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We demonstrated the synchronization of offset and repetition frequency between two independent Yb-doped fiber mode-locked lasers by injection locking. By injecting master-laser pulse-train into slave laser cavity, stability and accuracy of master frequency comb are transferred to slave comb. Passive stabilization of frequency comb offers robust and convenient way to duplicate frequency comb that can be applied to long-distance comb transfer. Injecting master pulse would also help to initiate and stabilize mode-locking of high repetition rate or ultrabroadband frequency combs. Additionally, we also demonstrated even more robust synchronization of combs can be achieved with the help of active stabilization of relative offset frequency difference.
© 2012 Optical Society of America
1. Introduction
The output of a mode-locked laser forms a comb of optical frequencies with a spacing set by the laser repetition frequency frep, and the offset from zero, f0, set by the carrier-envelope offset (CEO) frequency. Frequency combs have been applied to optical clocks, precision spectroscopies, length metrology, and the generation of stable microwaves [1]. Recently, frequency combs have been extended to XUV [2, 3] and mid-infrared regimes [4, 5].
Some applications require very precise control and manipulation of comb parameters such as offset frequency and/or repetition rate. For example, dual comb spectroscopy has been investigated as a powerful spectroscopic method to rapidly characterize broadband molecular or atomic absorption lines with comb resolution [6,7]. In this method, the frequency jitter of comb modes has to be minimized to obtain high sensitivity with good signal to noise ratio [8]. When comb is applied to astronomical applications to give a calibrated reference, absolute frequency of comb lines has to be referenced to some radio frequency reference that assures long-term-stable calibration over some years [9, 10]. Such precise control of frequency comb parameters sometimes requires sophisticated feedback techniques that may be technically demanding and expensive in cost. After sufficient effort is made to construct such stable frequency comb, it would be helpful and convenient if one can copy or transfer its stability and accuracy to some other frequency combs in a simple way without duplicating entire feedback system for each lasers. For this aim, we demonstrate passive synchronization of offset and repetition frequencies between two mode-locked lasers in this work. This can be applied to transfer comb stability and accuracy of “master” laser towards numbers of “slave” lasers that may be located in the place where sophisticated stabilization by state-of-the-art RF reference is hard to reach.
To synchronize both repetition and offset frequencies passively, we focus on the injection locking. Injection locking is a common technique to effectively amplify the power of the weaker master laser by making a higher-power slave laser to oscillate in phase with the master laser. Using two mode-locked lasers whose gain media are different, passive synchronization of only repetition frequency has been demonstrated [11–15], and relative timing jitter of those synchronized lasers is characterized to be as good as a few fs [13–15]. For synchronization of two lasers that have overlap between those spectra, Betz et al. observed the synchronization of both repetition and offset frequencies between two Ti:sapphire lasers sharing common gain crystal and pump laser [16], while Quraishi et al. demonstrated the synchronization between two independent Ti:sapphire lasers [17]. For fiber-laser system, where long distance transportation can be achieved with a low-loss optical fiber, Walbaum et al. demonstrated the injection locking of the repetition frequency between two Er-doped fiber lasers [18].
Injection locking is applied for lasers where the repetition frequency of one laser is integer multiple of the other [15,17]. High-repetition-rate frequency combs with very little pulse energy can thus be stabilized against low-repetition-rate master comb where offset frequency can be easily monitored and controlled by conventional self-referencing method with sufficient pulse energy.
In this paper, we investigated the passive synchronization of repetition and offset frequencies between two mode-locked Yb-doped fiber lasers. By injecting the master laser output into the slave oscillator, we observed the two synchronization cases depending on the cavity length mismatch between these lasers: one is that only repetition frequency synchronizes, and the other is that both repetition and offset frequencies synchronize. We also demonstrate the hybrid synchronization that only the repetition frequency is passively synchronized by the injection locking while offset frequency is actively controlled. It is found that excellent long term stability can be achieved with this hybrid synchronization.
2. Passive synchronization dynamics of repetition and offset frequencies
Figure 1 shows the schematic of the experimental setup. We built almost identical two mode-locked Yb-doped fiber lasers, and output of one laser (referred to as “master laser”) is injected into the other laser (referred to as “slave laser”). The details of those oscillators are described in the references [19, 20]. In short, the laser consists of ring cavity that includes YDF as a gain medium and mode locking was initiated and stabilized by nonlinear polarization rotation process [21]. We set net group-delay dispersion (GDD) slightly negative by adjusting a grating pair inside the oscillator. The repetition frequency was about 110 MHz. Master pulses were injected into the slave oscillator through a fiber coupler. Master pulses were coupled by 10 % and slave pulses transmitted by 90 % at the fiber coupler. Dispersion of master pulses was compensated by a transmission grating pair before injection in order to increase the pulse peak power and strengthen the nonlinear effect. Wave plates after the transmission grating pair were used to set the polarization of the master pulses to be the same as that of slave pulses.
Fig. 1 Schematic of experimental setup. WDM, wavelength division multiplexing mixer; SMF, single mode fiber; YDF, ytterbium-doped fiber; PBS, polarized beam splitter; HWP, half wave plate; QWP, quarter wave plate; PD, photo diode; PZT, piezoelectric transducer. Master and slave lasers are indicated by the dotted blue square and dotted red square, respectively.
In order to synchronize the repetition frequency, cavity length difference between master and slave oscillator has to be adjusted by a few hundreds nm, which corresponded to about 10 Hz of repetition frequency difference. This can be achieved by moving the grating pair (coarse adjustment) and the PZT or pump current (fine adjustment) in the slave oscillator while monitoring the pulse train of slave and master laser with a real-time oscilloscope: when repetition frequency difference becomes small enough, slave pulses synchronize with master pulses (Fig. 2 top right). When the repetition frequency synchronizes, additional peaks appear on the RF spectrum of the output of the slave laser as shown in Fig. 2 bottom. This is due to the beat between the master and slave combs, and the beat note (δ) corresponds to the offset frequency difference of two combs [16]. It should be noted that the output from the slave oscillator included a fraction of master pulses and these pulses have little time delay due to a nonlinear pulse-pair-formation inside the slave oscillator cavity [11]. Thus, optical beat between slave and master combs can be observed simply at the slave laser output. Since the offset frequencies of master and slave lasers are free running, δ moves slowly due to disturbance on those lasers such as air turbulence, mechanical vibration and temperature drift. When δ approaches close to zero frequency, it is found that δ vanishes suddenly, as referred to in ref [16]. To investigate this process further, we measured the RF spectrum and optical spectrum of slave laser output simultaneously while sweeping the cavity length of the slave oscillator by moving PZT. The results are shown in Fig. 3(a) and 3(b). In Fig. 3(a), we define the zero of the cavity length difference as the point where δ becomes zero. Synchronization dynamics is summarized as below. First, only repetition frequency synchronized, and δ was observed (dotted green line in Fig. 3(a) and 3(c)). Then, as the cavity length difference became smaller, δ shifted linearly towards zero (region “A” in Fig. 3(a)). The gradient is about 4.5 nm/MHz. When the cavity length difference became below about 10 nm, δ disappeared (dotted white line and region “B” in Fig. 3(a) and 3(e)). This situation continued when cavity length difference became about - 10 nm. Finally, as the cavity length difference became larger, δ appeared again.
Fig. 2 (Top) Pulse train of master and slave lasers on analog oscilloscope which was triggered by the master traces. Top left shows the case when repetition frequency doesn’t synchronize, and once slave pulses synchronize with master pulses, slave pulse trace is fixed to the master trace as top right. (Bottom) RF spectra of the output of slave laser. δ corresponds to the difference of offset frequencies between master and slave pulses
Fig. 3 (a) RF spectra of interference between master and slave pulses while changing the cavity length of the slave laser. (b) Optical spectra of interference between master and slave pulses while changing the cavity length of the slave laser. (c) RF spectrum at dotted green line in (a). (d) Optical spectrum at dotted green line in (b). (e) RF spectrum at dotted white line in (a). (f) Optical spectrum at dotted white line in (b). ’A’ is area where δ shifts linearly, and ’B’ is area where both repetition and offset frequency synchronize.
In the regime where the cavity length difference was between ± 10 nm (region “B”), the offset frequency of the slave pulses was likely to be pulled into that of the master pulses. In fact, we identified the spectral interference when δ disappeared (dotted white line in Fig 3(b) and 3(f)), as referred to in ref [16] and ref [17]. This spectral interference indicates not only the repetition frequency, but also the offset frequency were passively synchronized. Locking range in the offset frequency is about 5 MHz. When both repetition and offset frequencies are synchronized passively, it is found that the RF peak that corresponds to the repetition frequency becomes broader as shown in Fig. 3(e). This is because δ is locked to DC and phase noise of locked beat note is included in repetition frequency peak. From the broadened repetition frequency peak, we estimated the integrated relative phase noise of offset frequency difference to be about 1 rad (R.M.S., integrated from 1 Hz to 5 MHz). This value also supports that the relative phase noise between slave and master laser is significantly suppressed by injection locking.
2.1. Discussion
In this section, we focus on two issues in the passive synchronization process described in the previous section: what causes the shift of δ when the slave-cavity length is swept, and how to describe the locking range for comb-to-comb injection locking.
2.1.1. The drift of δ while sweeping the cavity length difference
We show carrier frequency of the slave pulse changes (with the amount of Δf in the following expression) along with the cavity length change to keep the passive repetition frequency synchronization, which causes δ shift as can be observed in Fig. 3(a). We assume carrier frequencies of master and slave pulses are identical before injection. We use following relations,
where frep and frep* are repetition frequencies of master laser and the slave laser, respectively. vg and vp are group and phase velocities respectively at carrier frequency of fc. Likewise, vg* and vp* are group and phase velocities at carrier frequency of fc + Δf. L is the cavity length of master oscillator, ΔL is the cavity length mismatch between master and slave oscillator. f0 and f0* are offset frequencies of master pulses and slave pulses, respectively. When repetition frequency is synchronized, frep = frep* can be applied. Using Eq. (1) to (6), the relation between δ shift and cavity length change is obtained as follows; where Δf can be related to ΔL as . δ shift can be ascribed to three contributions: relative phase shift due to geometric cavity length change (the first term), carrier frequency change (the second term), phase velocity change (the third term). Second and third terms come from the nonlinear effect to synchronize master and slave pulse trains. To evaluate each contribution to the δ shift, Eq. (7) can be rewritten as follows; Here, we introduced net group delay dispersion ϕ2 as , where ϕ2 is net group-deley dispersion. Assuming following values: fc = 1014 [Hz], frep = 108 [Hz], f0 = 107 [Hz], vp = 108 [m/s], vg = 108 [m/s], and |ϕ2| = 10−27 [s2], second term is small (< 10−2) compared with first term. Since is comparable to in the fiber, main contribution to δ shift is first and third term.2.1.2. Injection locking of multiple frequency-modes
Here, we consider the mechanism of the passive synchronization and the locking range of the offset frequency. Experimentally, as described in the previous section, we found that to compress the master pulses before injection is critical for repetition and offset locking. Thus, we believe peak-intensity-sensitive nonlinear interaction between master and slave pulses plays an important role in the injection locking of frequency comb. For example, constructive interference between slave and master field may strengthen the nonlinear polarization rotation inside the oscillator fiber and thus optimum mode-locking condition could be sustained when slave and master field is phase-locked to each other. Additionally, cross phase modulation between master and slave pulses could also contribute as in the case of phase locking between two lasers sharing a common gain crystal [16]. Although we don’t have decisive experimental clue yet to conclude the details of the nonlinear interaction, we can estimate the locking range as below. When the repetition frequency is synchronized, all beat frequencies of neighboring comb modes between master and slave pulses become identical. Thus, appropriate shift of offset frequency would be sufficient to overlap entire comb modes between slave and master laser. Here we assume that locking range of such multiple frequency modes lasers can be described in the same way as that of single-mode CW lasers with the same average power. For single-mode CW lasers, locking range is given by
where R is a field reflectivity of a coupling mirror, i. e. fiber coupler in our case, I1 is the intensity of one comb mode of the master laser outside the cavity, and I is the intensity of one comb mode of the slave laser inside the cavity [22]. Substituting , frep = 110 MHz, I1 =10 nW, and I = 200 nW, locking range is estimated to be about 17 MHz from this expression. In our experimental condition, imperfect polarization matching between master and slave laser would reduce the locking range. Still, we found that this CW model of injection locking for frequency comb nicely explains experimentally obtained value (5 MHz).3. Demonstration of transfer of the frequency stability
After we demonstrate passive synchronization of repetition and offset frequency as described in the previous section, we applied the method to transfer stability and accuracy of frequency comb structure between two Yb-fiber based frequency comb.
3.1. Development of Yb-fiber based optical frequency comb
In this section, we introduce our Yb-fiber based optical frequency comb system. There are a few reports about Yb fiber based optical frequency combs [23–25]. While they used specially designed suspended core fiber to generate octave-spanning supercontinuum [26], here we used commercially available photonic-crystal fiber (PCF) for spectral broadening.
Figure 4(a) shows our frequency comb system. The output of master oscillator was amplified in the preamplifier from 20 mW to 50 mW. The preamplifier consisted of 30-cm Yb fiber with 4-μm core diameter. Part of the amplified pulse was used for the injection locking and active stabilization of the repetition frequency. The rest (20 mW) were again amplified in the second amplifier, which consisted of 3-m Yb fiber with 10-μm core diameter, to 500 mW. Amplified pulses were compressed by a transmission grating pair to about 100 fs. Octave wide spectral broadening was achieved by coupling the compressed pulses into a 10-cm long PCF with 2.4-μm core diameter and 945-nm zero dispersion. Obtained supercontinuum was shown in Fig. 4(b). An f – 2f interferometer was set up for self-referenced offset frequency detection. Free-running offset frequency was shown in Fig. 4(c). To suppress the phase noise of offset frequency, mode locking was obtained in the stretched-pulse regime [25]. The repetition frequency was mixed with a radio frequency reference, and the error signal was fedback to the PZT-actuated end mirror in the oscillator for the stabilization of the repetition frequency. The offset frequency signal was frequency-divided by four, and compared with the radio frequency reference by a digital phase detector. The error signal was fedback to the current of the pump laser diode. Results of phase locking are described in the next section.
Fig. 4 (a) The schematic of Yb-doped fiber frequency comb system. (b) One-octave spectrum obtained after PCF. (c) Offset frequency detected by f–2f interferometer.
3.2. Transfer of the frequency stability
In the demonstration of the passive synchronization of both repetition and offset frequencies, we found that long-term stability of the synchronization is limited by environmental conditions such as temperature drift or acoustic vibrations that may disturb stable mode-locking of both oscillators. Although the synchronization of the only repetition frequency is kept for more than an hour, the passive synchronization of both offset and repetition frequencies is kept only for a few second. Thus, here we demonstrate more robust hybrid synchronization where the offset frequency is actively controlled while the repetition frequency is passively synchronized.
Figure 5 shows the schematic of the experimental setup. The repetition and offset frequencies of the master laser are stabilized in the same way as described in the previous section. Part of the preamplified pulses (20 mW) was injected into the slave oscillator in order to synchronize the repetition frequency passively. The beat note δ that corresponds to the offset frequency difference of two lasers, was filtered out and processed by a proportional-integral loop filter to give a control signal of slave laser current for active synchronization of offset frequency difference.
Fig. 5 The schematic of comb transfer experiment. Combs of master laser are stabilized. Repetition frequnecy of slave pulses synchronizes passively that of master pulses, and offset frequency of slave pulses synchronizes actively that of master pulses.
RF spectrum of the offset frequency of master laser, and comb-to-comb beat between master and slave oscillator are shown in Fig. 6(a) and 6(b). A coherent carrier peak with 30 dB of contrast from incoherent component was obtained at 1 kHz RBW, and integrated phase noise from 1 kHz to 400 kHz was below 0.85 rad. Temporal stability of the repetition and offset frequency of the master oscillator, the repetition frequencies of the slave oscillator, and δ were measured by using 1-s averaged counters. The results are shown in Fig. 6(c), 6(d), 6(e), and 6(f). Overall phase locking can be kept for about five minutes, limited by the temperature drift around the system.
Fig. 6 (a) RF spectrum of stabilized offset frequency of master pulses. (b) RF spectra of stabilized δ. (c) Time variation of repetition frequency of master pulses. (d) Time variation of repetition frequency of slave pulses. (e) Time variation of offset frequency of master pulses. (f) Time variation of δ.
4. Conclusion
In conclusion, we demonstrated the passive synchronization of both repetition and offset frequencies between two independent Yb-doped fiber oscillators. Integrated relative phase noise between master and slave pulses is 1 rad from 1 Hz to 5 MHz. Passive synchronization of offset and repetition frequencies was obtained when cavity length difference between master and slave oscillators is set to be less than 10 nm. This locking range in cavity-length mismatch would be extended by enhancing the injection power with additional amplifier. Improving the polarization matching between slave and master pulses inside the resonator would also help. Instead of all passive synchronization, we phase locked the offset-frequency difference actively and the repetition frequency passively for more robust synchronization. Although our frequency comb is locked to the RF reference, the passive-locking comb-transfer technique would be applied for ultra-stable combs locked to the optical-cavity stabilized cw lasers. This is because the passive-locking technique offers quite high feedback bandwidth due to ultrafast nonlinear interaction compared to the electrical feedback. Our result offers promising and simple way to precisely duplicate the comb structure, which can be applied to fiber-based long-distance transfer of frequency comb.
Acknowledgments
This research is supported by the Photon Frontier Network Program of MEXT, Japan.
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