Direct comparison of optical frequency combs using a comb-injection-lock technique

Direct comparison of optical frequency combs using a comb-injection-lock technique E. B. Kim, W. -K. Lee, C. Y. Park, D. -H. Yu, S. K. Lee, and S. E. Park* Division of physical Metrology, Korea Research Institute of Standards and Science, 1 Doryong-Dong, Yuseong-Gu, Daejeon 305-340, Korea [email protected]

Abstract: This paper demonstrates a direct comparison of optical frequency combs (OFCs) with different repetition rates without a stable intermediate laser using a single-mode comb-injection-lock technique. Two OFCs based on Ti:Sapphire mode-locked lasers were compared utilizing a single-mode diode laser for the selection and the amplification of one mode of an OFC by comb-injection, which makes the direct comb comparison possible. The frequencies of the two combs were found to agree within 0.019 Hz at 352 THz with the uncertainty of 0.25 Hz (7.1 × 10−16 ). This is one of the best results among the comparisons of combs referenced to a microwave frequency. This technique simplifies the comb comparison utilities and can be applied even when repetition rates differ. © 2008 Optical Society of America OCIS codes: (120.0120) Instrumentation, measurement, and metrology; (140.7090) Ultrafast lasers; (140.3520) Lasers, injection-locked; (140.2020) Diode lasers.

References and links 1. A. D. Ludlow, T. Zelevinsky, G. K. Campbell, S. Blatt, M. M. Boyd, M. H. G. de Miranda, M. J. Martin, J. W. Thomsen, S. M. Foreman, J. Ye, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, Y. Le Coq, Z. W. Barber, N. Poli, N. D. Lemke, K. M. Beck, C. W. Oates, “Sr lattice clock at 1 × 10−16 fractional uncertainty by remote optical evaluation with a Ca clock,” SCIENCE 319, 1805–1808 (2008). 2. M. M. Boyd, A. D. Ludlow, S. Blatt, S. M. Foreman, T. Ido, T. Zelevinsky, and J. Ye, “87 Sr lattice clock with inaccuracy below 10−15 ,” Phys. Rev. Lett. 98, 083002 (2007). 3. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100, 013902 (2008). 4. S. Bize, S. A. Diddams, U. Tanaka, C. E. Tanner, W. H. Oskay, R. E. Drullinger, T. E. Parker, T. P. Heavner, S. R. Jefferts, L. Hollberg, W. M. Itano, and J. C. Bergquist, “Testing the stability of fundamental constants with the 199Hg+ single-ion optical clock,” Phys. Rev. Lett. 90, 150802 (2003). 5. R. Holzwarth, Th. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. St. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85, 2264–2267 (2000). 6. J. Ye, J-L. Peng, P. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L-S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20, 1459–1467 (2003). 7. L.-S. Ma, L. Robertsson, S. Picard, M. Zucco, Z. Bi, S. Wu, and R. S. Windeler, “First international comparison of femtosecond laser comb at the International Bureau of Weights and Measures,” Opt. Lett. 29, 641–643, (2004). 8. P. Kubina, P. Adel, F. Adler, G. Grosche, T. W. Hansch, R. Holzwarth, A. Leitenstorfer, B. Lipphardt, and H. Schnatz, “Long term comparison of two fiber based frequency comb systems,” Opt. Express 13, 904–909, (2005). 9. S. A. Diddams, L. Hollberg, L.-S. Ma, and L. Robertsson, “Femtosecond-laser-based optical clockwork with instability ≤ 6.3 × 10−16 in 1 s,” Opt. Lett. 27, 58–60 (2002). 10. L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10−19 level,” SCIENCE 303, 1843–1845 (2004).

11. L.-S. Ma, Z. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “International comparisons of femtosecond laser frequency combs,” IEEE Trans. Instrum. Meas. 54, 746–749 (2005). 12. L.-S. Ma, Z. Bi, A. Bartels, K. Kim, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, and S. A. Diddams, “Frequency uncertainty for optically referenced femtosecond laser frequency combs,” IEEE J. Quantum Electron. 43, 139–146, (2007). 13. H. S. Moon, E. B. Kim, S. E. Park, and C. Y. Park, “Selection and amplification of modes of an optical frequency comb using a femtosecond laser injection-locking technique,” Appl. Phys. Lett. 89, 181110 (2006). 14. S. E. Park, E. B. Kim, Y-H. Park, D. S. Yee, T. Y. Kwon, C. Y. Park, H. S. Moon, T. H. Yoon, “Sweep optical frequency synthesizer with a distributed-Bragg-reflector laser injection locked by a single component of an optical frequency comb,” Opt. Lett. 31, 3594–3596 (2006). 15. H. S. Moon, S. E. Park, and E. B. Kim, “Coherent multi-frequency optical source generation using a femto-second laser and its application for coherent population trapping,” Opt. Express 19, 3265–3270 (2007). 16. Y-J. Kim, J. Jin, Y. Kim, S. Hyun, and S-W. Kim, “A wide-range optical frequency generator based on the frequency comb of a femtosecond laser,” Opt. Express 16, 258–264 (2008). 17. E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76, 054703 (2005). 18. S. T. Dawkin, J. J. McFerran, and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 53, 918–925 (2007). 19. Th. Udem, J. Reichert, T. W. Hansch, and M. Kourogi, “Absolute optical frequency measurement of the cesium D2 line,” Phys. Rev. A. 62, 031801(R) (2000). 20. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency reference via fiber networks,” Rev. Sci. Instrum. 78, 021101 (2007). 21. W-K. Lee, J. W. Kim, H-Y. Ryu, and E. B. Kim, “Active cancellation of phase noise induced by an optical fiber for delivery of optical frequency standard,” Hankook Kwanghak Hoeji, 18, 44–49 (2007).

1.

Introduction

OFCs based on mode-locked femtosecond lasers stabilized to microwave or optical frequency standards have been used in a variety of fundamental applications. These include absolute optical frequency measurements [1, 2], high-resolution spectroscopy [3], and in the determination of fundamental physical constants [4]. As these applications demand very high accuracy levels, there have been continuing efforts to investigate the practical and fundamental accuracy limits of the OFC technique via comparisons of comb frequencies [5, 6, 7, 8, 9, 10, 11, 12]. The experimental accuracy-test limit for the comb comparison is basically dependent upon two factors: the stability of the frequency reference for the stabilization of the comb and the total data acquisition time. A more stable frequency reference implies that a shorter averaging time is required to reach a specified uncertainty level. Although a relatively long averaging time is required for a lower level of uncertainty, there is practical limit to the data acquisition time due to the possibility of phase slips and unstable counting. The comb comparison results can be divided into two groups according to the frequency reference: a comparison between combs referenced to a microwave frequency and that between combs referenced to an optical frequency. The former comparison method [5, 6, 7, 8] is performed by measuring the frequency of a common optical radiation independently by two combs referenced to a common microwave frequency such as that of a hydrogen maser (H-maser), a Cs atomic clock, and a quartz oscillator. The frequency stability of the intermediate laser to be measured by combs must be better than that of the microwave reference in order to reach a low uncertainty level in a short time. Holzwarth et. al. [5] compared two Ti:Sapphire-based frequency combs referenced to a quartz oscillator with an uncertainty of 5.1 × 10−16 . Ye et. al. [6] measured a 1064 nm Nd:YAG laser quasi-simultaneously at JILA and at NIST using an optical fiber network connecting these two institutes. The two measurements agreed in 0.74 Hz with an uncertainty of 3.4 Hz (1.2 × 10−14 ) with a 100-s gate time. The frequency reference for the JILA comb was provided by a fiberdelivered H-maser signal. Ma et. al. [7] made the first international comparison of femtosecond laser combs using an H-maser as the frequency reference. The agreement among the three combs in their comparison was found to be on the sub-hertz level at 563 THz. Kubina et.

al. [8] compared two mode-locked erbium-doped fiber lasers referenced to an H-maser. The two measurements agree within 6 × 10−16 . Summarizing these results, the comparison of the uncertainty of the combs referenced to a microwave frequency with a typical stability of 10−13 at the gate time of 1s (in case of an H-maser) is in order of 10−15 ∼ 10−14 when 1-s-averaged data are used and is in order of 10−16 when 100 ∼ 1000-s-averaged data are used. In the latter comparison method [9, 10, 11, 12], the frequency comb is stabilized to an optical frequency in an optical clock configuration utilizing the excellent stability (order of 10−15 ) of a CW laser at optical frequency (locked to a supercavity) to decrease the upper limit for accuracy level of the comparison. Referencing to this optical standard provides improved stability and allows shorter averaging times, leading to lower uncertainty. However, the mode spacing of two combs, i.e., the repetition rate, should be identical or nearly identical to ensure a valid comparison using this method. Diddams et. al. [9] compared two octave-spanning Ti:Sapphirebased combs with identical repetition rates and that were both phase-locked to a low-frequencynoise diode laser. They demonstrated that the intrinsic fractional frequency noise of a comb is ≤ 6.3 × 10−16 with 1 s of averaging. Ma et. al. [10, 11, 12] compared optically referenced Ti:Sapphire laser frequency combs at a relative frequency uncertainty level as low as 8 × 10−20 . To reach this accuracy level, they averaged the data over 76000 s, enclosed the beam path, and arranged the optical path of two combs to have better common path rejection, as the mechanical and thermal fluctuations along the light path are a factor at this level of accuracy. In the present study a new experimental technique for a direct OFC comparison is introduced. Two Ti:Sapphire-based frequency combs are compared utilizing the recently developed singlemode comb-injection-lock technique [13, 14, 15, 16]. They have different repetition rates (1.05 GHz and 200 MHz) and are stabilized to an H-maser. A diode laser is injection-locked to one of the frequency comb modes enabling the direct comb comparison due to the single-mode selection and amplification ability with the consequence of a high signal-to-noise ratio of the optical heterodyne beat between two combs. An intermediate laser with superior frequency stability is unnecessary when using this method. Furthermore, using this novel scheme, a comparison between OFCs stabilized to an optical frequency does not require that the repetition rates of the two combs to be identical. This technique greatly simplifies the comb comparison utilities and is expected to be widely applied in OFC comparisons. The proposed comb comparison method was performed at a remote site. For the remote comb comparison, the output of a single-mode DBR diode laser injection-locked to one of the comb modes is transferred to the remote site where the second frequency comb is located through a single-mode fiber network. The frequency difference between the two combs using the weighted mean was found to be −0.019 ± 0.25 Hz at 352 THz with a relative uncertainty of 7.1 × 10−16 . This is one of the best results among comparisons of combs referenced to a microwave frequency. 2.

Experimental setup

Figure 1 shows the experimental setup for the direct comparison of OFCs using a single-mode comb-injection-locked diode laser. A femtosecond laser frequency comb (OFC1) based on a mode-locked Ti:Sapphire laser was used as a master laser for the comb-injection-lock process. The center wavelength of the OFC1 was 830 nm with a 50 nm spectral width and a repetition rate of approximately 1.05 GHz. An H-maser in the microwave domain as a reference frequency is used for the phase-locking of the repetition rate ( frep1 ) and the carrier-envelopeoffset frequency ( fceo1 ), which are the two degrees of freedom of the OFC1. A part of the OFC1 output was used during the comb-injection-lock process and the remainder of that was used for the detection of fceo1 using the f-to-2f method with the help of a photonic crystal fiber (PCF) for broadening of the comb spectrum. A single-mode distributed-Bragg-reflector (DBR) laser applied as a slaver laser had a wavelength of approximately 852.3 nm near the Cs D2 line. The

OI

DBR laser

Saturated absorption spectroscopy

BS

λ/2

λ/2 IF M

OFC1

OFC2

M SMF

Counter H-maser λ/2 M λ/2

PBS λ/2 PBS PD

Fig. 1. Experimental setup for the direct comb comparison using a single-mode combinjection-locked DBR laser. (OFC1: optical frequency comb 1 with the repetition rate of 1.05 GHz, OFC2: optical frequency comb 2 with the repetition rate of 200 MHz, M: mirror, IF: interference filter, OI: optical isolator, SMF: a 250-m-long single-mode fiber, PD: fast photodiode, PBS: polarizing beam splitter, BS: beam splitter) 0.8

Signal (a.u.)

Locking range

0.6

0.4 F=4

F'=3 F=4

0.2

0.0

10.0

F'=4 F=4

10.2

10.4

10.6

10.8

F'=5

11.0

11.2

Injected current of DBR laser (a.u.) Fig. 2. Saturated absorption spectra of the cesium D2 line as a function of the slave DBR laser frequency detuned by varying the supply current.

available output power was 150 mW, but it was typically operated at a power level around 50 mW for this experiment. An 852.3-nm interference filter (IF) with a full width at half-maximum of 1.5 nm was used to select the comb modes near the Cs D2 line and to prevent the optical damage to the slave laser. After passing through the IF, the number of transmitted modes was approximately 600 with a total power of approximately 200 µ W, which corresponds to 300 nW per mode. According to the comb-injection-lock process, a single mode of OFC1 was selected and the mode power was amplified to be 50 mW. A saturated absorption spectroscopy (SAS) setup in a Cs vapor cell was applied in order to confirm the single-mode injection locking and to determine the mode number of the selected mode of OFC1, as shown in Fig. 2. In this experiment, the hyperfine component F = 4 → F 0 = 4 of the Cs D2 line was used for the single-mode

injection locking of OFC1. Saturated absorption peak for the F = 4 → F 0 = 4 transition line remains unchanged since the DBR laser is injection-locked to the comb teeth positioned at a frequency that corresponds to F = 4 → F 0 = 4 of Cs D2 line. The locking range could be controlled by tuning the injection power levels, and the stability limit of the injection locking was found to be approximately 2.3 × 10−16 at a sampling time of 1 s. The experimental details of the comb-injection-lock process can be found in the literature [14]. For a direct comb comparison, output of the comb-injection-locked diode laser, which is essentially phase-coherently selected and amplified OFC1 output, was transferred to a nearby building where the OFC2 was located via a 0.25-km single-mode fiber network. OFC2, located at a remote site, had a center wavelength of 800 nm with a spectral width of 50 nm and a repetition rate of nearly 200 MHz. The repetition rate ( frep2 ) and the carrier-envelope offset frequency ( fceo2 = 20 MHz) of the OFC2 were phase-locked to the same H-maser that was used for the OFC1. To compare the frequency of the two OFCs, the frequency of the selected mode of OFC1 was measured by OFC2 via the optical heterodyne technique. The output spectrum of OFC2 was broadened by another PCF to measure fceo2 and to cover the wavelength range of the fiber-transferred single mode of the OFC1 (852.3 nm). The heterodyne beat signal ( fbeat ) between the selected single mode of OFC1 and that of the spectrally broadened OFC2 were detected using a high-speed photo detector with a signal-to-noise ratio of more than 30 dB in the spectrum analyzer resolution bandwidth of 300 kHz. The beat frequency was measured using a typical high-resolution “Λ-type” frequency counter (HP 53132A) [17, 18]. 3.

Results and discussion

The optical frequency of the comb-injection-locked DBR laser is given by the frequency of the OFC1 as [9] fn1 = n1 × frep1 ± fceo1 (1) Here, n1 is an integer and the selected mode number of OFC1, frep1 is the repetition rate corresponding to the spacing of the comb lines of OFC1. Additionally, fceo1 is the carrierenvelope-offset frequency that results from the difference between the phase and group velocity of the femtosecond pulse inside the laser cavity. In order to determine the mode number of n1 , The optical frequency of F = 4 → F 0 = 4 transition ( f4→40 ) of the Cs D2 line was used, as shown in Fig. 2. The n1 value can be clearly determined as it is an integer near the value of ( f4→40 ± fceo1 )/ frep1 ≈ f4→40 / frep1 where the f4→40 value is given with an accuracy of 100 kHz as explained in a recent study [19]. In this experiment, the active cancellation of the frequency (phase) noise introduced during the transmission of injection-locked optical frequency over the fiber network was not attempted [20]. According to a previous experiment by the authors, the transfer instability of the 250-m-long fiber network was measured as approximately 2 × 10−15 at a one-second averaging time even when the fiber-induced noise was not compensated [21]. Thus, the frequency instability caused by the fiber transmission can be ignored because the OFC1 is referenced to a H-maser with a stability of 2 × 10−13 at an averaging time of 1 s. For the direct comb comparison, the optical frequency of the transmitted single-mode of OFC1 was measured using the heterodyne beat signal ( fbeat ) between OFC1 and OFC2. Thus the measured optical frequency can be written as [7]: fn2 = n2 × frep2 ± fceo2 = fn1 ± fbeat

(2)

Here, frep2 and fceo2 are the repetition rate and the carrier-envelope-offset frequency of OFC2, respectively. n2 is the mode number of OFC2 near the hyperfine component F = 4 → F 0 = 4 of the Cs D2 line [19].

Table 1. Measurement summary of the frequency difference between OFC1 and OFC2.

Allan deviation 1.28 ×10−13 5.50 ×10−14 1.39 ×10−14 7.83 ×10−15

Allan deviation (σy(τ))

10

Weighted mean of comb frequency difference 0.41 ± 1.12 Hz -0.59 ± 0.58 Hz 0.04 ± 0.37 Hz 0.17 ± 0.45 Hz

-12

Relative uncertainty 3.2 ×10−15 1.6 ×10−15 1.0 ×10−15 1.3 ×10−15

Approved readings 1786 1000 322 68

Rejected readings 25 9 1 1

80

(b)

(a) 60

10

-13

10

-14

10

Occurrences

Gate time 1s 3s 10 s 30 s

1/τ

-15

1

10

Gate time (τ)

100

40

20

0 -150 -120 -90 -60 -30

0

30

60

90 120 150

Frequency differnece (Hz)

Fig. 3. (color online) (a) Measured Allan deviation derived from the beat frequency between selected single mode of OFC1 and stabilized OFC2. (b) The distribution of a sample data set of frequency difference with a gate time of 1 s after some bad data, which those are outside of three times of standard deviation, are removed. The curve fit is for the normal distribution.

The comb frequency difference was measured in 24 data sets in total with counter gate times of 1, 3, 10, and 30 s. The weighted mean of the frequency difference for the respective gate time is summarized in Table 1. Figure 3(a) show the Allan deviation for gate times of 1, 3 10, and 30 s. The short-term stability at a counter gate time of 1 second is 1.3 parts in 1013 and the Allan deviation is decreases as the inverse counter gate time. As there were a small number of bad data points that were possibly caused by the cycle slips or the abrupt polarization changes in the course of the fiber transmission, a few bad data points were removed from the original data. The discard criterion adopted for this was 3σ , which implies that data points originally located beyond three standard deviations were removed. This procedure is acceptable, as the resultant data distribution adheres to a normal distribution curve, as shown in Fig. 3(b). Finally, the weighted mean of the difference frequency with the total data set was calculated as (−0.019 ± 0.25) Hz with a total acquisition time of 10046 seconds. This shows that the frequencies of two combs agree with a relative uncertainty of 7.1 × 10−16 at 352 THz. 4.

Conclusion

A direct remote OFC comparison with a selected single mode of stabilized optical comb modes was demonstrated using a comb-injection-lock technique. Two OFCs with different repetition rate frequencies stabilized to a microwave reference frequency were compared using the proposed technique. One of the combs was used as a master laser, and a single-mode DBR diode laser was used as a slave laser for the selection and amplification of one comb mode. The frequencies of the two combs were shown to agree within 0.019 Hz at 352 THz with an uncertainty of 0.25 Hz (7.1 × 10−16 ). With a simple experimental setup, this study obtained one of best comb comparison results among comparisons between combs referenced to a microwave frequency. This result is limited by the stability of the reference provided by an H-maser. This

novel technique is expected to be applied widely with greater convenience as it does not require a stable intermediate laser and because it allows OFCs with different repetition rates to be compared.