## 3 Results and Discussion  
Figure 2 shows the output spectra of the dispersion-managed solitons generation from the developed TDFL for different PC positions. All spectra were measured using an optical spectrum analyzer (AQ6375, Yokogawa Tokyo Japan) with a resolution bandwidth of 0.1 nm. The spectrum shown in Figure 2a corresponds to a stretched-pulse generation. It is centered at a wavelength of 1967 nm and characterized by a full width at half maximum (FWHM) bandwidth of 24.7 nm. For 560 mW of pump power, the oscillator provided stable single-pulse CW-mode-locking operation with an average output power of 0.9 mW and a fundamental pulse repetition frequency of 15.795 MHz, which corresponded to the round-trip time of the laser cavity. This mode-locking operation, obtained after careful PC position adjustment, has been presented and discussed in [PERSON]'s previous work describing intracavity dispersion management in this TDFL setup [6]. In that paper, the soliton mode-locking and the generation of a dispersion-managed soliton were presented and discussed. Using different lengths of DCF in the NOLM, a mode-locking operation in the laser cavity with total net dispersion ranging from \(-\)0.016 ps\({}^{2}\) to \(-\)1.149 ps\({}^{2}\) was  
Figure 1: Experimental setup of the mode-locked TDFL with NOLM; EYDFL—Er/Yb-co-doped ring fiber laser, WDM—1560/2000 wavelength division multiplexer, TSF—single-mode thulium-doped fiber, OC—output coupler, ISO—fiber optic isolator, PM1950—PM passive fiber, DCF—dispersion compensation fiber, PC—polarization controller. obtained. Laser output pulses were positively chirped and, therefore, stretched in time. In the stretched-pulse mode-locking regime, the shortest laser pulses with Gaussian shape and a duration of 1.56 ps, compressed in the PM, single-mode fiber to 253 fs, were obtained. Figure 2b shows the generated optical spectrum of bound states of soliton. This spectrum was obtained for different PC positions and for a pump power of 513 mW. The bound states of soliton were measured at a slightly lower pump power than that applied for stretched-pulse generation, because it is affected by the PC position setting. The output spectrum, generated during the stable CW mode-locking operation, appeared centered at 1964.2 nm and characterized by a 21.9 nm spectral bandwidth at \(-\)3 dB level. It exhibited characteristic modulated fringes, as a result of spectral interference among solitons with small temporal intervals. The formation of multiple solitons in the laser cavity is caused by a peak power clamping effect [34]. Peak power clamping was induced in our laser by a sinusoidal transmission of the NOLM and made solitons stable in the cavity with a strong laser gain. The adjustment of the PC position changed the linear phase delay between two orthogonal polarization components in the cavity. For a certain linear cavity phase delay, a propagating soliton with a high peak power can generate such a high nonlinear phase shift that it switches the cavity feedback, which limits the soliton peak power. When the peak power is clamped, the high laser gain supports the formation of additional solitons with the same amplitude and pulse duration. In Figure 3a, part of the output spectrum of bound solitons spanning from 1962 to 1968 nm is displayed. The spectral lines are equidistantly spaced in the whole spectrum by \(\sim\)1.04 nm. Figure 3b presents the autocorrelation measurement results obtained using the interferometric autocorrelator Femtochrome FR 103 MC, USA. In the AC trace, four pulses separated by the time interval of 12.4 ps are present, which is consistent with a spectral modulation period of 1.04 nm. The peaks in the AC trace can be fitted with Gaussian shape, and the FWHM pulse duration of each peak is \(\sim\)1.98 ps, corresponding to the FWHM pulse durations after deconvolution of 1.4 ps. The pulse interval is 6.3 times the pulse width. By analyzing the AC measurement results, it can be concluded that the three dispersion-managed solitons were bound.