March 15, 2004 / Vol. 29, No. 6 / OPTICS LETTERS 641

First international comparison of femtosecond laser combs atthe International Bureau of Weights and Measures

Long-Sheng Ma,* Lennart Robertsson, Susanne Picard, and Massimo Zucco†

Bureau International des Poids et Mesures, Pavillon de Breteuil, F-92312, Sèvres Cedex, France

Zhiyi Bi and Shenghai Wu

Department of Physics, East China Normal University, Shanghai 200062, China

Robert S. Windeler

OFS Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey 070974

Received August 6, 2003

The first international comparison of femtosecond laser combs has been carried out at the InternationalBureau of Weights and Measures (BIPM). Three comb systems were involved: BIPM-C1 and BIPM-C2 fromthe BIPM and ECNU-C1 from the East China Normal University (ECNU). The agreement among the threecombs was found to be on the subhertz level in the vicinity of 563 THz. A frequency difference measurementscheme was demonstrated that is suitable for general comb comparisons. © 2004 Optical Society of America

OCIS codes: 120.3940, 120.4800, 140.4050.

Femtosecond laser comb systems have become one ofthe most important tools in optical frequency metrol-ogy.1 – 4 The long-awaited possibility to link opticalfrequencies directly to primary frequency standardscan now be realized in a one-step phase-coherent way.It also provides the possibility for the use of narrowoptical transitions as the basis for future clocks andcreates, as a result, a potential for a redefinition ofthe SI second.

High performance has already been demonstratedand reported for such systems. A comparison wasmade at the Max-Planck-Institut für Quantenoptikbetween two optical frequency synthesizers by useof mode-locked Ti:sapphire lasers, in which a meandeviation from the expected beat frequency of 71 mHzwith uc � 179 mHz at 345 THz was obtained.5 JILAand the National Research Council of Canada madea comparison of optical frequency measurement,by use of a femtosecond laser comb and traditionalfrequency synthesis, respectively, by transferringan iodine-stabilized He–Ne laser at 633 nm fromBoulder to Ottawa.6 The agreement between thesetwo measurements, both linked to Cs standards, wasfound to be 220 Hz with uc � 770 Hz limited by theHe–Ne laser standard. A comparison was made inBoulder by JILA, the National Institute of Standardsand Technology (NIST), and the International Bureauof Weights and Measures (BIPM).7 The frequencymeasurement of the IR radiation at 1064 nm of aniodine-stabilized Nd:YAG laser was made at JILA andquasi-simultaneously at NIST. In this comparisonan optical fiber transferred the Nd:YAG laser emis-sion from JILA to NIST, and a second optical fibertransferred a hydrogen maser time base from NISTto JILA. The average frequency difference foundbetween the two combs was 0.74 Hz with uc � 3.4 Hz.Recently, NIST, JILA, and the BIPM made a directfrequency comparison between two combs set to the

0146-9592/04/060641-03$15.00/0

same repetition rate, synchronized in the time domain,and phase locked to a low-frequency-noise cw laser.The beat measurement demonstrated a frequency sta-bility of 6 parts in 1016 at 1-s averaging time, and theagreement between two combs was better than 4 partsin 1017 at 275–550 THz.8 This is a very sensitiveway of comparing combs, but it is less well adaptedto general comb comparisons because the repetitionrates need to be identical and time synchronization ofthe pulses is necessary.

Continuing efforts to investigate systematically theperformance and eventually the practical and funda-mental accuracy limits of this technique are essentialsince the comb is considered a key element in opticalfrequency metrology. However, because of the excep-tionally high accuracy that optical comb techniques canprovide, the use of transfer standards for comb verifi-cation would inevitably be limited by the standard it-self, which leaves direct comb comparisons as the onlypossibility for such investigations.

With the aim of initiating a program of internationalcomb comparison, a femtosecond laser comb from theEast China Normal University (ECNU), Shanghai,was brought by invitation to the BIPM in Marchof 2003, and the first international comparison offemtosecond laser combs at the BIPM was carried outwith three combs. The BIPM-C1 has been describedin detail elsewhere.9 The femtosecond laser in theBIPM-C1, comprising a four-mirror ring-type cavitywith a repetition rate of 740 MHz, is contained in asealed aluminum box. The photonic crystal f iber10

and the self-referencing setup were mounted on thesame optical table but without additional protection.The BIPM-C2 and ECNU-C1 combs are of similardesign and configuration and incorporate six-mirrorring-type cavity femtosecond mode-locked Ti:sapphirelasers with a repetition rate of �800 MHz. Theyprovide an output power near 500 mW when pumped

© 2004 Optical Society of America

642 OPTICS LETTERS / Vol. 29, No. 6 / March 15, 2004

by a 532-nm light source with 4.5 W of power. Foreach of these two last systems the femtosecond laser,the photonic crystal fiber, and the self-referencingsetup are all arranged in a single sealed aluminumbox with dimensions of 69 cm 3 23 cm 3 54 cm.

The experimental configuration for the comparisonis shown in Fig. 1. The repetition rate, frep, andcarrier-envelope offset frequency, fceo, of the combswere phase locked to rf synthesizers that in turnwere referenced to a hydrogen maser. All the digitalcounters were referenced to the same hydrogen maserthrough a rf distribution amplif ier. A measurementscheme was adopted, inspired by previous work,11,12

in which the frequency difference between two combsis directly obtained independent of the frequencycharacteristics of the test laser measured. An iodine-stabilized frequency-doubled Nd:YAG laser13 was usedto obtain the optical beat signal between the two fem-tosecond laser combs. The output beam at 1064 nmof the Nd:YAG laser was transferred to BIPM-C1through an optical fiber. A second fiber was used totransfer the 532-nm radiation from the Nd:YAG laserto the BIPM-C2 or ECNU-C1 systems. In the case ofthe BIPM-C2 comb the 532-nm laser light was beatingdirectly with the green part of the comb, whereas forthe ECNU-C1 the IR part of the comb was frequencydoubled and then used for the beat. The beat signalfb1 generated with the 1064-nm light was frequencydoubled to get 2fb1 by use of a rf frequency doubler.The subsequent mixing of 2fb1 and fb2 was made witha double-balanced mixer. Four digital counters wereemployed to measure fceo1, fceo2, 2fb1 1 fb2, and 2fb1.Measuring the common beat signal allowed a directoptical frequency comparison between the two combs.

Comparing the BIPM-C2 with BIPM-C1 and includ-ing the two beats arising between the Nd:YAG laserand the femtosecond laser combs allows the laser fre-quency to be written as

f1064 � 6fceo1 1 N1frep1 6 fb1 , (1)

f532 � 6fceo2 1 N2frep2 6 fb2 , (2)

which is illustrated in Fig. 1. Here f1064 and f532 arethe optical frequencies of the iodine-stabilized Nd:YAGlaser at 1064 and 532 nm, respectively, and 2f1064 �f532. The subscripts 1 and 2 indicate BIPM-C1 andBIPM-C2, respectively. The fceo and the frep are de-fined in the rf range, whereas the detected beat 2fb1 6fb2 is generated by two optical comb lines close to thefrequency of the cw laser used. If the two combs donot link the rf to the optical ranges in the same way,the quantity

d � 2f1064 2 f532

� 2�6fceo1 1 N1frep1� 2 �6fceo2 1 N2frep2�

6 2fb1 2 �6fb2� (3)

will differ from zero, where the integer numbers N1 andN2 can be determined from knowledge of the other pa-

rameters. An analogous relation is valid for the com-parison of BIPM-C1 and ECNU-C1, denoted by sub-script 3, but for which

f532 � 2�6fceo3 1 N2frep3� 6 fb3 , (4)

since the IR part of the comb ECNU-C1 was fre-quency doubled and used for the beat. As can beseen in Eq. (3), this method of comb comparison isindependent of the frequency of the Nd:YAG laserand consequently of the frequency drift and noise.Furthermore, since the combs beat indirectly throughthe cw laser, pulse synchronization of the two combsis not needed. This is of major importance since suchsynchronization would make comparisons far moreelaborate.

In total, 21 data recordings were made during fourdays with a total integration time of 18,300 s; 7 ofthe measurements were made between ECNU-C1and BIPM-C1 and the other 14 were made betweenBIPM-C2 and BIPM-C1. For these recordings thecounter gate time was 10 s, with recording timesfrom 450 to 1100 s. In Fig. 2 the results of thetwo different comparisons are depicted. Since thedurations of the data recordings differ by as much as

Fig. 1. Experimental configuration for the comparison offemtosecond laser combs BIPM-C1 and BIPM-C2 from theBIPM and ECNU-C1 from ECNU. DBM, double-balancedmixer.

Fig. 2. Compilation of the frequency differences foundbetween ECNU-C1 and BIPM-C1 (f illed diamonds) andBIPM-C2 and BIPM-C1 (circles). The separate compari-son averages are indicated as solid lines.

arch 15, 2004 / Vol. 29, No. 6 / OPTICS LETTERS 643

M

Fig. 3. Relative Allan deviation for the comb beat note d.

a factor of 2, a weighted mean was used to f ind thefinal averages. The frequency differences found wereDf �ECNU-C1 2 BIPM-C1� � 0.15 Hz, uc � 1.24 Hz,and Df �BIPM-C2 2 BIPM-C1� � 0.09 Hz, uc � 0.83 Hzfrom which Df �ECNU-C1 2 BIPM-C2� � 0.06 Hz withuc � 1.49 Hz is deduced. For comparison it can benoted that in relative terms 0.1 Hz corresponds to1.7 parts in 1016 for 532-nm radiation. The averagefrequency difference for each comparison is alsoindicated as a solid line in Fig. 2. No significantdifferences were found among the three comb systems.Including all 21 data points, the average differenceis 0.11 Hz with uc � 0.69 Hz. The stability of thecomb beat d for one recording is shown in Fig. 3.The short-term stability at a 10-s averaging time is5.5 parts in 1014. This agrees well with the stabilityof the frequency synthesizers used for the frep phaselocks. Indeed, when we integrate over 18,300 s—thetotal measurement time—the estimated stabilityreaches a value of 0.72 Hz, which is in close agree-ment with the observed uncertainty of the full dataseries at 0.69 Hz. Because this noise is specif ic toeach comb, it limits the noise level in the measure-ments and would demand long integration times if aneven lower uncertainty is sought. On the other hand,long integration times increase the risk of phase slipsand unstable counting that sets a practical limit onthe duration of the measurements. It is thereforeclear that the employment of frequency synthesizersof the lowest possible phase noise is crucial whenusing this method. To reduce further the detectableupper limit of systematic differences between twofemtosecond laser combs, the combs can be arrangedin an optical clock configuration.4,12 The stability ofthe comb frequency can hence be controlled by a cwlaser with low frequency noise.

In conclusion, the f irst international comparisonof femtosecond laser combs has been carried out atthe BIPM. A subhertz level of agreement amongthree combs has been demonstrated. The dominantnoise source stems from the rf synthesizers used forthe phase lock of the repetition rate. This factor,hampered by practical restrictions of the integration

time, limits the final precision of the experiment.The present method of comparing combs is indepen-dent of the frequency drift of the measured laser andhas no need of precise pulse synchronization. Thissimplifies the measurements, which confirms thismethod as an effective means for future internationalcomb comparisons.

The project at the ECNU is supported by the Scienceand Technology Commission of Shanghai Municipality(01DJGK014 and 022261033), the Shanghai MunicipalEducation Commission, the National Natural ScienceFoundation of China (10274020), and the Ministry ofEducation of China (02106). L.-S. Ma’s e-mail addressis lsmaecnu@yahoo.com.cn.

*Permanent address, Department of Physics, EastChina Normal University, Shanghai 200062, China.

†On leave from Consiglio Nazionale delle Ricerche—Istituto di Metrologia “Gustavo Colonnetti,” Stradedelle Cacce 73, 10135 Torino, Italy.

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