1. Introduction

Picosecond laser sources with high spectral purity have applications in nonlinear frequency conversion [1] and coherent anti-stokes Raman scattering imaging [2], and they are desirable seed sources in the field of laser processing, such as in micromachining [3]. Such picosecond pulses are conventionally generated using solid-state [4] and modulated semiconductor lasers [5]. With the invention of an all-normal dispersion (ANDi) passively mode-locked fiber laser [6], it is found that high spectral purity dissipative solitons (DSs) with pulse durations of several to hundreds of picoseconds can be generated using an intracavity filter with a bandwidth below 1 nm [7–9]. The picosecond pulse fiber laser source has advantages such as good beam quality and compact structure, and it is less affected by the reflection of subsequent optical amplifiers. Thus far, several picosecond DS fiber lasers with different configurations have been proposed [10–13]; among them, all-polarization-maintaining (PM) linear-cavity fiber lasers constructed with fiber Bragg grating (FBGs) as the filter and semiconductor saturable absorber mirrors (SESAMs) as the mode-locked element have gradually become preferred owing to their high stability and reliability. However, unlike the conventional femtosecond DS fiber lasers with wide-band filters (usually around 10nm of bandwidth), the chirp induced by the group velocity dispersion (GVD) for the picosecond pulse in the cavity with narrow FBG filter is weak [14]. This results that the nonlinear phase shift accumulated in one round trip in the single-pulse (SP) mode-locking regime may have to be maintained at an extremely low value [15] to avoid multipulse operation caused by wave breaking [16], i.e., the tolerant value of nonlinear phase shift in SP regime for this kind of fiber laser is low (this reflects the intracavity filtering effect has great impact on the multipulse formation in DS fiber lasers [17]). Thus, the multipulse state is more easier to occur for the laser with a high pump power [13], i.e., the laser has to work in a weakly nonlinear regime to avoid multipulse operation. Moreover, the time domain evolution of the DS in the cavity exhibits an extremely low breathing ratio when the laser operates in a weakly nonlinear regime. The output picosecond pulse has excellent performance in terms of approaching the Fourier transform limit [7]. Since such properties are not sensitive to cavity length, the output pulse parameters can be controlled by manipulating FBG bandwidth, and the repetition rate can be reduced by increasing the cavity length without influencing the designed FBG bandwidth determined using the required pulse parameters [7].

When reducing the repetition rate by increasing cavity length, the pump power needs to be simultaneously decreased to reduce intracavity pulse energy in order to ensure that the nonlinear phase shift does not exceed the tolerated value in the SP regime. The problem is that the SP regime may not be achieved owing to Q-switching instability if the intracavity pulse energy is too low to bleach the saturable absorber [18]. SESAMs with lower saturation fluence can be used to alleviate this effect, but this will make it difficult to self-start the laser [19]. Existing research shows that reducing the FBG bandwidth can effectively filter out the nonlinear chirp located at pulse edges, which mainly causes wave breaking. Thus, pulse energy can be improved while maintaining the nonlinear phase shift. This is beneficial for alleviating Q-switching instability [20]. However, the limited nonlinear phase shift tolerated in the SP regime, which determines that it is easy to produce Q-switching instability when increasing cavity length, limits the reduction in the repetition rate of such lasers [15]. For example, when the FBG bandwidth is 0.7, 0.5, 0.1, and 0.04 nm, the lowest repetition rates that can be obtained to date are 34 MHz [21], 10 MHz [22], 1.13 MHz [15], and 0.7 MHz [7], respectively. Even though the FBG with a 0.04-nm bandwidth can reduce the repetition rate to 0.7 MHz, the nearly Fourier-transform limited pulse duration increases to 65 ps [7]. If the required pulse duration is narrow, for instance, 10 ps, the repetition rate (usually several tens of megahertz) cannot be effectively reduced. In this case, a pulse picker may have to be used to reduce the repetition rate of the pulse train, which not only leads to a complicated structure, but also introduces considerable energy loss [2]. Therefore, effectively reducing the pulse repetition rate without changing the output pulse characteristics remains a problem.

In this paper, we propose and demonstrate a method to reduce the repetition rate of an all-PM picosecond DS passively mode-locked fiber laser without changing the pulse characteristics. Our experimental results will show that, by inserting an optical coupler (OC) to extract pulse energy from a cavity and using a large mode area (LMA) fiber to increase cavity length and placing it at the rear end of the OC where the propagated pulse has lower energy, the nonlinear phase shift can be effectively reduced, and thus, the laser repetition rate can be significantly decreased. For an all-PM linear-cavity DS passively mode-locked fiber laser based on a 0.3-nm FBG, the repetition rate is successfully reduced to 1.77 MHz while pulse duration and bandwidth are basically unchanged. This method is applicable to lasers with any filter bandwidth.

2. Experimental setup

Figure 1 shows the schematic of our all-PM linear-cavity ANDi passively mode-locked fiber laser. A segment of a 1-m PM Yb-doped fiber with an absorption of 250 dB/m at 975 nm (Nufern, PM-YSF-6/125-HI) serves as the gain fiber, which is pumped by a 976-nm laser diode (LD) via a PM980 fiber-pigtailed (Nufern, PM980) wavelength division multiplexer (WDM). The WDM insertion loss is approximately 0.5 dB; the PM980 fiber has a GVD parameter and a nonlinear coefficient of 0.006 ps²/m and $3.5\times {10}^{-3}{\text{W}}^{-1}{\text{m}}^{-1}$, respectively. The linear cavity consists of a PM FBG and a pigtailed SESAM (Batop, SAM-1064-18-500 fs). The FBG is written in the PM980 fiber with a center wavelength, bandwidth, and reflectivity of 1064.2 nm, 0.3 nm, and 90%, respectively; the FBG also acts as a filter. The SESAM with PM980 pigtail is used as a mode-locking element with a modulation depth of 10%, saturation fluence of 130 μJ/cm², relaxation time of 500 fs, and the insertion loss of the fiber-pigtailed SESAM is measured to be between 1.1 and 1.5 dB, depending on its saturation degree operated. To reduce the nonlinear phase shift and suppress the multipulse effect, a 30:70 PM OC with a fast-axis cut-off is inserted into the cavity to extract pulse energy. An optical isolator (ISO) is connected to the 30% output port to prevent backward reflection. All in-cavity components including the FBG have a pigtail fiber length of approximately 30 cm. The total cavity length and loss are 2.8 m and 5.6 dB, respectively. The output pulse train is respectively measured with an optical power meter (Ophir, VEGA), a spectrum analyzer (Yokogawa, AQ6370D), an autocorrelator, a photodetector followed by an oscilloscope and a radio frequency (RF) analyzer.

 

Fig. 1 Schematic of the all-PM ANDi passively mode-locked fiber laser based on FBG and SESAM. (FBG: fiber Bragg grating; OC: optical coupler; YDF: Yb-doped fiber; WDM: wavelength division multiplexer; SESAM: semiconductor saturable absorber mirror; ISO: fiber isolator).

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3. Results and discussion

The output characteristics of the laser shown in Fig. 1 are studied at first. The laser starts to oscillate, and it gradually changes from a continuous wave regime to a low amplitude random pulsing state as the pump power increases. When the pump power is between 98 and 130 mW, the laser is in a stable SP regime, and multiple pulses occur spontaneously when the pump power exceeds 130 mW. In the SP regime, the pulse energy increases from 23 to 62 pJ with an increase in pump power.

Figure 2 shows the measured autocorrelation traces, spectra, and pulse trains for different pump powers in the SP regime. It can be seen that the bandwidths at pump powers of 98, 116, and 130 mW are 0.16, 0.17, and 0.18 nm, respectively. The pulse durations are estimated as 12.8, 12.2, and 11.2 ps with Gaussian fitting, and the corresponding time-bandwidth products are 0.55, 0.53, and 0.51, respectively, indicating that the output DSs are weakly chirped. Based on the measured pulse durations, the nonlinear phase shifts at pump powers of 98, 116, and 130 mW are estimated to be 0.103, 0.213, and 0.305 [23], respectively, indicating that the laser operates in a weakly nonlinear regime. The nonlinear phase shift increases with an increase in pump power, and the allowed maximum nonlinear phase shift for the SP regime is 0.305. From Fig. 2(g-i), one can clearly see that the repetition rate remains fixed at 35.2 MHz, corresponding to the cavity length of 2.8 m.

 

Fig. 2 Measured autocorrelation traces (color) and fitting curves (black) of output pulses from the 35.2 MHz repetition rate oscillators at pump power of 98 mW (a), 116 mW (b) and 130 mW (c), corresponding optical spectra (d) - (f), and pulse trains measured by a 2-GHz photodetector (Eot, ET3000A) and a 600-MHz oscilloscope (Agilent, MSO8064A) (g) - (i).

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Then, two segments of PM980 fibers with equal length are inserted into the cavity at positions A and B (see Fig. 1) to reduce the repetition rate. It is observed in the experiments that both the pump power and its range for the SP regime decrease with an increase in the inserted fiber length. The SP regime disappears when the total length of the inserted fiber reaches 5.5 m. Figure 3(a) shows the measured typical autocorrelation trace and spectrum of the output pulse when the repetition rate is reduced to 13.1 MHz (see Fig. 3(c)) by inserting whole length of 5-m fiber. As seen from the figure, the pulse duration is approximately 12.1 ps with a 0.18-nm bandwidth, giving a time-bandwidth product of 0.63. According to the measured pulse energy of 28 pJ, the estimated nonlinear phase shift is 0.314, which is slightly larger than the value of 0.305 for the 35.2 MHz laser at a pump power of 130 mW. This indicates that, by adjusting the interactions in the DS laser cavity for the self-consistent SP mode-locking, the laser can automatically reduce intracavity pulse energy to meet the tolerant value of the nonlinear phase shift limit of the SP regime. However, when the whole inserted fiber length is over 5.5 m, this automatic adjustment function fails because of the low pulse energy that causes the Q-switching instability [18]. Therefore, the tolerant nonlinear phase shift limit of the SP regime must not be exceeded when increasing cavity length for reducing the repetition rate.

 

Fig. 3 Measured autocorrelation traces (red) and fitting curves (black) of output pulses at repetition rates of 13.1MHz (a) and 7.7MHz (b), the insets show the corresponding optical spectra; measured pulse trains at repetition rates of 13.1MHz (c) and 7.7MHz (d).

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Considering that the nonlinear phase shift accumulated in the fiber inserted at position A is less than that of the fiber inserted at position B because the OC extracts a large amount of the pulse energy, we insert all fibers only at position A (Fig. 1) for reducing the repetition rate. When the PM980 fiber inserted at position A is 10 m long, the laser still operates in the SP regime at a pump power of 68–70 mW, and the repetition rate is reduced to 7.7 MHz as shown in Fig. 3(d). The measured output pulse autocorrelation trace and spectrum under this circumstance are shown in Fig. 3(b). The pulse duration, bandwidth, and the time-bandwidth product are 12.5 ps, 0.19 nm, and 0.64, respectively. Compared with the corresponding values for the aforementioned 13.1 MHz laser, the output pulse energy is further reduced to 20 pJ, and the nonlinear phase shift is slightly increased to 0.358. Inserting an additional fiber at the OC rear end facilitates the use of a longer insertion fiber without exceeding the nonlinear phase shift limit.

From the abovementioned experimental results, when the cavity length is increased to reduce the repetition rate from 35.2 MHz to 13.1 MHz and 7.7 MHz, the maximum nonlinear phase shift tolerated in the SP regime is increased from 0.305 to 0.314 and 0.358, respectively. The reason is that the multipulse operation is caused by wave breaking, which occurs based on the total amount of chirp induced by dispersion and nonlinearity in the ANDi fiber laser [24]. Although the chirp introduced by GVD for the picosecond pulse is weak for the lasers, the linear chirp induced by GVD in the normal dispersion fiber can still partially cancel the nonlinear chirp induced by the self-phase modulation (SPM) [16] and resist the wave-breaking effect, thereby eventually increasing the tolerant nonlinear phase shift of the SP regime with a longer cavity length. This is why in a conventional femtosecond ANDi laser with wideband filter a high-energy pulse can be obtained by significantly increasing the cavity length to increase the dispersion-induced chirp for improving the tolerant value of nonlinear phase shift and resist the wave breaking [25-27]. However, since the GVD-introduced chirp for the picosecond pulse here is excessively weak, the intracavity pulse-shaping mechanism is dominated by the SPM and filtering effects, resulting in a slight increase in the output pulse duration and bandwidth from 11.2 ps and 0.177 nm to 12.1 ps and 0.18 nm, and then to 12.5 ps and 0.19 nm during the process of reducing the repetition rate. For a given FBG bandwidth, the cavity length and the intracavity fiber distribution have little effect on the output pulse characteristics, and the additional nonlinear phase shift accumulated in the increased fiber may have to be controlled in further reducing the repetition rate.

Hence, we insert the PM-LMA fiber with a low nonlinear coefficient at position A instead of the PM980 fiber. The nonlinear coefficient and GVD parameter of the PM-LMA fiber are$7.3\times {10}^{-4}{\text{W}}^{-1}{\text{m}}^{-1}$and 0.005 ps²/m, respectively. The splice loss between LMA and PM980 is optimized to be approximately 0.16 dB by using thermally expanded core technique [28]. It is found that the laser can still operate in the SP regime for a pump power of 66 mW for a 50 m PM-LMA fiber.

Figure 4 (a) shows the measured pulse profile with a 20 GHz photodetector (A. L. S., Ultrafast-20-SM) and a 4 GHz oscilloscope (Agilent, DSO9404A), and the inset shows that the pulse repetition rate has been reduced to 1.77 MHz. Figure 4(b) shows the baseband RF signal spectrum for the pulse train measured with 300-Hz resolution and 1-MHz range, the signal-to-noise ratio is 51dB. The inset shows the higher harmonics with 3-kHz resolution and 20-MHz range, and no noise spike is observed. In addition, the pulse bandwidth is 0.18 nm (Fig. 4c), the Gaussian fitting of the autocorrelation trace yields a pulse width of approximately 10 ps (Fig. 4d), achieving a time-bandwidth product of 0.49. The measured output pulse energy is 22 pJ, and the corresponding nonlinear phase shift is 0.415. Therefore, based on experimental observations, the PM-LMA fiber effectively reduces the repetition rate with only minor changes in output characteristics, and the allowed nonlinear phase shift for operating in the SP regime is further increased slightly because of the increased normal GVD.

 

Fig. 4 Output pulse characteristics of the laser after inserting 50 m LMA fiber in position A: (a) measured pulse profile, the inset shows the pulse train; (b) measured RF spectrum of pulse train with resolution of 300 Hz, the inset shows the higher harmonics; (c) optical spectrum; (d) measured autocorrelation traces (blue) and fitting traces (red) of output pulses.

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By increasing the cavity length to reduce the repetition rate, it is necessary to reduce the intracavity pulse energy to meet the requirements of the nonlinear phase shift tolerated by the SP regime. This leads to a decrease in the output pulse energy with a decrease in the repetition rate. Obviously, this can be improved by optimizing the OC splitting ratio. Therefore, we replace the 30:70 OC in the 1.77 MHz repetitive rate laser with OCs having different splitting ratios but the same length of the pigtail fiber. It is found that, for a 50:50 OC (corresponding to a 9-dB cavity loss), the laser can operate in a SP regime at a pump power of 291–300 mW with a pulse energy between 34 and 60 pJ. This indicates that using the OC to extract more energy from the cavity is beneficial to suppress the nonlinearity caused by the excessively long fiber, which in turn allows the output of the single-pulse energy to be increased by increasing the pump power in the SP regime. Considering that the measured laser threshold pump power is 254 mW, which is much lower than the minimum pump power for the SP regime of 291 mW, it can be expected that if the length of the 50-m PLMA fiber is further increased, the laser repetition rate will be further reduced (no experimental demonstration was performed owing to the length limitation of the PM-LMA fiber available in our lab). When the output ratio of OC is increased to 70%, the laser cannot start operating owing to the limitation of the maximum output power of LD of 500 mW and total cavity loss of 13.5 dB. We believe that if a high-doped PM-LMA gain fiber and a high-power pump source are used, the laser can achieve greater pulse energy and lower repetition rate.

It is worth noting that the SESAM-based linear cavity DS passively mode-locked laser shown in Fig. 1 operates in a weak nonlinear regime, and the intracavity pulses of different bandwidths of FBG have similar shaping and evolution mechanisms. Therefore, the abovementioned reducing repetition rate method is applicable to lasers with any FBG bandwidth. If a narrower bandwidth FBG is selected, the repetition rate can be further reduced by using this method [7].

4. Conclusion

We demonstrated a method to effectively reduce the repetition rate of all-PM linear-cavity DS passively mode-locked fiber lasers based on FBG and SESAM. Our experimental results showed that, because of the weak nonlinear phase shift tolerated by the SP regime of the fiber laser, the output pulse characteristics can be kept almost constant when the repetition rate is reduced by increasing the cavity length; however, this may result in the intracavity pulse energy of the SP regime being too low, which may cause Q-switching instability. Inserting the OC to extract the pulse energy from the cavity and using the PM-LMA fiber to reduce the nonlinearity by placing it at the rear end of the OC where the propagated pulse has lower energy can effectively reduce the nonlinear phase shift and enable stable SP mode locking even when the cavity length (repetition rate) is greatly increased (decreased). For a laser constructed with a 0.3-nm bandwidth FBG, the repetition rate of the laser operated in the SP regime was successfully reduced to 1.77 MHz with the output pulse duration and bandwidth basically unchanged. Moreover, the output pulse energy could be improved further, and the repetition rate could be further reduced by optimizing the OC splitting ratio. The proposed method can therefore be used to develop a stable compact megahertz or sub-megahertz repetition rate near-transform limit picosecond fiber laser seed source, and then the use of the complex pulse picking technique may not be necessary in many applications.