Mode locking is a complex phenomenon in which a large number of longitude modes with different frequencies are coupled in phase together and picosecond- or femtosecond-pulses are generated. To obtain the mode locking, one can implement active mode locking and passive mode locking methods. In solid-state lasers, passive mode locking based on Kerr lens mode locking (KLM) or semiconductor saturable absorber mirror (SESAM) is widely used for its easy tuning and low cost. Since the first report of femtosecond Ti:sapphire laser in 1991^[1], femtosecond lasers based on other gain media were investigated over the past few decades, such as Er-doped, Yb-doped, Tm-doped, Cr-doped, and Ho-doped materials. Among them, Yb-doped lasers are desirable for high power applications due to their high efficiency, broad gain bandwidth, and simplicity of being directly pumped by laser diodes. Favoring the advantages, femtosecond oscillators based on Yb-doped media, such as Yb:CALGO, Yb:YAG, Yb:Lu2O3, Yb:CYA, Yb:KGW, Yb:KYW, Yb:YSO, and Yb:LSO, were developed successfully^[2–7]. Yb:KGW crystal, which exhibits superior properties of broad gain bandwidths (∼20nm), high-emission cross-sections (∼2.8×10−20cm2), and high thermal conductivity [∼3.3 W/(m · K)]^[8], has been used for constructing high-power femtosecond oscillators. Over the past two decades, many studies on Yb:KGW have been published^[9–14]. All the results have shown that Yb:KGW is a promising option for high-power femtosecond pulse generation, which has been applied in different fields^[15–17].

Although mode locking in the femtosecond regime can be readily obtained with proper selection of the gain crystal, proper cavity design, and deliberate dispersion control, the formation of mode locking is still difficult to be detected for its transient behavior. Exploring the buildup process of mode locking is beneficial for understanding the fast evolving process of mode locking and improving the performance of mode-locked lasers. Due to the electronic devices having speed limitations, the real-time oscilloscope hardly detects and records the transient evolution of the ultrashort pulse with the duration of <10ps. The recently developed dispersive Fourier transform (DFT) technique can provide a convenient way to detect and record ultrafast optical phenomena, which can obtain real-time and single-shot measurements. In 2012, DFT was reported to observe the dynamics in fiber lasers^[18]. Afterward, DFT has been widely used in the detection of the mode locking process in mode-locked fiber lasers and quite a lot of new phenomena were observed^[19-28]. In 2016, DFT was used to observe the spectral evolution in the buildup of mode locking for a mode-locked Ti:sapphire laser^[29]. However, the application of DFT in solid-state lasers has been seldom reported, except in Ti:sapphire lasers^[29,30]. Since different gain crystals have their distinctive properties, then different buildup processes of mode locking can be expected for different lasers. In addition, studies on passively mode-locked buildup dynamics could help researchers understand self-starting capability, buildup time, and Q-switched instability, which are critical for research of applications^[31–34]. In this paper, we introduce the DFT after a solid-state femtosecond Yb:KGW laser for the first time, and the fast evolving dynamics during buildup and extinction of the mode locking is recorded and discussed.

Figure 1 shows the schematic of the Yb:KGW mode-locked laser, which is pumped by a diode laser with a central wavelength of 976 nm. A 3-mm-long Yb:KGW crystal with a doping concentration of 5% (atomic fraction) is used as the gain medium, and a classical X-shaped cavity is adopted. The pump laser is focused into the gain medium with a pair of lenses, and mode matching is obtained for the pump and laser with a size of ∼210μm in the position of the crystal. To introduce the pump into the cavity effectively, a dichroic mirror (DM) coated for high transmission (HT) near 976 nm and high reflection (HR) across 1020–1200 nm is used. All the intra-cavity optical elements are designed with low energy loss and low dispersion for the laser wavelengths. Furthermore, a pair of Gires–Tournois interferometer (GTI) mirrors with a total group velocity dispersion (GVD) of −2600fs2 is used to provide negative dispersion. The laser is partly coupled out from an output coupler (OC) mirror with a transmittance of 2.5%. To help start the mode locking, a semiconductor saturable absorber mirror (SESAM) is introduced, whose modulation depth is 0.8%, the saturation fluence is Fsat=90μJ/cm2 at the center of 1064 nm, and the relaxation time is 1 ps. Both the gain crystal and the SESAM are mounted on water-cooled copper heat sinks and cooled to 16°C to avoid heat damage. The distance between the SESAM and GTI2 is carefully tuned to optimize the cavity mode size on SESAM for the stability of mode locking and increase of output power, and the cavity length is about 2.16 m.

The Yb:KGW laser is followed by a DFT device. The output of the Yb:KGW laser from the OC is coupled into a fiber with a fiber collimator (Col) and then separated by a fiber beam splitter (BS, 9:1) into the spectrometer and DFT system, respectively. A 10-km-long fiber (ITU-T G.652.D) in the DFT system is used as the dispersion medium, and its dispersion at 1036 nm is about −35.2ps/(nm·km). The large dispersion introduced by the long single-mode fiber helps with mapping the spectral information to the temporal domain after the photo-detector so that they can be recorded by a high-speed oscilloscope. The real-time temporal information and the time-averaged spectrum of the pulse are obtained by a high-speed (6-GHz), real-time oscilloscope (Tektronix 70604C) with a 12.5-GHz-bandwidth photodetector (PD) and an optical spectrum analyzer (OSA, Yokogawa AQ6370C), respectively. In order to obtain the transient process of the buildup and extinction of the mode locking, a mechanical chopper is positioned between the Yb:KGW laser and the pump source.

In the experiment, we preferred the stability of mode locking rather than the power scaling to assure the subsequent DFT detection. Thus, an output coupler with a transmittance of 2.5% is selected to emit the laser. Figure 2(a) shows the relationship between the pump power and the output power. The maximum of the average output power is 0.7 W at a pump power of 17 W. The main factor limiting the scaling of the output power is the saturation threshold of the SESAM, and further increasing the pumping power beyond the saturation threshold would result in multiple pulses, which affect the stability of the mode locking and cause an adverse effect in exploring the mode-locking dynamic process. Therefore, the following measurements are based on a pump power of 16 W corresponding to an output power of 0.6 W. In this situation, the mode locking is quite stable and without multi-pulse phenomenon. As shown in Fig. 2(b), the radio frequency (RF) spectra of the laser, with resolution bandwidths (RBWs) of 1 kHz and 100 kHz, respectively, are measured by an RF spectrum analyzer (Agilent E4447A), and the fundamental frequency is 69.4 MHz with a signal-to-noise ratio (SNR) of more than 86 dB. Seen from the longer-term of RF spectrum shown in the inset of Fig. 2(b), there are no additional peaks between the high-order modes, which reflects the stability of the mode locking. The autocorrelation trace of the mode-locked pulse is measured by a commercial intensity autocorrelator (APE SM2000), and the result is shown in Fig. 2(c), in which the pulse duration is derived to be 189 fs with a sech2-pulse assumption. The mode-locking spectrum is shown in Fig. 2(d), which is centered at a wavelength of 1036 nm with a full-width at half-maximum (FWHM) bandwidth of 6 nm, which corresponds to a transform limited pulse of 175 fs.

The buildup process of the mode locking in the Yb:KGW oscillator is implemented by a homemade DFT device shown in Fig. 1, and the entire buildup process of the mode locking is experimentally observed and recorded. Figures 3 and 4 illustrate the transient dynamics before stable mode locking. Figure 3(a) demonstrates the temporal behavior before and after mode locking, which shows that the pulse undergoes relaxation oscillation and transition before the stable mode locking is reached. It can be seen from the figure that it takes about several hundred microseconds to obtain the mode-locking state. Compared with Ti:sapphire lasers, which typically require only a few microseconds, longer relaxation times between the energy levels of the Yb:KGW laser and a longer fluorescence lifetime (∼243μs)^[35] are primary reasons. In addition, the absorption spectrum and emission spectrum of the Yb3+ overlap partly^[36], which results in a self-absorption phenomenon and hence affects the establishing speed of the mode locking for the Yb:KGW laser. The spectral information is mapped into the temporal domain by the DFT technique so that we can observe the spectral information in the real-time oscilloscope, as Fig. 3(b) shows. Figure 3(c) and 3(d) show the expanded views of the last spike before stable mode locking. In Fig. 3(e), there is a dominant pulse with a subordinate pulse together in the cavity, and the pulse interval is 14.5 ns, corresponding to the round-trip time of the pulse in the laser cavity.

Figure 4(a) reveals the spectral evolution during the mode locking, which demonstrates that the laser appears with several discrete spectral components. During this period, many pulses centered at different wavelengths coexist in the cavity with intensity fluctuations in case of gain competition. Near mode locking, the spectrum narrows and expands rapidly, which is believed to experience the stages of relaxation oscillation, Q-switch, quasi mode locking, and mode locking. Finally, the spectrum tends to be stable, which reveals that mode locking is established. A part of the transition from the relaxation oscillation to the stable mode locking is shown in Fig. 4(b). The spectral broadening process slows and even pauses momentarily. After this phase, nonlinear broadening improves rapidly, and a femtosecond pulse forms within a few hundred round trips. The laser ultimately realizes stable mode locking with only one soliton travelling in the cavity.

While using the DFT technique in the measurement of transient dynamics, it is crucial to ensure the reliability of the DFT device. In the DFT device, the function of the dispersive medium can be considered as a phase propagator. When the group delay is linear with respect to frequency, the group delay phase exhibits cascade superposition in the dispersive element. Thus, the frequency components of the spectrum are uniformly mapped to the time domain, which means the spectral envelope can be represented by the time-domain envelope. Figure 4(c) describes the last frame extracted from the whole buildup process, which is the mode-locking spectrum mapped into the temporal domain, and Fig. 4(d) shows the spectrum measured by the OSA while the chopper does not operate. Comparing Fig. 4(c) with Fig. 4(d), one can see that the approximate shape and width of the two curves are basically the same, which indicates the mapping relationship of the dispersion connection. The spectrum in Fig. 4(c) is not so smooth due to the limited resolution of the DFT device. It is noteworthy that the peak positions of Figs. 4(c) and 4(d) have a slight difference, which lies in that Fig. 4(c) is a single-shot spectrum, and it might have small fluctuations because of the interaction between the intracavity gain and loss.

To confirm that the spectral information has been mapped into time domain, the time domain information can be calculated by the formula Δt=|D|×L×Δλ, in which Δt is the temporal spacing after DFT, Δλ is the spectral width, D denotes the dispersion coefficient, and L is the length of the dispersion medium. Since D is about −35.2ps/(nm·km) and L is 10 km in the experiments, the above formula can be simply denoted as Δt=−35.2×10×Δλ. As Fig. 3(b) shows, the spectrum information derived from the DFT device confirms the theoretical prediction, which justifies the reliability of the DFT technique for recording the evolution processes of the Yb:KGW laser.

The extinction process of the mode locking could also be detected with DFT. In the detection of the extinction process, the pump light is blocked by the chopper. As a result, without effective gain, the pulse undergoes a decaying process, and the peak amplitude decreases with longer turn-off times, as shown in Fig. 5(a). At the beginning, the pulse intensity reduces gradually until the pulse energy is lower than a certain value. At the same time, pulses vanish rapidly. After ∼0.02ms, a lasing spike, more than five times in intensity higher than the mode locked pulse, can be observed due to the accumulation of population inversion. Since the gain is less than the intracavity loss, mode locking cannot be realized again. Thus, after several processes of accumulation of population inversion and then emitting lasing spikes, the laser disappears. Compared with the extinction process of mode-locked fiber lasers^[25], solid-state lasers have a longer relaxation oscillation time before the laser disappears, which is due to the higher pump power and shorter cavity length in comparison with fiber lasers^[37]. Figure 5(b) gives the spectral information mapped into the temporal domain by the DFT technique. It can be seen that the pulse interval is 14.5 ns, which coincides with the mode-locked pulse intervals without passing through 10-km SMF. Figures 5(c) and 5(d) show the enlarged views of the first spike after the mode locking disappears. As shown in Fig. 5(e), there is a dominant pulse with two subordinate pulses together in the cavity, and a similar pulse also appears during the buildup of mode locking. The period of the dominant pulse for Figs. 5(b) and 5(e) is 14.5 ns, corresponding to the round-trip time of the laser cavity.

Figure 6 shows the spectral evolution for the extinction of the laser. In Fig. 6(a), a complete and detailed process of the spectral evolution could be observed from stable mode locking to the extinguishment of laser. A part of the whole process is enlarged and shown in Fig. 6(b), where it is different from the buildup process that no more solitons are observed. Pulses with multiple wavelengths appear almost immediately after the mode locking elapses. The spectrum at this moment is extracted and shown in Fig. 6(c). Before obviously reduced post-lasing oscillations, the spectrum narrows rapidly, which is attributed to the fact that many laser modes oscillate in the cavity at the same time. The response of the mode-locked lasers to the pump is the essence of the buildup and extinction dynamics, which inevitably leads to relaxation oscillation in these processes. Furthermore, the saturable absorption effect facilitates the formation of ultrashort pulses from the background noise^[31].

To conclude, we have used the DFT technique for a mode-locked Yb:KGW laser and investigated the buildup and extinction processes of mode locking for the first time. The homemade Yb:KGW laser is mode locked at the repetition rate of 69.5 MHz with a pulse width of 189 fs. Then, a DFT device is built successfully, including the facility as well as the algorithm. The reliability of the DFT device is confirmed by observing and comparing the stable mode-locking spectrum between the DFT device and the OSA. Furthermore, the DFT device is used to observe and record the transient dynamics, including the buildup and the extinction processes of mode locking for the Yb:KGW laser. In the case of the buildup process, there are several spikes before mode locking and several subordinate pulses with a dominant pulse together in the laser cavity. For the extinction process, the entire process during the mode-locking state disappears and is recorded, and the spectral evolution is analyzed. Comparing the birth process with extinction process, it is found that the time of extinction is slightly shorter than the buildup time. The difference of the DFT results between fiber lasers and solid-state lasers is discussed. All the experimental results show that the DFT technique can be conveniently applied to observe and record the detailed transient processes effectively in mode-locked solid-state lasers, which helps to better understand the intrinsic mechanisms of mode locking in solid-state lasers and the characteristics of solid-state gain media. Moreover, we believe the precise detection of mode locking would be instructive for developing ultrafast sources for the fields such as laser processing and medical application.