## 3 Results and Discussion
However, the autocorrelation signal associated with bound-state soliton generation was longer than the available measurement time window of our autocorrelation system software. A complete AC trace should contain one more pulse on the right side, which is not present in Figure 3b due to the limitations of our measurement equipment. The intensity ratio of the peaks in the autocorrelation trace was 1:2:3.2, and an intensity ratio of 1:2:3:2:1 corresponds to propagation of three solitons in bound states with identical amplitude and equal pulse separation [9]. The average output power of this bound-state soliton was 1.42 mW, which corresponds to a pulse energy of each solitons of \(\sim\)30 pJ. For a higher pump power, the fill factor of the spectrum of the generated bound-state solitons decreased, and multi-pulse mode-locking operation occurred. Figure 2: Optical spectra of dispersion-managed solitons: (**a**) stretched-pulse generation; (**b**) bound-state soliton generation mode; the inset presents the same optical spectrum in the linear scale (red trace). Figure 3c displays the radio frequency (RF) spectrum of the generated bound states of the solitons. It was measured using an RF spectrum analyzer (Keysight Technologies N9918A, Malaysia) with a resolution bandwidth of 50 Hz. The measured repetition rate of 15.795 MHz confirmed that the oscillator operated at the fundamental pulse repetition frequency resulting from the cavity length. The signal-to-noise ratio (SNR) of the fundamental frequency was approximately 62 dB. This is a better result than those previously reported for TDFLs [11,12,14]. The RF spectrum measured in the long-range frequency span (0-2.5 GHz), presented as an inset in Figure 3c, did not contain any modulations and confirmed a stable, mode-locking operation. Figure 3d presents a pulse train generated during mode-locking operation yielding bound solitons and measured using a sampling digital oscilloscope with a 6 GHz bandwidth, 25 GSa/s sampling rate (DSA 70604, Tektronix, Beaverton, OR, USA), and a fast photodetector with a rising time of less than 35 ps (ET-5000F, EOTech, Traverse City, MI, USA). The inset depicts a single pulse recorded by an oscilloscope with a typical sinc function shape. Oscilloscope traces showed single-pulse mode-locking operation, and bound states of solitons cannot be noticed in Figure 3d because the time during which the solitons which were bound was too short to be measured by our photodetector. By adjusting the PC at a higher pump power level (mostly at a pump power of 1 W), an NLP operation mode was realized in the developed TDFL. An adjustment of the PC shifts the cavity phase delay, and the soliton operation is tuned into the mode-locking operation where a laser pulse consists of a bunch of ultrashort pulses. The formation of noise-like pulse was found to be connected with the soliton collapse effect [35]. In the laser cavity when the pulse peak power is unclamped (different PC position), the soliton peak power increases with the increase of pump power. As a result, the pulse duration decreases, and the soliton spectrum broadens so that it becomes comparable with the gain bandwidth of the active fiber. Then, the soliton experiences a sudden losses and collapses. When the soliton collapses, a new pulse is built up from the collapsed one. The process is repeated and, because of gain competition, a bunch of ultrashort pulses with randomly varying intensity and pulse duration is created. Figure 3: Output characteristics of the bound-state soliton generation mode: (**a**) part of the output spectrum of bound solitons spanning from 1962 to 1968 nm; (**b**) autocorrelation trace (**c**) radio-frequency spectrum with scanning ranges of 1.6 MHz and 2.5 GHz (inset), and (**d**) oscilloscope trace of the mode-locked pulse train (inset: single pulse). In Figure 4a, a typical broad and smooth NLP spectrum with FWHM bandwidth of 18.5 nm is presented. The output spectrum is centered at 1961.4 nm.