1. Introduction

Ultrafast mode-locked fiber lasers possess great application prospects in communication, medical, industry and military fields due to the characteristics of high peak power, ultra-short pulse duration, cost-effective design, compact and alignment-free structure. As the key component in a mode-locked laser, the saturable absorber (SA) has an important impact on laser performance. Various methods have been used to achieve saturable absorption, such as nonlinear polarization rotation, nonlinear polarization evolution, nonlinear optical loop mirror, semiconductor saturable absorber mirrors, graphene and other two-dimensional materials [1–10]. Most SA materials are easily deteriorated in atmospheric environments, and their damage thresholds are low. Using SAs based on all-fiber structures can avoid the above problems. The nonlinear multimode interference (NLMMI) technique based on single mode fiber-multimode fiber-single mode fiber (SMF-MMF-SMF) structure has been proposed to realize mode-locked operation in all-fiber laser cavity [11]. As light is coupled from SMF into MMF, multiple high-order modes will be excited in the MMF. The multimode interference effect between modes will leading to self-imaging phenomenon along the MMF [12]. When the incident light intensity is high enough, the nonlinear effect such as self-phase modulation and cross-phase modulation in the fiber cannot be ignored, which will lead to the nonlinear multimode interference effect [11]. Under this condition, the period of the self-imaging is related to the light intensity. Therefore, for the MMF with fixed length, the transmission efficiencies of the light with different intensity, coupling from MMF to SMF, are different. When the length of the MMF matches ${L_M} = ({2m + 1} )Z/2\; \; ({m = 0,1,2, \ldots } )$, where Z is the self-imaging period under low power, the low-power light will be coupled into the fiber cladding and consumed, while most of the high-power light will be coupled into the fiber core and remained, thus achieving saturable absorption [13–15]. Compared with traditional mode-locking methods, the NLMMI based fiber modulator possesses simple preparation method, low cost, long service life and high-power tolerance. Since Nazemosadat et al. proved theoretically that the SMF-MMF-SMF structure had typical saturable absorption characteristics in 2013 [11], the use of such all-fiber SAs in fiber lasers has aroused great interest of researchers. In recent years, various fiber structures based on NLMMI have been reported as artificial SAs, such as the SMF-GIMF-SMF [15–25], single mode fiber-step index multimode fiber-single mode fiber (SMF-SIMF-SMF) [14], single mode fiber-few mode fiber-single mode fiber (SMF-FMF-SMF) [26] and so on. In order to achieve the saturable absorption, the length of the MMF should satisfy an odd multiple of half of the self-imaging length. However, most of the self-imaging lengths of common MMFs are in the order of millimeters or even micrometers, which makes the fabrication of the SMF-MMF-SMF-based SAs require high-precision preparation during the fiber cutting and splicing steps. Since the current fiber cutting and splicing methods usually rely on manual operation, it is difficult to obtain a SMF-MMF-SMF structure that perfectly meets the requirements. Therefore, it is necessary to explore new fiber structure preparation methods or optimize the NLMMI fiber structures.

The output characteristics and operation mechanisms of different mode-locked fiber lasers have also caused extensive concern, such as conventional solitons, dissipation solitons, bound solitons, noise-like pulses, soliton explosion and so on. As most commercial optical spectrum analyzers can only measure the average results of ultrafast pulses accumulated over the equipment sweep time, the dispersive Fourier transform (DFT) technique is applied to study the real-time spectral dynamics and ultrafast transient processes of various mode-locking operations. When an ultrafast pulse is incident into a dispersive element with a large group velocity dispersion, the pulse will be fully stretched, and each component with a different wavelength in the pulse will be discrete in time domain due to the different group velocities of the light components, thus achieving the frequency-time mapping. The DFT method, as an analogy of the Fraunhofer diffraction in time domain based on the far-field approximation, can map the frequency spectrum of an ultrafast pulse to a stretched temporal pulse waveform with a profile similar to the spectrum [27]. As the DFT method can stretch the ultrashort pulse to nanosecond scale, the profile details of the pulse spectrum can be resolved by high-speed oscilloscopes and photodetectors, which enables high-resolution real-time spectral measurements. The formation mechanisms and real-time evolution processes of different kinds of solitons and pulsation behaviors in mode-locked fiber lasers have become a hot topic and have been widely studied based on the DFT method [28–31]. As an incomplete mode-locked state, the Q-switched mode-locked (QSML) state has both mode-locking and Q-switching output characteristics, which is widely reported in ultrafast fiber lasers [5,32–34]. It has been generally observed that the QSML pulses possess periodic dynamic oscillation characteristics in time domain. However, the dynamic characteristics of the QSML operation in frequency domain and its real buildup process have been rarely reported due to the limitation of the measurement equipment. With the development of the DFT technology, it becomes possible to study the spectral dynamics and real-time buildup evolution process of the QSML pulses, which is important for further understanding the QSML operation in fiber lasers.

In this paper, we proposed a mode-locked Yb-doped fiber laser based on a SMF-GIMF-SMF structure. We put 10 cm GIMF in the groove of an in-line fiber polarization controller (PC) to tune its birefringence, so that the saturable absorption effect based on NLMMI can be realized without strict length restriction by turning the PC. By increase the pump power and adjusting the PCs in the cavity, stable dissipation solitons and noise-like pulses were observed in the 1030 nm waveband. We also obtained QSML pulses at 1032.6 nm. Based on the DFT method, the entire buildup process of the QSML state was studied for the first time, which comprised unstable self-pulsation, relaxation oscillation, rogue Q-switching stage and finally stable QSML state. Moreover, the experimental results also show that the spectral evolution of the stable QSML pulses possesses periodic breathing property.

2. Experimental setup

A ring Yb-doped all-fiber laser cavity based on SMF-GIMF-SMF-SA was built, as shown in Fig. 1(a). The pump source was a 980 nm laser diode (LD) with 250 mW maximum output power. The pump light entered the fiber cavity through a 980/1030 nm wavelength division multiplexer (WDM). A section of 15 cm ytterbium-doped single-clad fiber (YDF) was fused with the 1030 nm output port of the WDM, serving as the gain medium. 10% of the light was output from the cavity for studying through a 90:10 fiber coupler (OC). A 1030 nm polarization independent isolator (PI-ISO) in the cavity limited the unidirectional propagation of light. Two manual paddle fiber PCs (PC1 and PC2) were used to regulate the intra-cavity birefringence to provide appropriate cavity conditions for the formation of mode-locking. The total cavity length was ∼12 m, with net normal dispersion. The characteristics of the laser output were monitored by an optical spectrum analyzer (OSA), a digital oscilloscope with a 5 GHz photodetector (PD), a radio-frequency (RF) spectrum analyzer, and an autocorrelator.

 

Fig. 1. Experimental setup of the Yb-doped fiber laser based on a SMF-GIMF-SMF SA. (a) Schematic diagram of the fiber laser. (b) The SMF-GIMF-SMF SA structure.

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The SA was prepared by splicing two sections of SMF (HI 1060) on both sides of a ∼10 cm long GIMF (YOFC, 62.5/125 µm) to form a SMF-GIMF-SMF structure, as shown in the Fig. 1(b). The self-imaging period of the GIMF is in the order of micrometers, which makes it hard to get accurate cutting length manually. In order to relieve the strict requirement on the GIMF length when acting as a SA, several methods have been proposed, such as offset splicing [19,20] or introducing an inner microcavity [21] when splicing SMF and GIMF, stretching the GIMF through a precision translation stage [15–18], or inserting a short piece of large-mode-area fiber between SMF and GIMF [22–24]. In our experiment, we placed the GIMF in the groove of an in-line manual fiber PC, and then adjusted the PC to mechanically compress the GIMF, which created stress-induced birefringence within the GIMF and introduced additional nonlinear phase shift of the light in the GIMF. Under an appropriate birefringence condition, the total phase shift of the high-power light reached an integer multiple of 2π, and the light was self-focused in the fiber core, while the low-power light was coupled into the fiber cladding. That is, the nonlinear phase shift of the light can be flexibly adjusted by rotating the PC to make the length of the GIMF satisfy an odd multiple of the half-beat length, thus realizing saturable absorption. This approach was more simple, flexible and low loss than other methods.

When the GIMF-SA was not inserted into the fiber cavity, no matter how to increase the pump power or adjust the intra-cavity PCs, stable pulses cannot be obtained, indicating that other devices in this cavity cannot provide effective saturable absorption to achieve self-mode-locking. By inserting the GIMF-SA into the fiber cavity and carefully adjusting the in-line PC, we obtained stable mode-locked pulses output. We studied the linear and nonlinear optical absorption characteristics of the GIMF-based SA at an effective status, and the results are presented in Fig. 2. The linear transmission spectrum of this GIMF-SA from 1010 nm to 1060 nm waveband shown in Fig. 2(a) was measured using a super-continuum broadband light source. The loss of the SA is measured to be about -4.56 dB at 1030 nm. The nonlinear transmission property of the GIMF-SA was investigated using a home-made 1030 nm mode-locked fiber laser with a pulse duration of ∼1 ps and a repetition rate of 12.5 MHz. Based on the balanced two-detector measurement method [35], we obtained the nonlinear transmission curve shown in Fig. 2(b). And the experiment result in Fig. 2(b) is fitted by the below function [36],

 

Fig. 2. Optical absorption characteristics of the SMF-GIMF-SMF based SA. (a) The transmission spectrum; (b) the nonlinear transmission curve of the GIMF-SA.

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3. Results and discussion

3.1 Dissipation solitons

By adjusting the intra-cavity PC1 and PC2 appropriately, and increasing the pump power to 100 mW, stable dissipative solitons were achieved. The spectra with the central wavelength of 1032 nm at different pump powers are presented in Fig. 3(a). The 3dB bandwidth of the spectrum increases from 5 nm to 6.5 nm due to the self-phase modulation effect in the fiber cavity. The spectrum has steep edges and “cat ear” structures on both sides of the spectral profile, which are the typical characteristics of dissipative solitons in normal dispersion fiber lasers [37,38]. The oscilloscope trace of the dissipative solitons is shown in Fig. 3(b). The pulse interval period is measured to be ∼60 ns, which is equal to the time it takes light to travel around the fiber cavity. And the low-amplitude parasitic peak adjacent to the main pulse is the oscillating signal induced by the imperfect impedance matching of the oscilloscope and PD used for measurement [42]. Figure 3(c) presents the soliton autocorrelation trace. The pulse duration is 10.67 ps given by the sech² fitting. We also measured the RF spectrum of the laser with a resolution of 3 kHz in different frequency measuring ranges, illustrated in Fig. 3(d) and the inset. The center frequency of the RF spectrum is located at 16.67 MHz matched well with the 12-m long cavity, demonstrating that the dissipative soliton operates at the fundamental frequency. The signal-to-noise ratio (SNR) is measured to be ∼50 dB indicating good stability of the mode-locked laser. We continuously monitored the spectrum for 2.5 hours. The result is shown in Fig. 3(e). It can be noted that the spectral profile is nearly unchanged, which further confirms the stable operation of the dissipative soliton.

 

Fig. 3. Characteristics of the dissipative solitons. (a) Optical spectra at different pump powers; (b) Oscilloscope trace of the soliton train; (c) Autocorrelation trace and the sech² fitting curve; (d) RF spectra in different frequency ranges; (e) Long-time spectrum monitoring result.

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3.2 Noise-like pulses

As the pump power was 105 mW, noise-like pulses can also be obtained in the same fiber cavity by adjusting the PC1 and PC2 with the in-line PC state unchanged. The spectra under different pump powers are shown in Fig. 4(a). The central wavelength is around 1030.5 nm with the 3dB bandwidth of ∼6 nm. With the increase of pump power, the 3dB bandwidth also increases slightly. It can be seen that compared with the dissipative soliton, the spectrum of the noise-like pulse is flatter, and there is no obvious sideband appearing on the spectrum. As shown in Fig. 4(b), the pulse interval is ∼60 ns corresponding to the cavity length of 12 m. Figure 4(c) presents the autocorrelation trace of the pulse. It shows that the pulse profile has a very narrow spike structure with a broad pedestal, presenting the characteristic feature of noise-like pulses [39,40]. The detail of the spike structure with sech² fitting curve is shown in the inset of Fig. 4(c). The durations of the narrow peak and the wide pedestal are 276 fs and ∼4.9 ps, respectively. The RF spectra of the laser measured in 15 MHz and 300 MHz spans with 3-kHz resolution are presented in Fig. 4(d) and the inset. The repetition frequency is 16.67 MHz. The SNR reaches ∼40 dB, indicating a relatively stable mode-locked state. The long-time spectrum is monitored and shown in Fig. 4(e). The spectrum of the noise-like pulse keeps relatively stable during the 2.5-hour-long operation.

 

Fig. 4. Characteristics of the noise-like pulses. (a) Optical spectra at different pump powers; (b) Oscilloscope trace of the noise pulse train; (c) Autocorrelation trace; (d) RF spectra in different frequency ranges; (e) Long-time spectrum monitoring result.

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3.3 Q-switched mode-locked state

When rotating the intra-cavity PCs, the introduced disturbances broke the balance of gain and loss in the laser, resulting in abrupt fluctuations of laser energy. In the meantime, the SA was not fully saturated, the gain saturation effect in the fiber cavity did not respond in time to suppress the sharp increase of laser energy, leading to Q-switching instability in the fiber laser [41]. And then the QSML operation was obtain.

The pump threshold of the QSML state was 112 mW. Figure 5 shows the characteristics of the QSML pulses. The time-domain QSML pulse sequences at different pump powers are presented in Fig. 5(a). With the pump power increasing, the interval period of the Q-switched envelope is gradually shortened and the width of the envelope is narrowed slightly. Figure 5(b) and the inset show the larger versions of a Q-switched envelope at different time ranges. Within the pulse envelope, the discrete narrow pulses always keep a stable time interval of 60 ns, indicating the mode-locked operation. Figure 5(c) illustrated the spectra at different pump powers. The central wavelength is at 1032.6 nm, and the 3 dB bandwidth increases from 1.38 nm to 2.1 nm with the pump power increasing from 112 mW to 200 mW. The RF spectra at the pump power of 125 mW are shown in Fig. 5(d) and the inset. It can be seen that the center frequency is 16.67 MHz, which is consistent with the fundamental frequency of the mode-locked state. The SNR is about 50 dB. Furthermore, there are multiple symmetrical frequency sidebands on both sides of the central peak, and the frequency interval between sidebands is 70 kHz. It verifies that the intensity of the mode-locked pulse train slowly oscillates with the repetition frequency of 70 kHz, which matches the oscillation period of the Q-switched envelop measured to be ∼14.3 µs at the 125-mW pump power shown in Fig. 5(a).

 

Fig. 5. Characteristics of the QSML pulses. (a) Oscilloscope traces at different pump powers; (b) Details of a single pulse envelope; (c) Optical spectra at different pump powers; (d) RF spectra.

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As can be seen in Fig. 5, the QSML state obviously has the periodic dynamic characteristic. The dynamic properties in time domain can be measured using the oscilloscope, but the dynamic changes of the QSML pulse spectra cannot be detected using the current OSA which can only measure the average spectra of pulses over the sweep time. In order to observe the pulse spectrum at each round trip and explore the real-time spectral dynamics of the QSML operation, the DFT method was applied by injecting the output pulses into a 20 km long SMF with a dispersion of −30 ps/nm/km at 1030 nm to map the real-time spectra to the stretched temporal pulse waveforms which can be detected by high-speed real-time oscilloscopes. The stretched pulses were detected by a 36 GHz real-time oscilloscope together with a 10 GHz high-speed PD. The resolution was calculated to be ∼0.167nm for the DFT measurement. The real-time oscilloscope captured the real-time evolution process from continuous wave (CW) to QSML operation. Figure 6(a) presents the shot-to-shot spectra from the 10000th round trip to the 25000th round trip (RT) in a time window, which includes the spectral evolution of the whole buildup process. Each round trip takes about 60 ns, equal to the mode-locked pulse interval period. It can be seen that from the 10000th RT to the 15000th RT, the laser presents a continuous low power output. It demonstrates that the laser is at CW state and there is no stable pulse, so the output laser stretching can only get diffuse spectra without clear profiles. From the 15000th RT to the 17000th RT, the laser spectrum exhibits an evolution process. After the 17000th RT, the laser output presents a relatively stable QSML state. It can be calculated that the buildup process of the QSML state lasts no more than 180 µs. Figure 6(b) and 6(c) present the real-time spectra of the CW and the dissipative solitons as the contrast groups. It can be seen that the real-time spectra of the CW laser exhibit a diffuse noise state because there is no pulse to be stretched to reproduce the laser spectrum profile. The shot-to-shot spectra of the dissipative solitons show a relatively stable state without obvious oscillations, which is quite different from the QSML state.

 

Fig. 6. Shot-to-shot spectra of (a) the buildup process of the QSML state captured by the DFT method, (b) the CW state and (c) the dissipative solitons.

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We extracted the transition process from the 13000th to the 17000th RT, as shown in Fig. 7(a). The corresponding oscilloscope trace of the laser output from 780 µs to 1020 µs is plotted in Fig. 7(b). The experimental results reveal that the whole buildup process can be divided into four stages, which are unstable self-pulsation stage (A), relaxation oscillation stage (B), rogue Q-switching stage (C), and finally stable QSML stage (D). The laser oscillates at a low peak power at the beginning. Under the background noise, a dominant noise is selected as the main pulse with relatively high intensity. Because of the nonlinear effect in the fiber laser, the spectrum gradually broadens and the pulse intensity increases, which manifests as an initial unstable self-pulsation state. It can be seen from Fig. 7(c) that the self-pulse is similar to the mode-locked pulse with 60 ns pulse interval period, but the pulse intensity is low and unstable. We analyze that the self-pulse is achieved due to the longitudinal mode beating and the self-phase modulation in the fiber cavity [43,44]. The whole self-pulsation stage lasts for ∼160 µs. Because of the unbalance between the gain, loss and nonlinear effect in the fiber cavity, the growing self-pulse state cannot be maintained for a long time, and then the laser relaxation oscillation occurs. The time interval between two laser oscillation spikes shown in the Fig. 7(b) is ∼11 µs. And there are three spikes with successively increasing peak powers. With the increase of the pulse intensity during the oscillation stage, the saturable absorption effect in the cavity is triggered, and the spectrum is rapidly broadened in C stage. It shows that there are twice severe fluctuations in C stage, which are similar to the final QSML pulses but have higher envelope peaks and wider variation ranges of spectral bandwidth. Figure 7(d) shows the expanded view of one rogue Q-switching envelop in Fig. 7(a). The maximum 3dB bandwidth of the spectrum reaches 3.84 nm. At this stage, the pulse intensity is greatly improved due to the bleaching of the saturable absorber and the reduced intra-cavity loss. However, because of the high pulse intensity, the gain saturation effect is induced, and the population inversion in the laser is greatly consumed, which leads to the sharp weakening of the gain in the cavity. Under this condition, it is impossible to maintain such high-power pulse operation, resulting in the Q-switching instability, which is manifested as a rapid decrease of the intensity and bandwidth of the spectrum. At a certain moment after going through the above process twice, the gain, loss, dispersion, saturable absorption and other nonlinear effects in the laser reach a balance state, and then the stable QSML operation is realized, as shown in the D stage in Fig. 7(a).

 

Fig. 7. (a) Real-time spectra evolution process from CW to QSML state measured by the DFT method; (b) the corresponding real-time temporal pulse evolution; (c) the detail oscilloscope trace of the self-pulse; (d) a larger version of one fluctuation period of the spectra in C stage.

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When the pump power is 125 mW, shot-to-shot spectral evolution of the stable QSML pulses is shown in Fig. 8(a). The averaged spectrum over 4165 RTs and the spectrum measured by an OSA in linear scale are presented in Fig. 8(b). It can be seen that these two spectra have almost the same profile, indicating that the DFT methods can map the spectrum of the pulse to the stretched temporal pulse waveform perfectly. We can also get from Fig. 8(a) that the real-time spectra show regular breathing process with the period of 238 RTs. The average breathing period is calculated to be ∼14.3µs and the corresponding repetition frequency is 70 kHz, which is consistent with the period of the Q-switched envelop. Due to the long gain recovery time for the population inversion to be fully accumulated to balance the cavity loss, the QSML pulses were at extremely low power level for about 8∼9 µs during each Q-switching oscillation period at the pump power of 125 mW, as shown in Fig. 5(a). Because of the low power of the pulses, the shot-to-shot spectra obtained by stretching the pulses based on the DFT method overlapped with the noise signals and were difficult to be resolved effectively, showing a noise gap in each Q-switching period for about 130∼150 RTs. Figure 8(c) and the inset show the details of the spectral evolution in a breathing period. We can observe that the spectral intensity increases first and then decreases, which is the same as the evolution process of the mode-locked pulses intensity in the Q-switched envelop. Furthermore, the 3dB bandwidth of the spectrum is widen first and then compressed, shown in Fig. 8(d). We briefly discuss the physical mechanism of the periodic breathing process. Due to the massive accumulation of the population inversion in the cavity, the pulse energy gradually increases under the effect of the strong gain and the low saturable absorption loss. The pulse power reaches the maximum when the population inversion is consumed in large quantities and strong gain saturation effect is excited. In this process, with the increase of the pulse energy, the self-phase modulation effect in the cavity is also enhanced, which leads to the spectral broadening. Then, during the recovery time of the gain, the pulse energy gradually decreases due to the strong spectral filtering effect and the enhanced loss of the SA when the pulse energy is lower than the absorber saturation energy. The pulse power reaches the minimum when the population inversion is fully accumulated and the gain is strong enough to balance the whole cavity loss. During the decrease of the pulse energy, the self-phase modulation effect is weakened, and the broadened spectrum experiences strong spectral filtering effect, which makes the pulse spectrum gradually narrowed.

 

Fig. 8. (a) Shot-to-shot spectra for the stable QSML state measured by the DFT method; (b) the averaged spectra measured by DFT and an OSA; (c) and the inset are the enlargement of the spectral evolution process and the spectra at different RTs in a breathing period; (d) the 3 dB bandwidth of the spectra at different RTs.

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4. Conclusion

In summary, we have built an Yb-doped all-fiber laser based on a SMF-GIMF-SMF SA. We placed the GIMF in the groove of an in-line manual PC, and adjusted the PC to change the fiber birefringence, which can relieve the strict length requirement of the GIMF as SA. In the experiment, stable dissipation solitons and noise-like pulses were achieved with good stability by rotating the intra-cavity PCs carefully. The central wavelengths were 1032 nm and 1030.5 nm with the pulse durations of 10.67 ps and 276 fs, respectively. By slightly adjusting the PCs, QSML pulses can be obtained at 1032.6 nm. The amplitude of the 16.67 MHz mode-locked pulse was periodically modulated and the Q-switched envelops formed. Moreover, the real-time spectral evolution process from CW to QSML operation was captured by the DFT method for the first time, to the best of our knowledge. It demonstrates that the whole buildup process includes four stages, which are unstable self-pulsation, relaxation oscillation, rogue Q-switching and finally stable QSML stage. And the spectra of the pulses in one Q-switched envelop displayed a periodic breathing process, resulting from the self-phase modulation effect and the spectral filtering effect in the cavity. This experiment confirms that the SMF-GIMF-SMF structure is a promising SA in ultrafast fiber systems. And the results obtained by the DFT method deepen the understanding of the transient dynamics of the QSML operation.