1. Introduction

The optical frequency comb has been an indispensable tool for precision optical frequency metrology [1] [2]. However, the most widely used Kerr-lens mode-locked Ti:sapphire laser systems are still rather bulky and expensive, and they require sporadic realignment, which prohibits the construction of a turnkey system. Furthermore, coupling into the photonic crystal fiber used to generate an octave-spanning optical comb is delicate and therefore requires bulky and sturdy mechanics and optics.

Recently, the mode-locked erbium-doped fiber (Er fiber) laser has attracted attention as a robust, compact and practical light source for generating an octave-spanning optical frequency comb. Its development trails slightly behind that of the Ti:sapphire laser-based comb. The first frequency measurement using a fiber-based frequency comb was reported in 2000 [3]. In 2003, observations and the phase locking of the carrier envelope offset frequency f _CEO signal were reported [4] [5] [6]. In 2004, the first absolute frequency measurement was demonstrated [7]. In the same year, a two-branch system and a two-octave spanning comb were described [8] [9]. In 2005, two fiber-based frequency comb systems were compared [10]. These systems have the potential to be operated continuously over long periods of time. Furthermore, combs based on Er fiber lasers are cost-effective and have a compact setup because their wavelength (1.5 µm) matches that of telecommunication bands. For these reasons, Er fiber lasers have been energetically investigated as regards their applicability to optical metrology.

This paper describes our fiber based frequency comb, which uses a simple mode-locked laser and a backward pumping amplifier combined with a highly nonlinear fiber with a short zero-dispersion wavelength. As a result, we obtain the highest signal to noise ratio (S/N) for an f _CEO beat signal as a fiber-based frequency comb. Furthermore, the excellent f _CEO beat enables us to undertake the long-term (more than one week) measurement of optical frequencies, which is the longest continuous measurement yet reported.

2. Setup of robust and low-noise fiber-based frequency comb system

Figure 1 shows a diagram of our fiber laser system, which includes an Er fiber oscillator, amplifiers, a highly nonlinear fiber (HNLF), an f _CEO detection part and a beat detection part. The Er fiber oscillator is a ring resonator that employs nonlinear polarization rotation as the mode-locking mechanism. Most fiber laser oscillators have four wave plates and a polarizer in the laser cavity [11]. In such cases, it takes some time to align the four wave plates to start the mode-locking operation. On the other hand, two polarizers are used in our cavity [12]. In this work, we install an in-line polarization controller containing a half lambda plate and a quarter lambda plate in the cavity to ensure its mode-locking operation. Nevertheless our cavity has only three polarization control plates, which significantly reduces the difficulty of the mode locking.

 

Fig. 1. Diagram of our fiber laser system. PSI: Polarization sensitive isolator, PII: Polarization independent isolator, λ/4 and λ/2: quarter and half lambda plates, PL: Polarizer, HNLF: Highly nonlinear fiber, L: Lens, PPLN: Periodically poled lithium niobate, PD: Photo detector, M: Mirror, HM: Half mirror, BPF: Optical bandpass filter

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The oscillator is pumped by a 1480 nm laser diode via a wavelength division multiplexing (WDM) coupler. The pump power is typically 45 mW. The spectral bandwidth (FWHM) and the repetition rate f _rep of the laser are 40 nm and 54 MHz, respectively. The Er fiber in the laser cavity is approximately 1 m long and wound on a drum-type piezo actuator (PZT) to stabilize f _rep. The peak absorption at 1530 nm and the mode field diameter at 1550 nm of the Er fiber are 40±4 dB and 6.5±0.5 µm, respectively. The net dispersion of the oscillator cavity is estimated to be -0.006±0.01 ps². The PZT allows us to tune f _rep over a range of approximately 200 Hz. 30% of the circulating power is coupled out of the cavity and distributed equally to two parallel amplifiers [8]. The total output power is approximately 2 mW. The oscillator is temperature controlled to within 10 mK with Peltier devices, which is important in terms of keeping f _rep and f _CEO stable. A polarization independent isolator is inserted between the oscillator and the two-branch amplifiers.

Each Er fiber amplifier is pumped by a 980 nm laser diode from its output side with a power of 200 mW (backward pumping only). The length, peak absorption at 1530 nm, and the mode field diameter at 1550 nm of the Er fiber are 4 m, 20±2 dB, and 6.5±0.5 µm, respectively. The first amplifier is used to detect f _rep and f _CEO. The second amplifier is used to detect the beat note f _beat between the frequency comb and a frequency-stabilized laser. A half lambda plate and a quarter lambda plate are inserted between the oscillator and each amplifier to enhance the comb components at a desirable wavelength in the super continuum. Each amplifier generates an average output power of 45 mW, corresponding to a pulse energy of 0.9 nJ. Several tens of centimeters of single mode fiber (SMF) is inserted between the amplifier and the HNLF to compensate for the chirp generated in the amplifier. The oscillator and amplifiers have an all-fiber configuration.

A 20 cm non-polarization-maintaining HNLF [13] is spliced to the output of the first amplifier. The zero dispersion wavelength and nonlinear coefficient γ of this HLNF are 1447 nm and 21/W/km, respectively. The output continuum from the HNLF covers a wavelength range of 1000 nm to more than 2050 nm, and is used to detect f _rep and f _CEO. As regards the second amplifier, the configuration is changed with the measured laser. We use a 30 cm length of HNLF to measure 1542 and 1064 nm lasers. A 2 GHz bandwidth InGaAs PIN photodiode is used to detect f _rep. The 16th harmonic frequency 863 MHz is filtered, amplified and used to stabilize f _rep with a previously reported method [14] to transfer the high short-term frequency stability of the hydrogen maser which is the microwave reference in this study.

 

Fig. 2. RF spectrum measured after the f-to-2f interferometer. The resolution bandwidth is 100 kHz.

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We employ a common-path interferometer [7] to obtain robust and simple f _CEO detection. The entire generated continuum is launched into periodically poled lithium niobate (PPLN) crystal with an aspheric lens; the component at 2020 nm is doubled and mixed with the component at 1010 nm. The optical paths for 1010 and 2020 nm are compensated with a 15 cm single mode fiber after the HNLF. A 1010 nm optical bandpass filter is inserted to eliminate other wavelength components of the comb. A 125 MHz bandwidth InGaAs PIN photodiode is used to detect the f _CEO beat. As a result, long-term f _CEO detection is achieved without any difficult alignment procedure. We were able to observe an excellent f _CEO beat for more than three months.

As shown in Fig. 2, we were able to obtain a signal to noise ratio of 45 dB at 100 kHz RBW in the f _CEO beat detection by using this configuration. The full width at half maximum of the f _CEO beat was approximately 200 kHz. The small spike at 38 MHz is the second harmonic of the f _CEO beat at 19 MHz. Small peaks appear at 3, 13, 22, 32, 41 and 51 MHz when the pump power of the amplifier is high, and the frequencies of these signals move with the f _CEO beats. We consider the small peaks to be beat notes between the comb modes and the amplified spontaneous emission (ASE) that exists on the longitudinal modes of the oscillator cavity.

The f _CEO stabilization was realized by feedback controlling the pump power for the fiber laser oscillator. In the feedback loop, the f _CEO signal was filtered at around 10.7 MHz, amplified and divided by 1000. The standard deviation of the f _CEO was 9.3 Hz with 1 s averaging and 1.1 Hz with 10 s averaging, which are sufficiently small values for this measurement.

We found that additional pumping of the amplifier in the forward direction increases the noise floor [15] during the f _CEO beat detection. In addition, when using only forward pumping, we were able to obtain a signal to noise ratio of approximately 40 dB, and we observed that additional pumping of the amplifier in the backward direction increased the noise floor. In this experiment, we used an HNLF with a short zero-dispersion wavelength (1447 nm) [13] to broaden the continuum towards a short wavelength with only backward pumping. Therefore, it is possible to detect an f _CEO beat in the 1000 nm region with pulse amplification solely by backward/forward pumping. This intrinsically stable and high S/N f _CEO beat is very important as regards the realization of long-term frequency stabilization.

3. Long-term measurement of 1542 nm acetylene-stabilized lasers and 532 nm iodine-stabilized lasers

We have developed 1542 nm acetylene-stabilized lasers as an optical frequency standard in the telecommunication band [3] [16] and have reported the absolute frequency [7] [17] [18]. In the present experiment, we measured a commercially available laser (Neoark, model C2H2LDS-1540; denoted as A4) based on our design with a fiber based frequency comb. The operating parameters and characteristics of the A4 laser system are the same as those for the measurement described in ref. 18. The beat note between the frequency stabilized laser and the optical comb was detected with a 125 MHz bandwidth InGaAs PIN photodiode. The S/N of the beat note was 40 dB at a 100 kHz bandwidth, which is sufficient to measure its frequency properly.

With the measured beat frequency f _beat between the frequency comb and the measured laser, the frequency of the measured laser (f _laser) can be expressed as f _laser=n×f _rep±f _beat±f _CEO. The signs of f _CEO and f _beat are determined by checking the increase or decrease in f _beat when f _rep or f _CEO is increased when f _CEO or f _rep is locked, respectively. The mode number n is determined when the optical frequency of the stabilized laser is known with an uncertainty that is much smaller than the f _rep. In addition, n can be determined by an independent method [19]. In this experiment, we determine n by using the former approach.

We employ ratio counting to verify the cycle slip in the fbeat counting. The f _beat signal was filtered, amplified and divided into three signals. One of these signals was frequency-divided by 10 and used for the ratio counting. One of the remainder was also used for ratio counting and the last signal was used for frequency counting. If all the counters and frequency dividers perform properly the result should be exactly 10. We measured f _rep, f _beat, f _CEO and the frequency ratio for f _beat synchronously by using four frequency counters (Agilent 53132A) and an external signal for the synchronization. The measured f _rep was used to monitor the f _rep locking. In the frequency calculation, we used the f _rep value set for the synthesizer. We excluded the cycle-slipped data, which denote the extraordinary ratio counting value.

 

Fig. 3. Measured frequency of the 1542-nm acetylene-stabilized laser A4 over a period of 1 week.

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Figure 3 shows the measured frequency of A4. The data are a sequence with a 10-s averaging frequency. 41 cycle-slipped data were excluded although these beat frequencies seemed proper. The data gap of 5 hours is the result of a forced restart of the computer used for the data accumulation caused by an automatic security upgrading of the operating system. The fiber-based frequency comb and the acetylene-stabilized laser continued working during the interruption.

The mean and standard deviations of the sequence after the interruption were 194 369 569 386.08 kHz and 0.36 kHz, respectively, which are consistent with our previous results [3] [7] [17] [18] and the differences from results obtained in other laboratories [20] [21] [22] are within 5 kHz. The undulations observed in the curves of the frequency plots were limited by the long-term stability of the acetylene-stabilized laser. Figure 4 shows the corresponding Allan standard deviation calculated from the sequence with the 10-s averaging frequency. The instability of A4 was 1.7×10^-12 for a 10-s averaging time, improving to 1×10^-13 for 4000 s and an increase in the deviation was observed for more than 10000 s.

 

Fig. 4. Allan deviation of the measured frequency of the acetylene-stabilized laser calculated from the sequence with the 10-s averaging frequency. Each value at more than 20-s averaging may not be proper Allan deviation [23].

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Next, we measured the optical frequency of a 532-nm iodine-stabilized Nd:YAG laser. We have developed iodine-stabilized Nd:YAG lasers and have already reported their frequencies [24] [25]. In this study, one of the four frequency stabilized lasers (denoted Y3) was measured with the comb. The operating parameters and characteristics of the laser system Y3 are same as those used for the measurement reported in ref. 25. The heterodyne beat-note signal between the laser and the comb was measured at 1064 nm (the fundamental laser frequency). The beat note between the stabilized laser and the comb was detected with a 125 MHz bandwidth InGaAs PIN photodiode. The S/N of the beat note was 35 dB at a bandwidth of 100 kHz, which is sufficient to measure its frequency properly without a tracking filter. The measurement scheme was the same as that employed for the acetylene-stabilized laser.

Figure 5 shows the measured frequency of Y3. The data are a sequence with a 10-s averaging frequency. No cycle-slipped data were found for more than one week. The mean and standard deviations of the sequence for 8 days were 563 260 223 505 857 Hz and 42 Hz, respectively. In Fig. 5, an almost imperceptible frequency drift can be recognized. The linear fitted line of the frequency sequence has a slope of approximately -24 Hz/week. We have also observed a frequency drift of approximately -740 Hz/year for Y3 during the past 2.5 years using different Ti:sapphire and fiber combs, which corresponds to -14 Hz/week. This small frequency drift of the iodine-stabilized Nd:YAG laser will be investigated further with the fiber comb.

 

Fig. 5. Measured frequency of the 532 nm iodine-stabilized Nd:YAG laser Y3 over a period of 8 days.

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Fig. 6. Allan deviation of the measured frequency of the iodine-stabilized Nd:YAG laser. The deviations of 1 s (red circle) and 3 s (blue circle) were measured independently (757 points for 1-s averaging and 103 points for 3-s averaging). The Allan deviations at more than 10-s averaging are calculated from the sequence with the 10-s averaging frequency. Each value at more than 20-s averaging may not be proper Allan deviation [23].

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Figure 6 shows the corresponding Allan standard deviation calculated from the sequence with a 10-s averaging frequency. The deviations for 1- and 3-s averaging were independently measured. The stability of Y3 was 2.8×10^-13 for a 1-s averaging time, a factor of two or three higher than our hydrogen maser reference (1×10^-13). We consider the stability to be primarily limited by that of the iodine-stabilized Nd:YAG laser. The stability improved to 5.7×10^-15 after 100 000 s, before reaching the flicker floor. This is the first time for us to observe the instability of Y3 below 10^-14. The limitation came from the instability of other frequency-stabilized lasers used in the heterodyne beat measurement in the previous experiment. The extremely robust and stable long-term operation of the fiber based frequency comb revealed the instability of Y3 at 10^-15.

4. Conclusion

We have presented a new design for a fiber-based frequency comb system consisting of a simple Er fiber laser oscillator, low-noise Er fiber amplifiers, short zero-dispersion HNLF and a further simplified common-path f-to-2f interferometer. This system enables us to obtain an excellent f _CEO beat and extremely long-term optical frequency measurement.

By using the fiber-based frequency comb, we demonstrated continuous frequency measurement without interruption that lasted more than one week. The long-term measurement of an iodine-stabilized Nd:YAG laser revealed its long-term stability of 5.7×10–15 with 100 000 s averaging. In addition, the measurement scheme can be easily and immediately extended to any IR wavelength region (1 to 2 µm).

On the other hand, fiber based combs show intrinsic phase noise compared with Ti:sapphire lasers in the linewidth of their f _CEO beat signal. However, their stability limitation originating from the phase noise has not yet been reported in a frequency measurement experiment. We believe the fiber-based frequency comb is an appropriate tool with which to link optical and microwave frequencies for optical clocks.

Recent developments on optical clocks mean that they have the potential to be established as the next generation time standards. This will require a comparison of the optical clock and international time scale (TAI) frequencies. Currently, 5 days are required for the comparison in order to obtain a fractional resolution of 10^-15. Therefore, a fiber-based frequency comb that works for more than one week provides an effective choice for frequency comparison.