1. Introduction

Passively mode-locked fiber laser has the advantages comparing with solid-state laser owing to improved simplicity, stability, and low cost. It has many potential applications in various domains such as optical communication, surgery and material processing. Many methods have been adopted to achieve passively mode-locked operation such as nonlinear polarization evolution [1], nonlinear amplifying loop mirror (NALM) [2] and saturable absorbers [3–5]. Normally passively mode-locked operation presents continuous pulses output in time domain. Opposing to the continuous mode-locked operation, Q-switched mode-locked (QML) operation can produce a higher pulse energy and peak power than continuous pulses. This improvement is realized by superimposing a Q-switched envelope on the continuous mode-locked pulse train. However the majority of QML lasers are focused on the solid-state lasers. Various techniques have been used to achieve QML operation such as the combined use of a passive mode-locker and an active Q-switch [6, 7], single acousto-optic modulating [8, 9] and single saturable absorber [10, 11]. Recently the subharmonic cavity modulation [12] and newly saturable absorber [13] are also applied to achieve QML operation in fiber laser structures. Furthermore, polarization controlling can be also used to achieve QML operation [14]. By using a semiconductor saturable absorber mirror in the cavity, continuous mode-locking, QML mode-locking and harmonic mode-locking pulses can be manipulated simply by detuning the polarization with a fixed pump power.

In general, passively mode-locked pulses are considered as Gaussian shape or hyperbolic secant shape at both continuous mode-locked and QML states. But in recent years, a newly discovered square-wave pulse (SWP) in passively mode-locked fiber laser has attracted much attention due to its special dynamics. In 2008 SWP is firstly theoretically proposed and investigated as dissipative soliton resonance (DSR) pulse by solving the complex cubic-quintic Ginzburg-Landau equation [15]. DSR pulses permit pulse width to broaden linearly without wave-breaking and the peak power keeps as constant. From then on, various DSR patterns have been experimental investigated in both normal dispersion region and anomalous dispersion region [16–20]. Additionally, it is verified that the DSR pulses can also operate at some special states such as harmonic and step-type states [21, 22]. Very recently, another SWP called square-wave noise-like pulse (NLP) is also demonstrated in passively mode-locked fiber laser [23]. The square-wave NLP has the similar pulse shape and evolution property with DSR. However, different from DSR, wave-breaking can be easily occurred at square-wave NLP operation when the cavity parameter is appropriately adjusted. Furthermore square-wave NLP can operate at multiple states such as normal mode-locked SWP, harmonic SWP, dual-SWP and coexistence of harmonic soliton and rectangular NLP [24–26]. References [15–26] allow us to recognize that the SWPs in passively mode-locked fiber laser have complicated and changeable dynamics. However most reports on SWP fiber laser are still focused on 1.55 μm and 1 μm. Although some SWP fiber lasers at 1.9 μm were reported in last years, they all only presented continuous mode-locked DSR states [27–29] and the mainly focal points were high power generation [28] and wavelength tuning [29]. Thus, it is meaningful to thoroughly investigate various patterns of SWP in 1.9 μm passively mode-locked fiber laser.

In this work, we propose a QML square-wave fiber laser at 1.9 μm. Continuous DSR pulse with 4.4 MHz repetition rate is obtained by using a nonlinear amplifying loop mirror. Q-switched mode-locked operation is achieved by properly setting the pump power and the polarization controllers. The Q-switched repetition rate can be varied from 41.6 kHz to 74 kHz by increasing pump power. Moreover, the characteristics of output energy are also discussed. The corresponding average single-pulse energy of QML pulse can be varied from 2.67 nJ to 5.2 nJ, which is almost three times higher than continuous SWP. Such improvement is also presented in the output peak power.

2. Experimental setup

The configuration considered is a figure of eight resonator including a NALM and a unidirectional loop (UL) (see Fig. 1). The NALM consists of a segment of 4.5 m single-mode thulium-holmium co-doped fiber (THDF), 30 m single mode fiber (SMF), a polarization controller (PC1) and a rotary squeezing PC (PC 2, Thorlabs PLC-900). The THDF is bidirectionally pumped by two 1570 nm laser sources via two 1570/1950 nm wavelength division multiplexers (WDMs). PC1 and PC2 which is applied on the SMF are used to control the linear phase bias and thus control the transmissivity of NALM [30]. The NALM is coupled to the UL by a 50/50 optical coupler (OC). The UL consists of PC3, a polarization independent isolator (PI-ISO) and a 20/80 OC. Considering all the fiber components the total cavity length is about 47 m corresponding to the estimated fundamental repetition rate of 4.4 MHz. The output laser is taken via the 20% port of fiber coupler and the 80% port serves as cavity feedback. The output spectrum can be observed by an optical spectrum analyzer (OSA, YOKOGAWA AQ6370D) through the 10% port of the external OC and the resolution of the OSA is 0.05 nm. The output pulses are detected by a 2 μm InGaAs PIN photodetector (PD) with 12GHz bandwidth and 28ps rising time. The radio frequency (RF) pulse is observed by an oscilloscope (OSC, Tetronix-OM 4006D) with the bandwidth of 20 GHz and the maximum sampling rate is 100 GSa/s. The RF spectrum is measured by a radio frequency spectrum analyzer (FSA, Agilent, N9030A) with the frequency range from 3 Hz to 44 GHz. In this case, the optical and RF spectrum can be simultaneously observed with high resolutions.

 

Fig. 1 Schematic of Q-witched mode-locked DSR thulium-doped fiber laser, THDF: Thulium-holmium co-doped fiber, WDM: Wavelength division multiplexer, SMF: Single-mode fiber, PC: Polarization controller, PI-ISO: Polarization insensitive isolator, OC: Optical coupler, PD: Photodetector

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3. Results and discussion

In the experiment, the mode-locking of the laser is achieved by means of the NALM and continuous DSR operation can be easily self-started when pump 1 and pump 2 reach 1 W and 250 mW respectively. The square-wave pulse profile obtained is shown in Fig. 2(a). The pulse presents approximate square profile with steep rising and falling edge. Fixing pump 1 at 1 W and increasing pump 2 to 1 W gradually, the square-wave pulse duration can be broadened from 1.7 ns to 3.2 ns while the amplitude can be nearly remained. The oscilloscope trace of the pulse train is shown in Fig. 2(b). One can see a flat pulse train in 2 μs scanning range and the cavity round-trip time is 227 ns. To further investigate the stability of the DSR, a real-time RF spectrum is shown in Fig. 2(c). One can see seven uniform RF signals in 30 MHz frequency range and the repetition rate is 4.4 MHz. The inset shows the detail of the fundamental frequency signal with 1 Hz resolution and the signal to noise ratio is about 50 dB. The corresponding optical spectrum is shown in Fig. 2(d). The center wavelength locates at 1885 nm and the 3 dB bandwidth is about 6 nm. The spectrum almost remains the broad and smooth shape with the increasing pump power and only a slight increase takes place in intensity. In the spectra one can observe some digs. In order to verify the cause of the digs, we measure the amplified spontaneous radiation (ASE) spectra of the used THDF. The results show that the digs also exist in the ASE spectra. As the digs almost concentrate near 1.9μm corresponding to the high absorption region of water, therefore, we can deduce that the dips are caused by the absorption of water.

 

Fig. 2 Continuous DSR operation (a) Single pulse variation (b) Pulse train (c) RF spectrum. Inset: Details of fundamental frequency RF spectrum (d) Optical spectrum

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As we know, in multiple previous reports, two types of square-wave pulses can be obtained in passive mode-locked fiber lasers. They are the square-wave dissipative soliton resonance pulses (DSRs) and the noise-like pulses (NLPs) respectively. In our experiment, the square-wave DSRs and NLPs are interchangeable by carefully adjusting the PCs. We can make a clear distinction between these two pulses from their optical spectrums and pulse shapes. The specific spectrums and pulse shapes are shown in Fig. 3. The 3dB spectrum bandwidth of DSR is only 6 nm and the pulse in time region has steep rising and falling edges, as shown in Fig. 3(a) and Fig. 3(b), respectively. The 3dB bandwidth broadens up to 15 nm when the DSR pulses evolve into NLPs, as shown in Fig. 3(c). The corresponding pulse has relative gentle edges, as shown in Fig. 3 (d). In this paper we only focus on the DSRs and fully detailed square-wave NLPs are discussed in our forthcoming paper.

 

Fig. 3 Differences between square-wave DSR and NLP (a) Spectrum of DSR (b) Pulse profile of DSR (c) Spectrum of NLP (d) Pulse profile of NLP

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Fixing pump 1 at 1 W and increasing pump 2 to 630 mW, continuous DSR pulses can involve into Q-switched mode-locked (QML) operation by properly setting the PCs. Note that if pump 2 is fixed at 1W and pump 1 is gradually increased, similar QML-DSR pulses can also be obtained and the only difference is a slight rising of threshold. The changes of PC states can lead to complex variations of cavity loss, which is equivalent to the variations of Q-value. As PC orientation leads to the modification of the transmission curve of the NALM, hence the saturation power and switching speed may also lead to QML generation. In this case, Q-switched operation can be started and the uniform DSR train is modulated into periodic Q-switched envelope as shown in Fig. 4(a). The envelope interval is about 17μs, corresponding to 58.8 kHz Q-switched repetition rate. Figure. 4(b) shows details of a single Q-switched envelope. One can see that the temporal width of the Q-switched envelope is about 2.9 μs. The Q-switched envelope contains multiple mode-locked pulses with 227ns interval, corresponding to cavity round trip time. Single mode-locked pulse remains square-wave profile, as shown in the inset of Fig. 4(b), indicating that laser keeps running at DSR state. Figure. 4(c) shows the corresponding RF spectrum. The RF spectrum also displays periodically modulated envelope. Zooming in the frequency range from 2 MHz to 8 MHz, one can see the details around fundamental frequency spectrum. The center peak signal locates at 4.4 MHz, corresponding to the mode-locked repetition rate. The signal to noise ratio of center peak is about 50 dB. On both sides of the peak signal there exist many side frequency signals with uniform interval of 58.8 kHz, corresponding to the Q-switched repetition rate. The RF spectrum indicates that an amplitude modulation at a frequency of 58.8 kHz is imposed onto the continuous 4.4 MHz mode-locked pulse train [12]. The corresponding optical spectrum is also shown in Fig. 4(d) and it is practically identical to the spectra in Fig. 2(d). It indicates that Q-switched effect only modulates the DSR pulses in time domain and the optical spectra character is determined by mode-locked effect. Thanks to the pump hysteresis effect, the Q-switched mode-locked operation can still remain when we gradually decrease the pump 2 power to only 315 mW. The oscilloscope traces of QML under different pump power are shown in Fig. 5. It can be clearly seen that the repetition rate of Q-switched envelope increases with a rising pump 2 power. It presents the similar evolution property to conventional Q-switched pulses.

 

Fig. 4 Q-switched mode-locked DSR operation (a) Oscilloscope trace of Q-switched mode-locked DSR envelopes. Inset: Single DSR pulse (b) Details of single a Q-switched mode-locked DSR envelope. Inset: Single mode-locked pulse (c) Corresponding RF spectrum. Inset: Details around fundamental frequency RF spectrum, (d) Corresponding optical spectrum

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Fig. 5 Oscilloscope trace of Q-switched mode-locked DSR pulses, (a)-(f) Pulse train with an increasing pump2 power (a) 315mW (b) 397mW (c) 500mW (d) 630mW (e) 793mW (f) 1W

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Finally the variation of output pulse characteristics is measured. Figure 6(a) presents the average output power as a function of pump 2 power at both continuous DSR and QML-DSR state. One can see the two operation states have the similar output power and slope efficiency. As a result of the rising pump power the duration of both continuous DSR and QML-DSR pulses are broadened. The differences of pulse duration between continuous DSR and QML-DSR can be understood as the variation of the pulse energy and peak power. With the increasing pump 2 power, the Q-switched envelope decreases from 4.48 μs to 2.8 μs, shown as the black curve in Fig. 6(c). As a result of the narrowing envelope width the number of DSR pulses in an envelope decreases from 34 to 21, shown as the red curve in Fig. 6(c). To further investigate the energy characteristics of QML-DSR pulse, a series of comprehensive test and calculation are carried out, as shown in Fig. 7. As a typical feature of Q-switched pulse, the repetition rate of Q-switched envelope increases with the pump power. The repetition rate varies from 41.6 kHz to 74 kHz, which is shown as the black curve in Fig. 7(a). Considering the Q-switched envelope as a whole, the corresponding Q-switched envelope energy varies between 91.5 nJ and 105.2 nJ, which is shown as the red curve in Fig. 7(a). As the Q-switched envelope consists of multiple short square-wave mode-locked pulses, the average single-pulse energy of DSR can be calculated by formula $Q_{DSR}=\frac{P}{f_Q\times N}$, where P is the output power of QML-DSR pulses, $f_Q$ is the repetition of the Q-switched envelope and N is the number of DSR pulses in an envelope. The calculated values are shown as the red curve in Fig. 7(b). One can see the average single-pulse energy increases from 2.67 nJ to 5.2 nJ and it is practically three times as high as continuous DSR pulses at same pump power. This is because Q-switched operation has the effect that the continuous and uniform mode-locked pulses are compacted into a series of separate envelopes with short duration. Such improvement is also presented in the output peak power. The average peak power of DSR pulses can be calculated by formula $P_{peak}=\frac{Q_{DSR}}{\tau }$, where $\tau$ is the DSR pulse width. The calculated values are shown in Fig. 7(c), the average peak power of mode-locked pulse is changed from 0.6 W to 1.1 W when continuous DSR operation is changed into QML-DSR operation. Consequently, QML operation is an effective method to increase the pulse energy and peak power of DSR pulse. Much higher output power and pulse energy can be obtained by several subsequent improvements such as increasing the pump power, optimizing the conversion efficiency, and using external amplification.

 

Fig. 6 (a) Average output power as a function of pump2 power (b) Pulse duration as a function of pump2 power (c) Envelope width and pulse number in an envelope as a function of pump 2 power

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Fig. 7 Energy characteristics of QML-DSR pulse and continuous DSR pulse, (a) Repetition rate and Q-switched envelope power as a function of pump2 power (b) Average single-pulse energy as a function of pump2 power (c) Average peak power as a function of pump2 power

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4. Conclusion

In conclusion, we have proposed and demonstrated a square-wave QML fiber laser at 1.9 μm. Continuous DSR pulse with 4.4 MHz repetition rate is firstly obtained by using a nonlinear amplifying loop mirror. On the basis of continuous DSR operation, QML operation is achieved. The QML-DSR pulse shows controllable repetition rate and the repetition rate can be varied from 41.6 kHz to 74 kHz by increasing pump power. Furthermore, a comprehensive analysis of the energy characteristics is given. The experimental results show that QML operation can effectively increase the SWP energy and peak power. This work would be beneficial to achieving high energy pulses in fiber lasers and it may have potential applications in specific areas such as mid-infrared source generation, medical surgery and industrial processing.