received 27 May 2009; revised 6 Aug 2009; accepted 21 Aug 2009; published 8 Sep 2009
(C) 2009 OSA 14 September 2009 / Vol. 17, No. 19 / OPTICS EXPRESS 16859
Beyond this in-house distribution network, an extensive distribution network that will link
the Max-Planck-Institut für Quantenoptik (MPQ) to the Physikalisch-Technische
Bundesanstalt (PTB) in Braunschweig is now under construction. The target of the project is
the comparison of optical frequencies at distant places. In contrast to previous methods of
modulation techniques, the frequency of a cw signal at 195 THz (i. e. 1.55 µm) will be
directly transferred via a 900 km long glass fiber link. To achieve a projected accuracy better
than 10−18
several effects like damping, stimulated Brillouin scattering, polarization mode
dispersion, amplifier noise as well as thermal and acoustic impacts have to be taken into
account [19].
This accurate transfer of optical frequencies over those unprecedented distances of
hundreds of kilometers will make precision metrology in principle accessible to every
laboratory that is within the grasp of the new far-reaching fiber distribution system.
Acknowledgements
The helpful discussions with Thomas Udem are warmly acknowledged. We also would like to
thank Arthur Matveev and Janis Alnis for providing the data record of the Cesium clock and
Hydrogen maser measurements.
#112018 - $15.00 USD Received 27 May 2009; revised 6 Aug 2009; accepted 21 Aug 2009; published 8 Sep 2009
(C) 2009 OSA 14 September 2009 / Vol. 17, No. 19 / OPTICS EXPRESS 16860