1. Introduction

Optical frequency combs have important applications in a wide range of fields, such as optical frequency metrology, time-frequency transfer based on optical clocks, and precise coherent measurement [1–4]. Recently fiber-laser-based optical frequency comb (FL-OFC) has attracted more attention because of its simple structure with cost efficient and easy operability [5–7]. For some application fields, for instance, precision laser spectroscopy [8] and microwave photonics [9], the comb-teeth spacing is a very important parameter. The comb-teeth spacing for an FL-OFC is basically determined by the repetition rate of the mode-locked pulse trains, which is usually in the range of 100-300-MHz [10]. The comb-teeth spacing may be adjusted several MHz by using the intracavity fiber-stretcher or modulator [11]; however, if a larger adjustment range for the comb-teeth spacing is required, one may have to face the difficulty regarding redesign of the cavity length. Both the minimal fiber length allowed for the splicing operations and the lengths for different kinds of optical fiber used to adjust the balance among dispersion, nonliearity and gain in the cavity for lock-moding, determine the shortest cavity length available, making the largest FL-OFC comb-teeth spacing about 3 GHz currently [12]. To further enhance the comb-teeth spacing, the external Fabry–Perot filter method or the harmonicly mode-locking technique [13, 14] may have to be ultilized. However, the former method requires complex stabilization systems and expensive high-finesse etalons, whereas, for the latter, a high supermode noise causes comb structure disturbance and broadens the comb linewidth. On the other hand, an FL-OFC with small mode spacing corresponds to a longer cavity. In that case, it is also very difficult to control the relationship between the cavity dispersion and nonlinear effect for short pulse generation [15]. In addition, a longer cavity has higher sensitivity to environmental disturbance, which deteriorates the phase-locked comb performance [16]. Fortunately, several research groups have recently reported polarization-maintaining based-fiber optical combs [17–20], which provides a very good solution to solve the environmental instability of OFCs, especially for the combs with small mode spacing to overcome the defect that easily influenced by environmental disturbances.

However, the saturable absorber based on nonlinear polarization evolution (NPE) effect has the advantages of fast response and large modulation depth. The femtosecond pulse generated by the NPE based passive mode-locked fiber laser has a relatively narrower pulse width, higher energy and more excellent noise characteristics. In the laboratory environment, the technology of generating high repetition rate optical combs with the NPE based fiber oscillator is relatively mature and still highly attractive. Furthermore, previous research results [21, 22] have shown that, for a mode-locked fiber laser based on NPE, if the pump power is high enough that the pulse peak power in the cavity can greatly exceed the NPE switch threshold, the accumulated round-trip excessive nonlinear phase shift of the pulse interacting with the passive polarizer contained in NPE may result in the period-doubling mode-locked (PD-ML) state for laser, generating a cavity-mode-dependent fundamental repetition frequency and its sub-harmonics [23] in the frequency domain. Recently, Zhao et al. [24] have studied the characteristics of the carrier envelope offset (CEO) frequency in the PD-ML fiber laser, showing that the entire comb tooth for the period-doubling state can shrink to half the size of the corresponding fundamental mode-locked (FML) state. Hence, using the PD-ML state can generate a comb spacing with the same size as the normal NPE based passive mode-locked laser whose cavity length, however, is double. Therefore, the PD-ML fiber laser can overcome the disadvantages of long-cavity method such as environmental instability, providing a new solution to achieve low-noise combs with small mode spacing. However, no reports of a phase-locked comb based on the PD-ML laser are available at present. Furthermore, the associated feedback mechanism and intrinsic correlation for such a novel comb with both fundamental and sub-harmonic comb tooth structures require further illumination.

In this paper, we present the achievement of phase locking of the entire comb tooth based on a PD-ML fiber laser, and investigate the associated feedback mechanism and intrinsic correlation for such an optical comb. Our experimental results show that, with a suitably designed length of OFS-980 fiber inserted into the cavity, a fiber laser that can be switched it from the FML to the PD-ML state simply by adjusting the pump bias current is realized. For such a fiber laser, the new comb teeth produced by the PD-ML are strongly correlated with the original comb teeth and have a consistent CEO frequency. As a result, phase locking of optical combs with two different repetition rates of 104.66 and 209.32 MHz is achieved, along with switching between these combs. This switching may present a high potential for the future use in the metrology laboratory and coherent optical pulse synthesis systems.

2. Experiment setup

Figure 1 shows the schematic diagram of the optical frequency comb, which is based on a PD-ML Er-doped fiber oscillator. A 0.37 m Er-doped fiber (EDF; Liekki Er110-4/125) with an absorption coefficient of approximately 60 dB/m at 980 nm is used in the oscillator cavity, which is backward pumped by a 980 nm laser diode with a maximum output power of 1 W through an integrated wavelength-division multiplexer/isolator (WDM-ISO; labeled with “Hybrid” in the figure). This gain fiber has a group velocity dispersion (GVD) of approximately + 0.011 ps²/m at 1550 nm; therefore, the total positive cavity dispersion is approximately + 0.00407 ps². Two quarter-wave plates (Q), a half-wave plate (H), and a polarization beam splitter (PBS) positioned between two collimators (Col) form a saturable absorber via NPE. The free space length for the NPE is about 8 cm. The two fiber pigtails of the Cols are standard single-mode fibers (SMF-28) with a GVD of approximately −0.022 ps²/m at 1550 nm; the total length is 0.28 m (that spliced with the gain fiber has a 0.15 m length), corresponding to a negative cavity dispersion of approximately −0.006407 ps². OFS-980 fiber (the cutoff wavelength for single guided mode is below 960 nm) with almost zero GVD dispersion (i.e., −0.0013 ps²/m @ 1550 nm) is used for the pigtail fiber of hybrid. In the experiment, the PD-ML state of laser is obtained and adjusted through optimization of OFS-980 fiber length.

 

Fig. 1 Schematic diagram of Er-doped fiber optical frequency comb. Col: collimator; Q: quarter-wave plate; H: half-wave plate; PBS: polarization beam splitter; PZT: piezoelectric transducer; ISO: fiber optic isolator; Hybrid: integrated WDM-ISO; M: folded mirror; OC: fused fiber coupler; CPA: chirped pulse amplifier; HNLF: highly nonlinear fiber; L: lens; PPLN: periodically poled lithium niobate; BPF: band pass filter; PD: photodetector; FROG: frequency-resolved optical gating; OSA: optical spectrum analyzer; OFS: OFS-980 fiber.

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The direct output of the mode-locked laser is split in two by the OC-1 fiber coupler. One part enters OC-2 to be further split, with one part used for detection of the repetition rate $f_r$ by a photodetector (PD1) and the other for determination of the mode structure of the PD-ML state through the heterodyne beat note with a 1550-nm CW laser. The other part output from OC-1 passes through the chirped pulse amplification fiber link, is injected into a piece of highly nonlinear fiber (HNLF) for spectral broadening to a full octave, and passed through collinear f-to-2f heterodyne beat device composed of PPLN crystal for detection of CEO frequency $f_0$ [1]. The detected $f_r$ and $f_0$ are both referenced to a rubidium clock and achieve phase-locking of optical comb through feedback control PZT (The size is 5 × 5 × 18 mm³, measured PZT loop-controlled bandwidth is about 200 Hz) and laser pumping current, respectively. Moreover, the optical part of fiber comb includes the fiber oscillator and the fiber amplifer link, which are respectively housed in the temperature-controlled box made of temperature-insensitive Teflon plates and thermally conductive Aluminum boards under a temperature adjustable within 22 ± 2 °C with an accuracy of ± 0. 1°C.

3. Results and discussion

The length of the OFS-980 fiber in the cavity was first optimized for the PD-ML state. When the length is set at any value between 0.13 and 0.28 m, the oscillator can always achieve self-starting mode locking once the pump reaches the threshold, with the wave plates being rationally adjusted. Moreover, with further increasing of the pump beyond the threshold, the pulsed output switches sequentially from the FML to the stable PD-ML and then to the multi-pulsing state. To meet the experimental requirements, the OFS-980 fiber length was selected and fixed at 0.19 m, for which the oscillator can obtain the self-starting mode locked pulse train with uniform amplitude displayed by an oscilloscope once the pump reaches 600 mW. The corresponding pulse repetition frequency measured with the spectrum analyzer is 209.32 MHz. The pulsed laser can be switched to the PD-ML state once the pump is increased to 805 mW, and persisted the PD-ML state until the pump is increased to 900 mW. Figures 2(a) and 2(b) show the measured pulse train and RF spectrum in the PD-ML state, respectively. Obviously, the pulse intensity loses uniformity and only returns every two round trips. In the RF spectrum, some symmetric sidebands are apparent beside the main fundamental peaks; the first sideband differs from the nearest main peak at 209.32 MHz by an approximately 25 dB attenuation and has a frequency of exactly half $f_r$ (i.e., 104.66 MHz). [Note: this kind of difference in SNR can be changed by changing the length of OFS-980 fiber length]. In the experiments, with an optical spectrum analyzer (OSA) and a frequency-resolved optical gating (FROG), the output spectra and pulse widths for the laser were measured in FML and PD-ML states, and the results are shown in the Figs. 3(a) and 3(b). It is clear that the spectra almost overlap, and the pulse durations after compression with the optimized length of fibers are 55 and 58 fs for the FML and PD-ML cases, respectively. Thus, the pulsed output performances are almost the same for the two states.

 

Fig. 2 (a) Measured pulse train and (b) RF spectrum in PD-ML state.

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Fig. 3 (a) Measured output spectra and (b) pulse widths for FML (red) and PD-ML (blue) states.

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In the Er-doped fiber oscillator shown in Fig. 1, the dispersion of the OFS-980 fiber at the back end of gain fiber is close to zero, and it mainly plays the role of increasing nonlinearity and broadening the pulse spectrum in the cavity [25, 26]. When the oscillator is in self-starting FML state, the cavity loss determined by the NPE transmittance is in positive feedback regime [27]. In this regime, the pulse peak power can be increased with the increase of the pump. When the pulse peak power is increased to such an extent that it is beyond the NPE switch threshold, overdriving effect for the saturable absorber occurs, resulting that the cavity loss determined by NPE transmittance switches from the positive to the negative feedback regime. The larger the overload quantity is, the higher the proportion of energy outputted by pulse through PBS will be and the lower the proportion of returning back to the cavity is. In the next round trip, the pulse accumulates a less nonlinear phase shift to cause the cavity to possibly switch back to the positive feedback regime. In that case, any tiny deviation of cavity loss corresponding to original NPE transmittance generated by high pulse peak power due to high pump will make the proportion of pulse via PBS output lower; then, more energy returns to the cavity, facilitating accumulation of a greater nonlinear phase shift, which again generates negative feedback for the cavity loss. The process elucidated above undergoes repeated iterations. Consequently, the laser outputs two kinds of pulses with different ampilitudes and periodicity change (i.e., the PD-ML state), for which the “newly” emerged comb modes render the entire comb half the size of the corresponding FML state in the frequency domain. Note that we consciously selected an OFS-980 fiber length of 0.19 m when designing the oscillator. In that case, the accumulated nonlinear phase shift of the pulse in the PD-ML state differs slightly from that in the FML case, ensuring that the pulsed output performances are almost the same for the two states. This facilitates phase locking of the optical frequency combs with different mode spacing, as will be described below.

With the laser operating in the PD-ML state, the $f_r$ signal and its sub-harmonics $f_r/2$detected were respectively compared with suitable Rb-stabilized microwaves and the cavity length was controlled with the help of a PZT in the phase-locked loop. Then, it was always found that the measured $f_r/2$ and $f_r$ could be locked. The frequency fluctuations recorded by the counter for more than 2.5 h when the fourth harmonic of $f_r$ is referenced to Rb clock as shown in Fig. 4. At a 1-s counter gate time, the $f_r$ and $f_r/2$ signals were well phase locked with a frequency fluctuation of 0.68 and 0.32 mHz; these results mean that there is very strong mutual correlation between the new and original comb modes. Further, it is apparent that the implementation of feedback control on the PZT can simultaneously act on the two kinds of comb modes to stabilize the comb spacing. In fact, the original optical modes (mode spacing: $f_r$) can be locked by feedback controlling the cavity length [1]. The new comb modes are generated by the pulse amplitude modulation caused by the dynamic balance between the cavity loss and intensity-dependent NPE [24, 28], and the modulation function can be determined by the NPE transmittance. For a fixed cavity linear phase shift, the actual NPE transmittance is a sinusoidal function of the cavity nonlinear phase shift (${\varphi }_{NL}$) with a period of every two round-trip time$2T_r$ . That is, the modulation frequency is$f_r/2$, and is inversely proportional to the cavity length$L$. Then, the comb tooth function of the PD-ML laser in the frequency domain can be described as the convolution between the original fundamental comb and the amplitude modulation, and the new comb teeth spacing corresponds to the amplitude modulation frequency, i.e., $f_r/2$. Hence, the new comb modes can also be locked via feedback control of the cavity length.

 

Fig. 4 Recorded residual fluctuation of (a) phase-locked $f_r$ and (b) $f_r/2$ signals with 1-s gate time in PD-ML state.

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Figure 5(a) shows the RF spectrum of the offset beat signal ($f_0$) in the PD-ML state detected using the f-to-2f heterodyne method at a resolution bandwidth (RBW) of 300 kHz. The signal-to-noise ratio (SNR) of $f_0$ reached 30 dB, with the $f_r/2$ signal peak still in existence and some beat sidebands (i.e., $k{f}_r/2\pm f_0\text{,}k=0,1,\mathrm{2...}$) emerging regularly. When the pump drive current was adjusted, $f_0$ and $f_r/2+f_0$ signals were shifted almost linearly by a slope of 0.132 MHz/mA, indicating that the pump power can be changed to control$f_0$ . That is, $f_0$ can be locked via feedback control of the pump power. Figure 5(b) shows the recorded residual fluctuation of the phase-locked $f_0$ signal with 1 s gate time; the measured standard deviation is approximately 12.24 mHz.

 

Fig. 5 (a) RF spectrum of $f_0$ beat signal in PD-ML state with RBW of 300 kHz and (b) recorded residual fluctuation of phase-locked $f_0$ signal with 1-s gate time.

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However, as the PD-ML laser outputs high and low amplitude pulses, the detected $f_0$ may come from the octave supercontinuum produced by the high-amplitude pulses only (in other words, the high-amplitude pulses dominate). This means that phase locking $f_0$ stabilizes the CEO of the high-amplitude pulse-train only. To remove this obstacle, in our experiment, the output pulse of OC-2 in Fig. 1 was used directly as the heterodyne beat note with a 1550-nm CW laser (frequency fluctuation: within 1 MHz @ 3 h). Hence, the comb structure of the PD-ML state was determined and the characteristics of the comb CEO frequency were examined.

Figure 6 shows the RF spectrum of the heterodyne beat detection with the CW laser when $f_r/2$is locked but $f_0$ is not: some symmetric beat sidebands are apparent beside $f_r/2$ and $f_r$ as well as its harmonics. In this figure, $f_1$ is the difference in frequency of the CW laser and the nearest comb mode, and $f_a$ and $f_b$ are the beat frequencies between the continuous light and each of the two second nearest comb modes (happens to be the newly generated comb teeth here, as shown in the figure). These quantities satisfy the relations $f_a=f_r/2-f_1$ and$f_b=f_r/2+f_1$, indicating that the comb-tooth structure of the period-doubling laser truly shrinks such that the comb spacing is halved ($f_r/2$). Moreover, it was found in our experiment that $f_1$ and $f_b$ can be linearly shifted as the pump current increases, while always satisfying$f_b=f_r/2+f_1$. Considering that the repetition frequency has been stabilized and the frequency drift of the reference CW laser in the measuring time can be ignored, the linearly shifted process indicates that the new comb tooth has the same offset frequency as the original one.

 

Fig. 6 RF spectrum of heterodyne beat detection between PD-ML laser and 1550-nm CW laser with 300-kHz RBW.

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When both $f_r/2$ and $f_0$ are stabilized to the Rb-stabilized microwave, it was observed in the experiment that $f_1$ and $f_b$ frequency positions drift synchronously and continue to satisfy$f_b=f_r/2+f_1$. The measured frequency drifts of $f_1$ and $f_b$ are ~1 MHz; this measurement is limited by the frequency stability of the CW laser used. Hence, it is apparent that the original and new comb modes can both be controlled completely by phase locking $f_r/2$ and$f_0$. Moreover, in Fig. 6, there are no random beat structures originating from the random jitter pulse-to-pulse phase shift [29], which may often occur in a harmonic mode-locked laser; this characteristic further indicates that the phase shift between the adjacent pulses in the period doubling is fixed, which is mainly due to the intrinsic dynamics of the PD-ML state.

Finally, when the pump power was reduced to less than 805 mW, the laser automatically switched from the PD-ML back to FML state. The SNR of $f_0$ reached 32 dB, as measured by the same f-to-2f heterodyne beat system under the same experimental conditions as previously. Further, using the same locking circuit through the standard locking scheme [6], we achieved a phase-locked FML comb. The measured jitter values were 0.64 and 9.65 mHz for the two quantities, i.e., the repetition rate and the CEO frequency. Hence, we finally achieved phase locking of the optical comb under two different comb teeth spacing of 104.66 and 209.32 MHz, with switching between them being accomplished by simply controlling the pump power (current) only. This switching operation benefits from the similar pulsed-output performance of the two mode-locked states, which is due to the careful design of the OFS-980 fiber length in the oscillator. Such a fast large-span changing of comb-teeth spacing realized by switching between PD-ML and regular FML comb and with fine tuning of PZT on cavity length largely can improve the flexibility of optical comb in application of microwave photonics; besides, it is also expected to be used in precision laser spectrum field, such as dual-comb spectroscopy [30], to improve spectral resolution [31]. Finally, It is worthwhile to point out that the key point of this paper is to study the feedback mechanism of PD-ML fiber optical comb and the intrinsic correlation characteristic and with design and optimization, it achieved switching between PD-ML and FML only by changing pump power. Therefore, we did not pay special attention to phase lock high accuracy, so the residual fluctuation of $f_r$, $f_r/2$ and $f_0$ is not very small. However, because the phase lock scheme that we adopted is the standard scheme, the developed techniques that are used for improving phase lock accuracy, such as those discussed in [6-7, 10], are all suitable for our optical comb.

4. Conclusion

We have studied the phase-locking mechanism and locking results of a frequency comb based on a PD-ML fiber laser. By optimizing the length of the OFS-980 fiber in the cavity, a fiber laser that can be switched from the FML to PD-ML state, with almost the same output pulse characteristics between them, simply by changing the pump bias current only was designed. Our experimental results show that the new comb teeth produced by the PD-ML are strongly correlated with the original comb teeth. Through feedback control of the cavity length, $f_r$ and its sub-harmonics $f_r/2$ can be phase locked; the measured standard deviations are 0.68 and 0.32 mHz, respectively. The SNR of the detected $f_0$ in the PD-ML state reaches 30 dB with a recorded residual fluctuation of 12.24 mHz when locked using feedback control of the pump power. Further, the RF spectrum of the heterodyne beat detection between the period-doubling laser and the CW laser shows that the regenerated and original comb teeth have a consistent CEO frequency. Hence, by phase locking $f_r/2$ and $f_0$, we have achieved a phase-locked comb based on a PD-ML laser, for which both the original and new comb modes are completely controlled. Furthermore, by tuning the pump bias current only, we have realized an FML-based phase-locked optical comb through the same f-to-2f heterodyne beat system and locked circuit. Hence, we have achieved phase locking of optical combs with two different repetition rates, and switching between them.