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 OSA
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 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 . 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.
2.1 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 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.
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 (Symmetricon model 5071A). In the meantime, our system could even be improved by the introduction of a Hydrogen maser (CH1-75A, Stability: ). 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.
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 . The FP Allan deviation of this beat note reaches a minimum of 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.
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.
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.
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 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 . 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 -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).
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 . 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 .
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 .
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.
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  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 ).
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 
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, 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 ).
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.
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 equation. k is the wave number. is the ratio between refraction index change and temperature change and 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.
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.
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.
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 . 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.
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 .
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.
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.
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